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R/mediate.R
In mediation: Causal Mediation Analysis
Defines functions
mediate
med.fun
med.fun.ordered
summary.mediate
print.summary.mediate
summary.mediate.mer
print.summary.mediate.mer
print.summary.mediate.mer.2
print.summary.mediate.mer.3
summary.mediate.order
print.summary.mediate.order
plot.process
plot.mediate
plot.process.mer
plot.mediate.mer
plot.process.order
plot.mediate.order
pval
Documented in
mediate
plot.mediate
plot.mediate.mer
plot.mediate.order
print.summary.mediate
print.summary.mediate.mer
print.summary.mediate.mer.2
print.summary.mediate.mer.3
print.summary.mediate.order
summary.mediate
summary.mediate.mer
summary.mediate.order
#' Causal Mediation Analysis
#'
#' 'mediate' is used to estimate various quantities for causal mediation
#' analysis, including average causal mediation effects (indirect effect),
#' average direct effects, proportions mediated, and total effect.
#'
#' @details This is the workhorse function for estimating causal mediation
#' effects for a variety of data types. The average causal mediation effect
#' (ACME) represents the expected difference in the potential outcome when the
#' mediator took the value that would realize under the treatment condition as
#' opposed to the control condition, while the treatment status itself is held
#' constant. That is,
#' \deqn{\delta(t) \ = \ E\{Y(t, M(t_1)) - Y(t, M(t_0))\},}{%
#' \delta(t) = E[Y(t, M(t1)) - Y(t, M(t0))],}
#' where \eqn{t, t_1, t_0}{t, t1, t0} are particular values of the treatment
#' \eqn{T} such that \eqn{t_1 \neq t_0}{t1 != t0}, \eqn{M(t)} is the potential
#' mediator, and \eqn{Y(t,m)} is the potential outcome variable. The average
#' direct effect (ADE) is defined similarly as,
#' \deqn{\zeta(t) \ = \ E\{Y(t_1, M(t)) - Y(t_0, M(t))\},}{%
#' \zeta(t) = E[Y(t1, M(t)) - Y(t0, M(t))],}
#' which represents the expected difference in the potential outcome when the
#' treatment is changed but the mediator is held constant at the value that
#' would realize if the treatment equals \eqn{t}. The two quantities on
#' average add up to the total effect of the treatment on the outcome,
#' \eqn{\tau}. See the references for more details.
#'
#' When both the mediator model ('model.m') and outcome model ('model.y') are
#' normal linear regressions, the results will be identical to the usual LSEM
#' method by Baron and Kenny (1986). The function can, however, accommodate
#' other data types including binary, ordered and count outcomes and mediators
#' as well as censored outcomes. Variables can also be modeled
#' nonparametrically, semiparametrically, or using quantile regression.
#'
#' If it is desired that inference be made conditional on specific values of
#' the pre-treatment covariates included in the model, the `covariates'
#' argument can be used to set those values as a list or data frame. The list
#' may contain either the entire set or any strict subset of the covariates in
#' the model; in the latter case, the effects will be averaged over the other
#' covariates. The `covariates' argument will be particularly useful when the
#' models contain interactions between the covariates and the treatment and/or
#' mediator (known as ``moderated mediation'').
#'
#' The prior weights in the mediator and outcome models are taken as sampling
#' weights and the estimated effects will be weighted averages when non-NULL
#' weights are used in fitting 'model.m' and 'model.y'. This will be useful
#' when data does not come from a simple random sample, for example.
#'
#' As of version 4.0, the mediator model can be of either 'lm', 'glm' (or
#' `bayesglm'), 'polr' (or `bayespolr'), 'gam', 'rq', `survreg', or `merMod'
#' class, corresponding respectively to the linear regression models,
#' generalized linear models, ordered response models, generalized additive
#' models, quantile regression models, parametric duration models, or
#' multilevel models.. For binary response models, the 'mediator' must be a
#' numeric variable with values 0 or 1 as opposed to a factor.
#' Quasi-likelihood-based inferences are not allowed for the mediator model
#' because the functional form must be exactly specified for the estimation
#' algorithm to work. The 'binomial' family can only be used for binary
#' response mediators and cannot be used for multiple-trial responses. This
#' is due to conflicts between how the latter type of models are implemented
#' in \code{\link{glm}} and how 'mediate' is currently written.
#'
#' For the outcome model, the censored regression model fitted via package
#' \code{VGAM} (of class 'vglm' with 'family@vfamily' equal to "tobit") can be
#' used in addition to the models listed above for the mediator. The
#' 'mediate' function is not compatible with censored regression models fitted
#' via other packages. When the quantile regression is used for the outcome
#' model ('rq'), the estimated quantities are quantile causal mediation
#' effects, quantile direct effects and etc., instead of the average effects.
#' If the outcome model is of class 'survreg', the name of the outcome
#' variable must be explicitly supplied in the `outcome' argument. This is due
#' to the fact that 'survreg' objects do not contain that information in an
#' easily extractable form. It should also be noted that for
#' \code{\link{survreg}} models, the \code{\link{Surv}} function must be
#' directly used in the model formula in the call to the survreg function, and
#' that censoring types requiring more than two arguments to Surv (e.g.,
#' interval censoring) are not currently supported by 'mediate'.
#'
#' The quasi-Bayesian approximation (King et al. 2000) cannot be used if
#' 'model.m' is of class 'rq' or 'gam', or if 'model.y' is of class 'gam',
#' 'polr' or 'bayespolr'. In these cases, either an error message is returned
#' or use of the nonparametric bootstrap is forced. Users should note that use
#' of the nonparametric bootstrap often requires significant computing time,
#' especially when 'sims' is set to a large value.
#'
#' The 'control' argument must be provided when 'gam' is used for the outcome
#' model and user wants to allow ACME and ADE to vary as functions of the
#' treatment (i.e., to relax the "no interaction" assumption). Note that the
#' outcome model must be fitted via package \code{\link{mgcv}} with
#' appropriate formula using \code{\link{s}} constructs (see Imai et al. 2009
#' in the references). For other model types, the interaction can be allowed
#' by including an interaction term between \eqn{T} and \eqn{M} in the linear
#' predictor of the outcome model. As of version 3.0, the 'INT' argument is
#' deprecated and the existence of the interaction term is automatically
#' detected (except for 'gam' outcome models).
#'
#' When the treatment variable is continuous or a factor with multiple levels,
#' user must specify the values of \eqn{t_1}{t1} and \eqn{t_0}{t0} using the
#' 'treat.value' and 'control.value' arguments, respectively. The value of
#' \eqn{t} in the above expressions is set to \eqn{t_0}{t0} for 'd0', 'z0',
#' etc. and to \eqn{t_1}{t1} for 'd1', 'z1', etc.
#'
#' @param model.m a fitted model object for mediator. Can be of class 'lm',
#' 'polr', 'bayespolr', 'glm', 'bayesglm', 'gam', 'rq', 'survreg', or
#' 'merMod'.
#' @param model.y a fitted model object for outcome. Can be of class 'lm',
#' 'polr', 'bayespolr', 'glm', 'bayesglm', 'gam', 'vglm', 'rq', 'survreg', or
#' 'merMod'.
#' @param sims number of Monte Carlo draws for nonparametric bootstrap or
#' quasi-Bayesian approximation.
#' @param boot a logical value. if 'FALSE' a quasi-Bayesian approximation is
#' used for confidence intervals; if 'TRUE' nonparametric bootstrap will be
#' used. Default is 'FALSE'.
#' @param boot.ci.type a character string indicating the type of bootstrap
#' confidence intervals. If "bca" and boot = TRUE, bias-corrected and
#' accelerated (BCa) confidence intervals will be estimated. If "perc" and
#' boot = TRUE, percentile confidence intervals will be estimated. Default is
#' "perc".
#' @param conf.level level of the returned two-sided confidence intervals.
#' Default is to return the 2.5 and 97.5 percentiles of the simulated
#' quantities.
#' @param treat a character string indicating the name of the treatment variable
#' used in the models. The treatment can be either binary (integer or a
#' two-valued factor) or continuous (numeric).
#' @param mediator a character string indicating the name of the mediator
#' variable used in the models.
#' @param covariates a list or data frame containing values for a subset of the
#' pre-treatment covariates in 'model.m' and 'model.y'. If provided, the
#' function will return the estimates conditional on those covariate values.
#' @param outcome a character string indicating the name of the outcome variable
#' in `model.y'. Only necessary if 'model.y' is of class 'survreg'; otherwise
#' ignored.
#' @param control a character string indicating the name of the control group
#' indicator. Only relevant if 'model.y' is of class 'gam'. If provided, 'd0',
#' 'z0' and 'n0' are allowed to differ from 'd1', 'z1' and 'n1', respectively.
#' @param control.value value of the treatment variable used as the control
#' condition. Default is 0.
#' @param treat.value value of the treatment variable used as the treatment
#' condition. Default is 1.
#' @param long a logical value. If 'TRUE', the output will contain the entire
#' sets of simulation draws of the the average causal mediation effects,
#' direct effects, proportions mediated, and total effect. Default is 'TRUE'.
#' @param dropobs a logical value indicating the behavior when the model frames
#' of 'model.m' and 'model.y' (and the 'cluster' variable if included) are
#' composed of different observations. If 'TRUE', models will be re-fitted
#' using common data rows. If 'FALSE', error is returned. Default is 'FALSE'.
#' @param robustSE a logical value. If 'TRUE', heteroskedasticity-consistent
#' standard errors will be used in quasi-Bayesian simulations. Ignored if
#' 'boot' is 'TRUE' or neither 'model.m' nor 'model.y' has a method for
#' \code{vcovHC} in the \code{sandwich} package. Default is 'FALSE'.
#' @param cluster a variable indicating clusters for standard errors. Note that
#' this should be a vector of cluster indicators itself, not a character
#' string for the name of the variable.
#' @param group.out a character string indicating the name of the lmer/glmer
#' group on which the mediate output is based. Can be used even when a merMod
#' function is applied to only one of the mediator or the outcome. If merMod
#' functions are applied to both the mediator and the outcome, default is the
#' group name used in the outcome model; if the mediator group and the outcome
#' group are different and the user is interested in the mediate output based
#' on the mediator group, then set group.out to the group name used in the
#' mediator merMod model. If a merMod function is applied to only one of the
#' mediator or the outcome, group.out is automatically set to the group name
#' used in the merMod model.
#' @param use_speed a logical value indicating whether, if nonparametric
#' bootstrap is used, \code{lm} and \code{glm} models should be re-fit using
#' functions from the \code{speedglm} package. Ignored if 'boot' is 'FALSE' or
#' if neither 'model.m' nor 'model.y' is of class 'lm' or 'glm'. Default is
#' 'FALSE'.
#' @param ... other arguments passed to \code{vcovHC} in the \code{sandwich}
#' package: typically the 'type' argument, which is ignored if 'robustSE' is
#' 'FALSE'. Arguments to the \code{boot} in the \code{boot} package may also
#' be passed, e.g. 'parallel' and 'ncpus'.
#'
#' @return \code{mediate} returns an object of class "\code{mediate}",
#' "\code{mediate.order}" if the outcome model used is 'polr' or 'bayespolr',
#' or "\code{mediate.mer}" if 'lmer' or 'glmer' is used for the outcome or the
#' mediator model, a list that contains the components listed below. Some of
#' these elements are not available if 'long' is set to 'FALSE' by the user.
#'
#' The function \code{summary} (i.e., \code{summary.mediate},
#' \code{summary.mediate.order}, or \code{summary.mediate.mer}) can be used to
#' obtain a table of the results. The function \code{plot} (i.e.,
#' \code{plot.mediate}, \code{plot.mediate.order}, or \code{plot.mediate.mer})
#' can be used to produce a plot of the estimated average causal mediation,
#' average direct, and total effects along with their confidence intervals.
#'
#' \item{d0, d1}{point estimates for average causal mediation effects under
#' the control and treatment conditions.}
#' \item{d0.ci, d1.ci}{confidence intervals for average causal mediation
#' effects. The confidence level is set at the value specified in
#' 'conf.level'.}
#' \item{d0.p, d1.p}{two-sided p-values for average causal mediation effects.}
#' \item{d0.sims, d1.sims}{vectors of length 'sims' containing simulation
#' draws of average causal mediation effects.}
#' \item{z0, z1}{point estimates for average direct effect under the control
#' and treatment conditions.}
#' \item{z0.ci, z1.ci}{confidence intervals for average direct effects.}
#' \item{z0.p, z1.p}{two-sided p-values for average causal direct effects.}
#' \item{z0.sims, z1.sims}{vectors of length 'sims' containing simulation
#' draws of average direct effects.}
#' \item{n0, n1}{the "proportions mediated", or the size of the average causal
#' mediation effects relative to the total effect.}
#' \item{n0.ci, n1.ci}{confidence intervals for the proportions mediated.}
#' \item{n0.p, n1.p}{two-sided p-values for proportions mediated.}
#' \item{n0.sims, n1.sims}{vectors of length 'sims' containing simulation
#' draws of the proportions mediated.}
#' \item{tau.coef}{point estimate for total effect.}
#' \item{tau.ci}{confidence interval for total effect.}
#' \item{tau.p}{two-sided p-values for total effect.}
#' \item{tau.sims}{a vector of length 'sims' containing simulation draws of
#' the total effect.}
#' \item{d.avg, z.avg, n.avg}{simple averages of d0 and d1, z0 and z1, n0 and
#' n1, respectively, which users may want to use as summary values when those
#' quantities differ.}
#' \item{d.avg.ci, z.avg.ci, n.avg.ci}{confidence intervals for the above.}
#' \item{d.avg.p, z.avg.p, n.avg.p}{two-sided p-values for the above.}
#' \item{d.avg.sims, z.avg.sims, n.avg.sims}{vectors of length 'sims'
#' containing simulation draws of d.avg, z.avg and n.avg, respectively.}
#' \item{d0.group, d1.group}{group-specific point estimates for average
#' causal mediation effects under the control and treatment conditions.}
#' \item{d0.ci.group, d1.ci.group}{group-specific confidence intervals for
#' average causal mediation effects. The confidence level is set at the value
#' specified in 'conf.level'.}
#' \item{d0.p.group, d1.p.group}{group-specific two-sided p-values for average
#' causal mediation effects.}
#' \item{d0.sims.group, d1.sims.group}{group-specific vectors of length 'sims'
#' containing simulation draws of average causal mediation effects.}
#' \item{z0.group, z1.group}{group-specific point estimates for average direct
#' effect under the control and treatment conditions.}
#' \item{z0.ci.group, z1.ci.group}{group-specific confidence intervals for
#' average direct effects.}
#' \item{z0.p.group, z1.p.group}{group-specific two-sided p-values for average
#' causal direct effects.}
#' \item{z0.sims.group, z1.sims.group}{group-specific vectors of length 'sims'
#' containing simulation draws of average direct effects.}
#' \item{n0.group, n1.group}{the group-specific "proportions mediated", or the
#' size of the group-specific average causal mediation effects relative to the
#' total effect.}
#' \item{n0.ci.group, n1.ci.group}{group-specific confidence intervals for the
#' proportions mediated.}
#' \item{n0.p.group, n1.p.group}{group-specific two-sided p-values for
#' proportions mediated.}
#' \item{n0.sims.group, n1.sims.group}{group-specific vectors of length 'sims'
#' containing simulation draws of the proportions mediated.}
#' \item{tau.coef.group}{group-specific point estimate for total effect.}
#' \item{tau.ci.group}{group-specific confidence interval for total effect.}
#' \item{tau.p.group}{group-specific two-sided p-values for total effect.}
#' \item{tau.sims.group}{a group-specific vector of length 'sims' containing
#' simulation draws of the total effect.}
#' \item{d.avg.group, z.avg.group, n.avg.group}{group-specific simple averages
#' of d0 and d1, z0 and z1, n0 and n1, respectively, which users may want to
#' use as summary values when those quantities differ.}
#' \item{d.avg.ci.group, z.avg.ci.group, n.avg.ci.group}{group-specific
#' confidence intervals for the above.}
#' \item{d.avg.p.group, z.avg.p.group, n.avg.p.group}{group-specific two-sided
#' p-values for the above.}
#' \item{d.avg.sims.group, z.avg.sims.group, n.avg.sims.group}{group-specific
#' vectors of length 'sims' containing simulation draws of d.avg, z.avg and
#' n.avg, respectively.}
#' \item{boot}{logical, the 'boot' argument used.}
#' \item{treat}{a character string indicating the name of the 'treat' variable
#' used.}
#' \item{mediator}{a character string indicating the name of the 'mediator'
#' variable used.}
#' \item{INT}{a logical value indicating whether the model specification
#' allows the effects to differ between the treatment and control conditions.}
#' \item{conf.level}{the confidence level used. }
#' \item{model.y}{the outcome model used.}
#' \item{model.m}{the mediator model used.}
#' \item{group.m}{the name of the mediator group used.}
#' \item{group.y}{the name of the outcome group used.}
#' \item{group.name}{the name of the group on which the output is based.}
#' \item{group.id.m}{the data on the mediator group.}
#' \item{group.id.y}{the data on the outcome group.}
#' \item{group.id}{the data on the group on which the output is based.}
#' \item{control.value}{value of the treatment variable used as the control
#' condition.}
#' \item{treat.value}{value of the treatment variable used as the treatment
#' condition.}
#' \item{nobs}{number of observations in the model frame for 'model.m' and
#' 'model.y'. May differ from the numbers in the original models input to
#' 'mediate' if 'dropobs' was 'TRUE'.}
#' \item{robustSE}{`TRUE' or `FALSE'.}
#' \item{cluster}{the clusters used.}
#'
#' @author Dustin Tingley, Harvard University,
#' \email{dtingley@@gov.harvard.edu}; Teppei Yamamoto, Massachusetts Institute
#' of Technology, \email{teppei@@mit.edu}; Luke Keele, Penn State University,
#' \email{ljk20@@psu.edu}; Kosuke Imai, Princeton University,
#' \email{kimai@@princeton.edu}; Kentaro Hirose, Princeton University,
#' \email{hirose@@princeton.edu}.
#'
#' @seealso \code{\link{medsens}}, \code{\link{plot.mediate}},
#' \code{\link{summary.mediate}}, \code{\link{summary.mediate.mer}},
#' \code{\link{plot.mediate.mer}}, \code{\link{mediations}}, \code{vcovHC}
#'
#' @references Tingley, D., Yamamoto, T., Hirose, K., Imai, K. and Keele, L.
#' (2014). "mediation: R package for Causal Mediation Analysis", Journal of
#' Statistical Software, Vol. 59, No. 5, pp. 1-38.
#'
#' Imai, K., Keele, L., Tingley, D. and Yamamoto, T. (2011). Unpacking the
#' Black Box of Causality: Learning about Causal Mechanisms from Experimental
#' and Observational Studies, American Political Science Review, Vol. 105, No.
#' 4 (November), pp. 765-789.
#'
#' Imai, K., Keele, L. and Tingley, D. (2010) A General Approach to Causal
#' Mediation Analysis, Psychological Methods, Vol. 15, No. 4 (December), pp.
#' 309-334.
#'
#' Imai, K., Keele, L. and Yamamoto, T. (2010) Identification, Inference, and
#' Sensitivity Analysis for Causal Mediation Effects, Statistical Science,
#' Vol. 25, No. 1 (February), pp. 51-71.
#'
#' Imai, K., Keele, L., Tingley, D. and Yamamoto, T. (2009) "Causal Mediation
#' Analysis Using R" in Advances in Social Science Research Using R, ed. H. D.
#' Vinod New York: Springer.
#'
#' @export
#' @examples
#' # Examples with JOBS II Field Experiment
#'
#' # **For illustration purposes a small number of simulations are used**
#'
#' data(jobs)
#'
#' ####################################################
#' # Example 1: Linear Outcome and Mediator Models
#' ####################################################
#' b <- lm(job_seek ~ treat + econ_hard + sex + age, data=jobs)
#' c <- lm(depress2 ~ treat + job_seek + econ_hard + sex + age, data=jobs)
#'
#' # Estimation via quasi-Bayesian approximation
#' contcont <- mediate(b, c, sims=50, treat="treat", mediator="job_seek")
#' summary(contcont)
#' plot(contcont)
#'
#' \dontrun{
#' # Estimation via nonparametric bootstrap
#' contcont.boot <- mediate(b, c, boot=TRUE, sims=50, treat="treat", mediator="job_seek")
#' summary(contcont.boot)
#' }
#'
#' # Allowing treatment-mediator interaction
#' d <- lm(depress2 ~ treat + job_seek + treat:job_seek + econ_hard + sex + age, data=jobs)
#' contcont.int <- mediate(b, d, sims=50, treat="treat", mediator="job_seek")
#' summary(contcont.int)
#'
#' # Allowing ``moderated mediation'' with respect to age
#' b.int <- lm(job_seek ~ treat*age + econ_hard + sex, data=jobs)
#' d.int <- lm(depress2 ~ treat*job_seek*age + econ_hard + sex, data=jobs)
#' contcont.age20 <- mediate(b.int, d.int, sims=50, treat="treat", mediator="job_seek",
#' covariates = list(age = 20))
#' contcont.age70 <- mediate(b.int, d.int, sims=50, treat="treat", mediator="job_seek",
#' covariates = list(age = 70))
#' summary(contcont.age20)
#' summary(contcont.age70)
#'
#' # Continuous treatment
#' jobs$treat_cont <- jobs$treat + rnorm(nrow(jobs)) # (hypothetical) continuous treatment
#' b.contT <- lm(job_seek ~ treat_cont + econ_hard + sex + age, data=jobs)
#' c.contT <- lm(depress2 ~ treat_cont + job_seek + econ_hard + sex + age, data=jobs)
#' contcont.cont <- mediate(b.contT, c.contT, sims=50,
#' treat="treat_cont", mediator="job_seek",
#' treat.value = 4, control.value = -2)
#' summary(contcont.cont)
#'
#' # Categorical treatment
#' \dontrun{
#' b <- lm(job_seek ~ educ + sex, data=jobs)
#' c <- lm(depress2 ~ educ + job_seek + sex, data=jobs)
#'
#' # compare two categories of educ --- gradwk and somcol
#' model.cat <- mediate(b, c, treat="educ", mediator="job_seek", sims=50,
#' control.value = "gradwk", treat.value = "somcol")
#' summary(model.cat)
#' }
#'
#' ######################################################
#' # Example 2: Binary Outcome and Ordered Mediator
#' ######################################################
#' \dontrun{
#' jobs$job_disc <- as.factor(jobs$job_disc)
#' b.ord <- polr(job_disc ~ treat + econ_hard + sex + age, data=jobs,
#' method="probit", Hess=TRUE)
#' d.bin <- glm(work1 ~ treat + job_disc + econ_hard + sex + age, data=jobs,
#' family=binomial(link="probit"))
#' ordbin <- mediate(b.ord, d.bin, sims=50, treat="treat", mediator="job_disc")
#' summary(ordbin)
#'
#' # Using heteroskedasticity-consistent standard errors
#' ordbin.rb <- mediate(b.ord, d.bin, sims=50, treat="treat", mediator="job_disc",
#' robustSE=TRUE)
#' summary(ordbin.rb)
#'
#' # Using non-parametric bootstrap
#' ordbin.boot <- mediate(b.ord, d.bin, sims=50, treat="treat", mediator="job_disc",
#' boot=TRUE)
#' summary(ordbin.boot)
#' }
#'
#' ######################################################
#' # Example 3: Quantile Causal Mediation Effect
#' ######################################################
#' require(quantreg)
#' c.quan <- rq(depress2 ~ treat + job_seek + econ_hard + sex + age, data=jobs,
#' tau = 0.5) # median
#' contquan <- mediate(b, c.quan, sims=50, treat="treat", mediator="job_seek")
#' summary(contquan)
#'
#' ######################################################
#' # Example 4: GAM Outcome
#' ######################################################
#' \dontrun{
#' require(mgcv)
#' c.gam <- gam(depress2 ~ treat + s(job_seek, bs="cr") +
#' econ_hard + sex + age, data=jobs)
#' contgam <- mediate(b, c.gam, sims=10, treat="treat",
#' mediator="job_seek", boot=TRUE)
#' summary(contgam)
#'
#' # With interaction
#' d.gam <- gam(depress2 ~ treat + s(job_seek, by = treat) +
#' s(job_seek, by = control) + econ_hard + sex + age, data=jobs)
#' contgam.int <- mediate(b, d.gam, sims=10, treat="treat", mediator="job_seek",
#' control = "control", boot=TRUE)
#' summary(contgam.int)
#' }
#' ######################################################
#' # Example 5: Multilevel Outcome and Mediator Models
#' ######################################################
#' \dontrun{
#' require(lme4)
#'
#' # educ: mediator group
#' # occp: outcome group
#'
#' # Varying intercept for mediator
#' model.m <- glmer(job_dich ~ treat + econ_hard + (1 | educ),
#' family = binomial(link = "probit"), data = jobs)
#'
#' # Varying intercept and slope for outcome
#' model.y <- glmer(work1 ~ treat + job_dich + econ_hard + (1 + treat | occp),
#' family = binomial(link = "probit"), data = jobs)
#'
#' # Output based on mediator group ("educ")
#' multilevel <- mediate(model.m, model.y, treat = "treat",
#' mediator = "job_dich", sims=50, group.out="educ")
#'
#' # Output based on outcome group ("occp")
#' # multilevel <- mediate(model.m, model.y, treat = "treat",
#' mediator = "job_dich", sims=50)
#'
#' # Group-average effects
#' summary(multilevel)
#'
#' # Group-specific effects organized by effect
#' summary(multilevel, output="byeffect")
#' # plot(multilevel, group.plots=TRUE)
#' # See summary.mediate.mer and plot.mediate.mer for detailed explanations
#'
#' # Group-specific effects organized by group
#' summary(multilevel, output="bygroup")
#' # See summary.mediate.mer for detailed explanations
#' }
mediate <- function(model.m, model.y, sims = 1000,
boot = FALSE, boot.ci.type = "perc",
treat = "treat.name", mediator = "med.name",
covariates = NULL, outcome = NULL,
control = NULL, conf.level = .95,
control.value = 0, treat.value = 1,
long = TRUE, dropobs = FALSE,
robustSE = FALSE, cluster = NULL, group.out = NULL,
use_speed = FALSE, ...){
cl <- match.call()
# Warn users who still use INT option
if(match("INT", names(cl), 0L)){
warning("'INT' is deprecated - existence of interaction terms is now automatically detected from model formulas")
}
# Warning for robustSE and cluster used with boot
if(robustSE && boot){
warning("'robustSE' is ignored for nonparametric bootstrap")
}
if(!is.null(cluster) && boot){
warning("'cluster' is ignored for nonparametric bootstrap")
}
if(robustSE & !is.null(cluster)){
stop("choose either `robustSE' or `cluster' option, not both")
}
if(boot.ci.type != "bca" & boot.ci.type != "perc"){
stop("choose either `bca' or `perc' for boot.ci.type")
}
# Drop observations not common to both mediator and outcome models
if(dropobs){
odata.m <- model.frame(model.m)
odata.y <- model.frame(model.y)
if(!is.null(cluster)){
if(is.null(row.names(cluster)) &
(nrow(odata.m)!=length(cluster) | nrow(odata.y)!=length(cluster))
){
warning("cluster IDs may not correctly match original observations due to missing data")
}
odata.y <- merge(odata.y, as.data.frame(cluster), sort=FALSE,
by="row.names")
rownames(odata.y) <- odata.y$Row.names
odata.y <- odata.y[,-1L]
}
newdata <- merge(odata.m, odata.y, sort=FALSE,
by=c("row.names", intersect(names(odata.m), names(odata.y))))
rownames(newdata) <- newdata$Row.names
newdata <- newdata[,-1L]
rm(odata.m, odata.y)
call.m <- getCall(model.m)
call.y <- getCall(model.y)
call.m$data <- call.y$data <- newdata
if(c("(weights)") %in% names(newdata)){
call.m$weights <- call.y$weights <- model.weights(newdata)
}
model.m <- eval.parent(call.m)
model.y <- eval.parent(call.y)
if(!is.null(cluster)){
cluster <- factor(newdata[, ncol(newdata)]) # factor drops missing levels
}
}
# Model type indicators
isGam.y <- inherits(model.y, "gam")
isGam.m <- inherits(model.m, "gam")
isGlm.y <- inherits(model.y, "glm") # Note gam and bayesglm also inherits "glm"
isGlm.m <- inherits(model.m, "glm") # Note gam and bayesglm also inherits "glm"
isLm.y <- inherits(model.y, "lm") # Note gam, glm and bayesglm also inherit "lm"
isLm.m <- inherits(model.m, "lm") # Note gam, glm and bayesglm also inherit "lm"
isVglm.y <- inherits(model.y, "vglm")
isRq.y <- inherits(model.y, "rq")
isRq.m <- inherits(model.m, "rq")
isOrdered.y <- inherits(model.y, "polr") # Note bayespolr also inherits "polr"
isOrdered.m <- inherits(model.m, "polr") # Note bayespolr also inherits "polr"
isSurvreg.y <- inherits(model.y, "survreg")
isSurvreg.m <- inherits(model.m, "survreg")
isMer.y <- inherits(model.y, "merMod") # Note lmer and glmer do not inherit "lm" and "glm"
isMer.m <- inherits(model.m, "merMod") # Note lmer and glmer do not inherit "lm" and "glm"
# Record family and link of model.m if glmer
if(isMer.m && class(model.m)[[1]] == "glmerMod"){
m.family <- as.character(model.m@call$family)
if(m.family[1] == "binomial" && (is.na(m.family[2]) || m.family[2] == "logit")){
M.fun <- binomial(link = "logit")
} else if(m.family[1] == "binomial" && m.family[2] == "probit"){
M.fun <- binomial(link = "probit")
} else if(m.family[1] == "binomial" && m.family[2] == "cloglog"){
M.fun <- binomial(link = "cloglog")
} else if(m.family[1] == "poisson" && (is.na(m.family[2]) || m.family[2] == "log")){
M.fun <- poisson(link = "log")
} else if(m.family[1] == "poisson" && m.family[2] == "identity"){
M.fun <- poisson(link = "identity")
} else if(m.family[1] == "poisson" && m.family[2] == "sqrt"){
M.fun <- poisson(link = "sqrt")
} else {
stop("glmer family for the mediation model not supported")
} ### gamma & inverse gaussian excluded (no function to estimate parameters of S4 glmer vs. S3 glm)
}
# Record family and link of model.y if glmer
if(isMer.y && class(model.y)[[1]] == "glmerMod"){
y.family <- as.character(model.y@call$family)
if(y.family[1] == "binomial" && (is.na(y.family[2]) || y.family[2] == "logit")){
Y.fun <- binomial(link = "logit")
} else if(y.family[1] == "binomial" && y.family[2] == "probit"){
Y.fun <- binomial(link = "probit")
} else if(y.family[1] == "binomial" && y.family[2] == "cloglog"){
Y.fun <- binomial(link = "cloglog")
} else if(y.family[1] == "poisson" && (is.na(y.family[2]) || y.family[2] == "log")){
Y.fun <- poisson(link = "log")
} else if(y.family[1] == "poisson" && y.family[2] == "identity"){
Y.fun <- poisson(link = "identity")
} else if(y.family[1] == "poisson" && y.family[2] == "sqrt"){
Y.fun <- poisson(link = "sqrt")
} else {
stop("glmer family for the outcome model not supported")
} ### gamma & inverse gaussian excluded (no function to estimate parameters of S4 glmer vs. S3 glm)
}
# Record family of model.m if glm
if(isGlm.m){
FamilyM <- model.m$family$family
}
# Record family of model.m if glmer
if(isMer.m && class(model.m)[[1]] == "glmerMod"){
FamilyM <- M.fun$family
}
# Record vfamily of model.y if vglm (currently only tobit)
if(isVglm.y){
VfamilyY <- model.y@family@vfamily
}
# Warning for unused options
if(!is.null(control) && !isGam.y){
warning("'control' is only used for GAM outcome models - ignored")
control <- NULL
}
if(!is.null(outcome) && !(isSurvreg.y && boot)){
warning("'outcome' is only relevant for survival outcome models with bootstrap - ignored")
}
# Model frames for M and Y models
m.data <- model.frame(model.m) # Call.M$data
y.data <- model.frame(model.y) # Call.Y$data
if(!is.null(cluster)){
row.names(m.data) <- 1:nrow(m.data)
row.names(y.data) <- 1:nrow(y.data)
if(!is.null(model.m$weights)){
m.weights <- as.data.frame(model.m$weights)
m.name <- as.character(model.m$call$weights)
names(m.weights) <- m.name
m.data <- cbind(m.data, m.weights)
}
if(!is.null(model.y$weights)){
y.weights <- as.data.frame(model.y$weights)
y.name <- as.character(model.y$call$weights)
names(y.weights) <- y.name
y.data <- cbind(y.data, y.weights)
}
}
# group-level mediator
if(isMer.y & !isMer.m){
m.data <- eval(model.m$call$data, environment(formula(model.m))) ### add group ID to m.data
m.data <- na.omit(m.data)
y.data <- na.omit(y.data)
}
# Specify group names
if(isMer.m && isMer.y){
med.group <- names(model.m@flist)
out.group <- names(model.y@flist)
n.med <- length(med.group)
n.out <- length(out.group)
if(n.med > 1 || n.out > 1){
stop("mediate does not support more than two levels per model")
} else {
group.m <- med.group
group.y <- out.group
if(!is.null(group.out) && !(group.out %in% c(group.m, group.y))){
warning("group.out does not match group names used in merMod")
} else if(is.null(group.out)){
group.out <- group.y
}
}
} else if(!isMer.m && isMer.y){
out.group <- names(model.y@flist)
n.out <- length(out.group)
if(n.out > 1){
stop("mediate does not support more than two levels per model")
} else {
group.m <- NULL
group.y <- out.group
group.out <- group.y
}
} else if(isMer.m && !isMer.y){
med.group <- names(model.m@flist)
n.med <- length(med.group)
if(n.med > 1){
stop("mediate does not support more than two levels per model")
} else {
group.m <- med.group
group.y <- NULL
group.out <- group.m
}
} else {
group.m <- NULL
group.y <- NULL
group.out <- NULL
}
# group data if lmer or glmer
if(isMer.m){
group.id.m <- m.data[,group.m]
} else {
group.id.m <- NULL
}
if(isMer.y){
group.id.y <- y.data[,group.y]
} else {
group.id.y <- NULL
}
# group data to be output in summary and plot if lmer or glmer
if(isMer.y && isMer.m){
if(group.out == group.m){
group.id <- m.data[,group.m]
group.name <- group.m
} else {
group.id <- y.data[,group.y]
group.name <- group.y
}
} else if(!isMer.y && isMer.m){
group.id <- m.data[,group.m]
group.name <- group.m
} else if(isMer.y && !isMer.m){ ### group-level mediator
if(!(group.y %in% names(m.data))){
stop("specify group-level variable in mediator data")
} else {
group.id <- y.data[,group.y]
group.name <- group.y
Y.ID<- sort(unique(group.id))
if(is.character(m.data[,group.y])){
M.ID <- sort(as.factor(m.data[,group.y]))
} else {
M.ID <- sort(as.vector(data.matrix(m.data[group.y])))
}
if(length(Y.ID) != length(M.ID)){
stop("groups do not match between mediator and outcome models")
} else {
if(FALSE %in% unique(Y.ID == M.ID)){
stop("groups do not match between mediator and outcome models")
}
}
}
} else {
group.id <- NULL
group.name <- NULL
}
# Numbers of observations and categories
n.m <- nrow(m.data)
n.y <- nrow(y.data)
if(!(isMer.y & !isMer.m)){ ### n.y and n.m are different when group-level mediator is used
if(n.m != n.y){
stop("number of observations do not match between mediator and outcome models")
} else{
n <- n.m
}
m <- length(sort(unique(model.frame(model.m)[,1])))
}
# Extracting weights from models
weights.m <- model.weights(m.data)
weights.y <- model.weights(y.data)
if(!is.null(weights.m) && isGlm.m && FamilyM == "binomial"){
message("weights taken as sampling weights, not total number of trials")
}
if(!is.null(weights.m) && isMer.m && class(model.m)[[1]] == "glmerMod" && FamilyM == "binomial"){
message("weights taken as sampling weights, not total number of trials")
}
if(is.null(weights.m)){
weights.m <- rep(1,nrow(m.data))
}
if(is.null(weights.y)){
weights.y <- rep(1,nrow(y.data))
}
if(!(isMer.y & !isMer.m)){
if(!all(weights.m == weights.y)) {
stop("weights on outcome and mediator models not identical")
} else {
weights <- weights.m
}
} else{
weights <- weights.y ### group-level mediator
}
# Convert character treatment to factor
if(is.character(m.data[,treat])){
m.data[,treat] <- factor(m.data[,treat])
}
if(is.character(y.data[,treat])){
y.data[,treat] <- factor(y.data[,treat])
}
# Convert character mediator to factor
if(is.character(y.data[,mediator])){
y.data[,mediator] <- factor(y.data[,mediator])
}
# Factor treatment indicator
isFactorT.m <- is.factor(m.data[,treat])
isFactorT.y <- is.factor(y.data[,treat])
if(isFactorT.m != isFactorT.y){
stop("treatment variable types differ in mediator and outcome models")
} else {
isFactorT <- isFactorT.y
}
if(isFactorT){
t.levels <- levels(y.data[,treat])
if(treat.value %in% t.levels & control.value %in% t.levels){
cat.0 <- control.value
cat.1 <- treat.value
} else {
cat.0 <- t.levels[1]
cat.1 <- t.levels[2]
warning("treatment and control values do not match factor levels; using ", cat.0, " and ", cat.1, " as control and treatment, respectively")
}
} else {
cat.0 <- control.value
cat.1 <- treat.value
}
# Factor mediator indicator
isFactorM <- is.factor(y.data[,mediator])
if(isFactorM){
m.levels <- levels(y.data[,mediator])
}
# Eventually, we want to use only objects collected in K,
# passing K into intermediate functions, and clean up all stray objects.
K <- as.list(environment())
# rm(list = ls())
############################################################################
############################################################################
### CASE I: EVERYTHING EXCEPT ORDERED OUTCOME
############################################################################
############################################################################
if (!isOrdered.y) {
########################################################################
## Case I-1: Quasi-Bayesian Monte Carlo
########################################################################
if(!boot){
# Error if gam outcome or quantile mediator
if(isGam.m | isGam.y | isRq.m){
stop("'boot' must be 'TRUE' for models used")
}
# Get mean and variance parameters for mediator simulations
if(isSurvreg.m && is.null(survival::survreg.distributions[[model.m$dist]]$scale)){
MModel.coef <- c(coef(model.m), log(model.m$scale))
scalesim.m <- TRUE
} else if(isMer.m){
MModel.fixef <- lme4::fixef(model.m)
MModel.ranef <- lme4::ranef(model.m)
scalesim.m <- FALSE
} else {
MModel.coef <- coef(model.m)
scalesim.m <- FALSE
}
if(isOrdered.m){
if(is.null(model.m$Hess)){
cat("Mediator model object does not contain 'Hessian';")
}
k <- length(MModel.coef)
MModel.var.cov <- vcov(model.m)[(1:k),(1:k)]
} else if(isSurvreg.m){
MModel.var.cov <- vcov(model.m)
} else {
if(robustSE & !isMer.m){
MModel.var.cov <- vcovHC(model.m, ...)
} else if(robustSE & isMer.m){
MModel.var.cov <- vcov(model.m)
warning("robustSE does not support mer class: non-robust SEs are computed for model.m")
} else if(!is.null(cluster)){
if(nrow(m.data)!=length(cluster)){
warning("length of cluster vector differs from # of obs for mediator model")
}
dta <- merge(m.data, as.data.frame(cluster), sort=FALSE,
by="row.names")
fm <- update(model.m, data=dta)
MModel.var.cov <- sandwich::vcovCL(fm, dta[,ncol(dta)])
} else {
MModel.var.cov <- vcov(model.m)
}
}
# Get mean and variance parameters for outcome simulations
if(isSurvreg.y && is.null(survival::survreg.distributions[[model.y$dist]]$scale)){
YModel.coef <- c(coef(model.y), log(model.y$scale))
scalesim.y <- TRUE # indicates if survreg scale parameter is simulated
} else if(isMer.y){
YModel.fixef <- lme4::fixef(model.y)
YModel.ranef <- lme4::ranef(model.y)
scalesim.y <- FALSE
} else {
YModel.coef <- coef(model.y)
scalesim.y <- FALSE
}
if(isRq.y){
YModel.var.cov <- summary(model.y, covariance=TRUE)$cov
} else if(isSurvreg.y){
YModel.var.cov <- vcov(model.y)
} else {
if(robustSE & !isMer.y){
YModel.var.cov <- vcovHC(model.y, ...)
} else if(robustSE & isMer.y){
YModel.var.cov <- vcov(model.y)
warning("robustSE does not support mer class: non-robust SEs are computed for model.y")
} else if(!is.null(cluster)){
if(nrow(y.data)!=length(cluster)){
warning("length of cluster vector differs from # of obs for outcome model")
}
dta <- merge(y.data, as.data.frame(cluster), sort=FALSE,
by="row.names")
fm <- update(model.y, data=dta)
YModel.var.cov <- sandwich::vcovCL(fm, dta[,ncol(dta)])
} else {
YModel.var.cov <- vcov(model.y)
}
}
# Draw model coefficients from normal
se.ranef.new <- function (object) {
se.bygroup <- lme4::ranef(object, condVar = TRUE)
n.groupings <- length(se.bygroup)
for (m in 1:n.groupings) {
vars.m <- attr(se.bygroup[[m]], "postVar")
K <- dim(vars.m)[1]
J <- dim(vars.m)[3]
names.full <- dimnames(se.bygroup[[m]])
se.bygroup[[m]] <- array(NA, c(J, K))
for (j in 1:J) {
se.bygroup[[m]][j, ] <- sqrt(diag(as.matrix(vars.m[,
, j])))
}
dimnames(se.bygroup[[m]]) <- list(names.full[[1]], names.full[[2]])
}
return(se.bygroup)
}
if(isMer.m){
MModel.fixef.vcov <- as.matrix(vcov(model.m))
MModel.fixef.sim <- rmvnorm(sims,mean=MModel.fixef,sigma=MModel.fixef.vcov)
Nm.ranef <- ncol(lme4::ranef(model.m)[[1]])
MModel.ranef.sim <- vector("list",Nm.ranef)
for (d in 1:Nm.ranef){
MModel.ranef.sim[[d]] <- matrix(rnorm(sims*nrow(lme4::ranef(model.m)[[1]]), mean = lme4::ranef(model.m)[[1]][,d], sd = se.ranef.new(model.m)[[1]][,d]), nrow = sims, byrow = TRUE)
}
} else {
if(sum(is.na(MModel.coef)) > 0){
stop("NA in model coefficients; rerun models with nonsingular design matrix")
}
MModel <- rmvnorm(sims, mean=MModel.coef, sigma=MModel.var.cov)
}
if(isMer.y){
YModel.fixef.vcov <- as.matrix(vcov(model.y))
YModel.fixef.sim <- rmvnorm(sims,mean=YModel.fixef,sigma=YModel.fixef.vcov)
Ny.ranef <- ncol(lme4::ranef(model.y)[[1]])
YModel.ranef.sim <- vector("list",Ny.ranef)
for (d in 1:Ny.ranef){
YModel.ranef.sim[[d]] <- matrix(rnorm(sims*nrow(lme4::ranef(model.y)[[1]]), mean = lme4::ranef(model.y)[[1]][,d], sd = se.ranef.new(model.y)[[1]][,d]), nrow = sims, byrow = TRUE)
}
} else {
if(sum(is.na(YModel.coef)) > 0){
stop("NA in model coefficients; rerun models with nonsingular design matrix")
}
YModel <- rmvnorm(sims, mean=YModel.coef, sigma=YModel.var.cov)
}
if(robustSE && (isSurvreg.m | isSurvreg.y)){
warning("`robustSE' ignored for survival models; fit the model with `robust' option instead\n")
}
if(!is.null(cluster) && (isSurvreg.m | isSurvreg.y)){
warning("`cluster' ignored for survival models; fit the model with 'cluster()' term in the formula\n")
}
#####################################
## Mediator Predictions
#####################################
### number of observations are different when group-level mediator is used
if(isMer.y & !isMer.m){
n <- n.m
}
pred.data.t <- pred.data.c <- m.data
if(isFactorT){
pred.data.t[,treat] <- factor(cat.1, levels = t.levels)
pred.data.c[,treat] <- factor(cat.0, levels = t.levels)
} else {
pred.data.t[,treat] <- cat.1
pred.data.c[,treat] <- cat.0
}
if(!is.null(covariates)){
for(p in 1:length(covariates)){
vl <- names(covariates[p])
if(is.factor(pred.data.t[,vl])){
pred.data.t[,vl] <- pred.data.c[,vl] <- factor(covariates[[p]], levels = levels(m.data[,vl]))
} else {
pred.data.t[,vl] <- pred.data.c[,vl] <- covariates[[p]]
}
}
}
mmat.t <- model.matrix(terms(model.m), data=pred.data.t)
mmat.c <- model.matrix(terms(model.m), data=pred.data.c)
### Case I-1-a: GLM Mediator
if(isGlm.m){
muM1 <- model.m$family$linkinv(tcrossprod(MModel, mmat.t))
muM0 <- model.m$family$linkinv(tcrossprod(MModel, mmat.c))
if(FamilyM == "poisson"){
PredictM1 <- matrix(rpois(sims*n, lambda = muM1), nrow = sims)
PredictM0 <- matrix(rpois(sims*n, lambda = muM0), nrow = sims)
} else if (FamilyM == "Gamma") {
shape <- gamma.shape(model.m)$alpha
PredictM1 <- matrix(rgamma(n*sims, shape = shape,
scale = muM1/shape), nrow = sims)
PredictM0 <- matrix(rgamma(n*sims, shape = shape,
scale = muM0/shape), nrow = sims)
} else if (FamilyM == "binomial"){
PredictM1 <- matrix(rbinom(n*sims, size = 1,
prob = muM1), nrow = sims)
PredictM0 <- matrix(rbinom(n*sims, size = 1,
prob = muM0), nrow = sims)
} else if (FamilyM == "gaussian"){
sigma <- sqrt(summary(model.m)$dispersion)
error <- rnorm(sims*n, mean=0, sd=sigma)
PredictM1 <- muM1 + matrix(error, nrow=sims)
PredictM0 <- muM0 + matrix(error, nrow=sims)
} else if (FamilyM == "inverse.gaussian"){
disp <- summary(model.m)$dispersion
PredictM1 <- matrix(SuppDists::rinvGauss(n*sims, nu = muM1,
lambda = 1/disp), nrow = sims)
PredictM0 <- matrix(SuppDists::rinvGauss(n*sims, nu = muM0,
lambda = 1/disp), nrow = sims)
} else {
stop("unsupported glm family")
}
### Case I-1-b: Ordered mediator
} else if(isOrdered.m){
if(model.m$method=="logistic"){
linkfn <- plogis
} else if(model.m$method=="probit") {
linkfn <- pnorm
} else {
stop("unsupported polr method; use 'logistic' or 'probit'")
}
m.cat <- sort(unique(model.frame(model.m)[,1]))
lambda <- model.m$zeta
mmat.t <- mmat.t[,-1]
mmat.c <- mmat.c[,-1]
ystar_m1 <- tcrossprod(MModel, mmat.t)
ystar_m0 <- tcrossprod(MModel, mmat.c)
PredictM1 <- matrix(,nrow=sims, ncol=n)
PredictM0 <- matrix(,nrow=sims, ncol=n)
for(i in 1:sims){
cprobs_m1 <- matrix(NA,n,m)
cprobs_m0 <- matrix(NA,n,m)
probs_m1 <- matrix(NA,n,m)
probs_m0 <- matrix(NA,n,m)
for (j in 1:(m-1)) { # loop to get category-specific probabilities
cprobs_m1[,j] <- linkfn(lambda[j]-ystar_m1[i,])
cprobs_m0[,j] <- linkfn(lambda[j]-ystar_m0[i,])
# cumulative probabilities
probs_m1[,m] <- 1-cprobs_m1[,m-1] # top category
probs_m0[,m] <- 1-cprobs_m0[,m-1] # top category
probs_m1[,1] <- cprobs_m1[,1] # bottom category
probs_m0[,1] <- cprobs_m0[,1] # bottom category
}
for (j in 2:(m-1)){ # middle categories
probs_m1[,j] <- cprobs_m1[,j]-cprobs_m1[,j-1]
probs_m0[,j] <- cprobs_m0[,j]-cprobs_m0[,j-1]
}
draws_m1 <- matrix(NA, n, m)
draws_m0 <- matrix(NA, n, m)
for(ii in 1:n){
draws_m1[ii,] <- t(rmultinom(1, 1, prob = probs_m1[ii,]))
draws_m0[ii,] <- t(rmultinom(1, 1, prob = probs_m0[ii,]))
}
PredictM1[i,] <- apply(draws_m1, 1, which.max)
PredictM0[i,] <- apply(draws_m0, 1, which.max)
}
### Case I-1-c: Linear
} else if(isLm.m){
sigma <- summary(model.m)$sigma
error <- rnorm(sims*n, mean=0, sd=sigma)
muM1 <- tcrossprod(MModel, mmat.t)
muM0 <- tcrossprod(MModel, mmat.c)
PredictM1 <- muM1 + matrix(error, nrow=sims)
PredictM0 <- muM0 + matrix(error, nrow=sims)
rm(error)
### Case I-1-d: Survreg
} else if(isSurvreg.m){
dd <- survival::survreg.distributions[[model.m$dist]]
if (is.null(dd$itrans)){
itrans <- function(x) x
} else {
itrans <- dd$itrans
}
dname <- dd$dist
if(is.null(dname)){
dname <- model.m$dist
}
if(scalesim.m){
scale <- exp(MModel[,ncol(MModel)])
lpM1 <- tcrossprod(MModel[,1:(ncol(MModel)-1)], mmat.t)
lpM0 <- tcrossprod(MModel[,1:(ncol(MModel)-1)], mmat.c)
} else {
scale <- dd$scale
lpM1 <- tcrossprod(MModel, mmat.t)
lpM0 <- tcrossprod(MModel, mmat.c)
}
error <- switch(dname,
extreme = log(rweibull(sims*n, shape=1, scale=1)),
gaussian = rnorm(sims*n),
logistic = rlogis(sims*n),
t = rt(sims*n, df=dd$parms))
PredictM1 <- itrans(lpM1 + scale * matrix(error, nrow=sims))
PredictM0 <- itrans(lpM0 + scale * matrix(error, nrow=sims))
rm(error)
### Case I-1-e: Linear Mixed Effect
} else if(isMer.m && class(model.m)[[1]]=="lmerMod"){
M.RANEF1 <- M.RANEF0 <- 0
for (d in 1:Nm.ranef){
name <- colnames(lme4::ranef(model.m)[[1]])[d]
if(name == "(Intercept)"){
var1 <- var0 <- matrix(1,sims,n) ### RE intercept
} else if(name == treat){ ### RE slope of treat
var1 <- matrix(1,sims,n) ### T = 1
var0 <- matrix(0,sims,n) ### T = 0
}
else {
var1 <- var0 <- matrix(data.matrix(m.data[name]),sims,n,byrow=T) ### RE slope of other variables
}
M.ranef<-matrix(NA,sims,n)
MModel.ranef.sim.d <- MModel.ranef.sim[[d]]
Z <- data.frame(MModel.ranef.sim.d)
if(is.factor(group.id.m)){
colnames(Z) <- levels(group.id.m)
for (i in 1:n){
M.ranef[,i]<-Z[,group.id.m[i]==levels(group.id.m)]
}
} else {
colnames(Z) <- sort(unique(group.id.m))
for (i in 1:n){
M.ranef[,i]<-Z[,group.id.m[i]==sort(unique(group.id.m))]
}
}
M.RANEF1 <- M.ranef*var1 + M.RANEF1 # sum of (random effects*corresponding covarites)
M.RANEF0 <- M.ranef*var0 + M.RANEF0
}
sigma <- attr(lme4::VarCorr(model.m), "sc")
error <- rnorm(sims*n, mean=0, sd=sigma)
muM1 <- tcrossprod(MModel.fixef.sim, mmat.t) + M.RANEF1
muM0 <- tcrossprod(MModel.fixef.sim, mmat.c) + M.RANEF0
PredictM1 <- muM1 + matrix(error, nrow=sims)
PredictM0 <- muM0 + matrix(error, nrow=sims)
rm(error)
### Case I-1-f: Generalized Linear Mixed Effect
} else if(isMer.m && class(model.m)[[1]]=="glmerMod"){
M.RANEF1 <-M.RANEF0 <- 0 ### 1=RE for M(1); 0=RE for M(0)
for (d in 1:Nm.ranef){
name <- colnames(lme4::ranef(model.m)[[1]])[d]
if(name == "(Intercept)"){
var1 <- var0 <- matrix(1,sims,n) ### RE intercept
} else if(name == treat){ ### RE slope of treat
var1 <- matrix(1,sims,n) ### T = 1
var0 <- matrix(0,sims,n) ### T = 0
} else {
var1 <- var0 <- matrix(data.matrix(m.data[name]),sims,n,byrow=T) ### RE slope of other variables
}
M.ranef<-matrix(NA,sims,n)
MModel.ranef.sim.d <- MModel.ranef.sim[[d]]
Z <- data.frame(MModel.ranef.sim.d)
if(is.factor(group.id.m)){
colnames(Z) <- levels(group.id.m)
for (i in 1:n){
M.ranef[,i]<-Z[,group.id.m[i]==levels(group.id.m)]
}
} else {
colnames(Z) <- sort(unique(group.id.m))
for (i in 1:n){
M.ranef[,i]<-Z[,group.id.m[i]==sort(unique(group.id.m))]
}
}
M.RANEF1 <- M.ranef*var1 + M.RANEF1 # sum of (random effects*corresponding covarites)
M.RANEF0 <- M.ranef*var0 + M.RANEF0
}
muM1 <- M.fun$linkinv(tcrossprod(MModel.fixef.sim,mmat.t) + M.RANEF1)
muM0 <- M.fun$linkinv(tcrossprod(MModel.fixef.sim,mmat.c) + M.RANEF0)
FamilyM <- M.fun$family
if(FamilyM == "poisson"){
PredictM1 <- matrix(rpois(sims*n, lambda = muM1), nrow = sims)
PredictM0 <- matrix(rpois(sims*n, lambda = muM0), nrow = sims)
} else if (FamilyM == "binomial"){
PredictM1 <- matrix(rbinom(n*sims, size = 1,
prob = muM1), nrow = sims)
PredictM0 <- matrix(rbinom(n*sims, size = 1,
prob = muM0), nrow = sims)
}
} else {
stop("mediator model is not yet implemented")
}
### group-level mediator : J -> NJ
if(isMer.y & !isMer.m){
J <- nrow(m.data)
if(is.character(m.data[,group.y])){
group.id.m <- as.factor(m.data[,group.y])
} else {
group.id.m <- as.vector(data.matrix(m.data[group.y]))
}
v1 <- v0 <- matrix(NA, sims, length(group.id.y))
num.m <- 1:J
num.y <- 1:length(group.id.y)
for (j in 1:J){
id.y <- unique(group.id.y)[j]
NUM.M <- num.m[group.id.m == id.y]
NUM.Y <- num.y[group.id.y == id.y]
v1[, NUM.Y] <- PredictM1[, NUM.M]
v0[, NUM.Y] <- PredictM0[, NUM.M]
}
PredictM1 <- v1
PredictM0 <- v0
}
rm(mmat.t, mmat.c)
#####################################
## Outcome Predictions
#####################################
### number of observations are different when group-level mediator is used
if(isMer.y & !isMer.m){
n <- n.y
}
effects.tmp <- array(NA, dim = c(n, sims, 4))
if(isMer.y){
Y.RANEF1 <- Y.RANEF2 <- Y.RANEF3 <- Y.RANEF4 <- 0
### 1=RE for Y(1,M(1)); 2=RE for Y(1,M(0)); 3=RE for Y(0,M(1)); 4=RE for Y(0,M(0))
for (d in 1:Ny.ranef){
name <- colnames(lme4::ranef(model.y)[[1]])[d]
if(name == "(Intercept)"){
var1 <- var2 <- var3 <- var4 <- matrix(1,sims,n)
} else if(name == treat){
var1 <- matrix(1,sims,n)
var2 <- matrix(1,sims,n)
var3 <- matrix(0,sims,n)
var4 <- matrix(0,sims,n)
} else if(name == mediator){
var1 <- PredictM1
var2 <- PredictM0
var3 <- PredictM1
var4 <- PredictM0
} else {
if(name %in% colnames(y.data)){
var1 <- var2 <- var3 <- var4 <- matrix(data.matrix(y.data[name]),sims,n,byrow=T)
} else {
int.term.name <- strsplit(name, ":")[[1]]
int.term <- rep(1, nrow(y.data))
for (p in 1:length(int.term.name)){
int.term <- y.data[int.term.name[p]][[1]] * int.term
}
var1 <- var2 <- var3 <- var4 <- matrix(int.term,sims,n,byrow=T)
}
}
Y.ranef<-matrix(NA,sims,n)
YModel.ranef.sim.d <- YModel.ranef.sim[[d]]
Z <- data.frame(YModel.ranef.sim.d)
if(is.factor(group.id.y)){
colnames(Z) <- levels(group.id.y)
for (i in 1:n){
Y.ranef[,i]<-Z[,group.id.y[i]==levels(group.id.y)]
}
} else {
colnames(Z) <- sort(unique(group.id.y))
for (i in 1:n){
Y.ranef[,i]<-Z[,group.id.y[i]==sort(unique(group.id.y))]
}
}
Y.RANEF1 <- Y.ranef*var1 + Y.RANEF1 # sum of (random effects*corresponding covarites)
Y.RANEF2 <- Y.ranef*var2 + Y.RANEF2
Y.RANEF3 <- Y.ranef*var3 + Y.RANEF3
Y.RANEF4 <- Y.ranef*var4 + Y.RANEF4
}
}
for(e in 1:4){
tt <- switch(e, c(1,1,1,0), c(0,0,1,0), c(1,0,1,1), c(1,0,0,0))
Pr1 <- matrix(, nrow=n, ncol=sims)
Pr0 <- matrix(, nrow=n, ncol=sims)
for(j in 1:sims){
pred.data.t <- pred.data.c <- y.data
if(!is.null(covariates)){
for(p in 1:length(covariates)){
vl <- names(covariates[p])
if(is.factor(pred.data.t[,vl])){
pred.data.t[,vl] <- pred.data.c[,vl] <- factor(covariates[[p]], levels = levels(y.data[,vl]))
} else {
pred.data.t[,vl] <- pred.data.c[,vl] <- covariates[[p]]
}
}
}
# Set treatment values
cat.t <- ifelse(tt[1], cat.1, cat.0)
cat.c <- ifelse(tt[2], cat.1, cat.0)
cat.t.ctrl <- ifelse(tt[1], cat.0, cat.1)
cat.c.ctrl <- ifelse(tt[2], cat.0, cat.1)
if(isFactorT){
pred.data.t[,treat] <- factor(cat.t, levels = t.levels)
pred.data.c[,treat] <- factor(cat.c, levels = t.levels)
if(!is.null(control)){
pred.data.t[,control] <- factor(cat.t.ctrl, levels = t.levels)
pred.data.c[,control] <- factor(cat.c.ctrl, levels = t.levels)
}
} else {
pred.data.t[,treat] <- cat.t
pred.data.c[,treat] <- cat.c
if(!is.null(control)){
pred.data.t[,control] <- cat.t.ctrl
pred.data.c[,control] <- cat.c.ctrl
}
}
# Set mediator values
PredictMt <- PredictM1[j,] * tt[3] + PredictM0[j,] * (1 - tt[3])
PredictMc <- PredictM1[j,] * tt[4] + PredictM0[j,] * (1 - tt[4])
if(isFactorM) {
pred.data.t[,mediator] <- factor(PredictMt, levels=1:m, labels=m.levels)
pred.data.c[,mediator] <- factor(PredictMc, levels=1:m, labels=m.levels)
} else {
pred.data.t[,mediator] <- PredictMt
pred.data.c[,mediator] <- PredictMc
}
ymat.t <- model.matrix(terms(model.y), data=pred.data.t)
ymat.c <- model.matrix(terms(model.y), data=pred.data.c)
if(isVglm.y){
if(VfamilyY=="tobit") {
Pr1.tmp <- ymat.t %*% YModel[j,-2]
Pr0.tmp <- ymat.c %*% YModel[j,-2]
Pr1[,j] <- pmin(pmax(Pr1.tmp, model.y@misc$Lower), model.y@misc$Upper)
Pr0[,j] <- pmin(pmax(Pr0.tmp, model.y@misc$Lower), model.y@misc$Upper)
} else {
stop("outcome model is in unsupported vglm family")
}
} else if(scalesim.y){
Pr1[,j] <- t(as.matrix(YModel[j,1:(ncol(YModel)-1)])) %*% t(ymat.t)
Pr0[,j] <- t(as.matrix(YModel[j,1:(ncol(YModel)-1)])) %*% t(ymat.c)
} else if(isMer.y){
if(e == 1){ ### mediation(1)
Y.RANEF.A <- Y.RANEF1
Y.RANEF.B <- Y.RANEF2
} else if(e == 2){ ### mediation(0)
Y.RANEF.A <- Y.RANEF3
Y.RANEF.B <- Y.RANEF4
} else if(e == 3){ ### direct(1)
Y.RANEF.A <- Y.RANEF1
Y.RANEF.B <- Y.RANEF3
} else { ### direct(0)
Y.RANEF.A <- Y.RANEF2
Y.RANEF.B <- Y.RANEF4
}
Pr1[,j] <- t(as.matrix(YModel.fixef.sim[j,])) %*% t(ymat.t) + Y.RANEF.A[j,]
Pr0[,j] <- t(as.matrix(YModel.fixef.sim[j,])) %*% t(ymat.c) + Y.RANEF.B[j,]
} else {
Pr1[,j] <- t(as.matrix(YModel[j,])) %*% t(ymat.t)
Pr0[,j] <- t(as.matrix(YModel[j,])) %*% t(ymat.c)
}
rm(ymat.t, ymat.c, pred.data.t, pred.data.c)
}
if(isGlm.y){
Pr1 <- apply(Pr1, 2, model.y$family$linkinv)
Pr0 <- apply(Pr0, 2, model.y$family$linkinv)
} else if(isSurvreg.y){
dd <- survival::survreg.distributions[[model.y$dist]]
if (is.null(dd$itrans)){
itrans <- function(x) x
} else {
itrans <- dd$itrans
}
Pr1 <- apply(Pr1, 2, itrans)
Pr0 <- apply(Pr0, 2, itrans)
} else if(isMer.y && class(model.y)[[1]] == "glmerMod"){
Pr1 <- apply(Pr1, 2, Y.fun$linkinv)
Pr0 <- apply(Pr0, 2, Y.fun$linkinv)
}
effects.tmp[,,e] <- Pr1 - Pr0 ### e=1:mediation(1); e=2:mediation(0); e=3:direct(1); e=4:direct(0)
rm(Pr1, Pr0)
}
if(!isMer.m && !isMer.y){
rm(PredictM1, PredictM0, YModel, MModel)
} else if(!isMer.m && isMer.y){
rm(PredictM1, PredictM0, YModel.ranef.sim)
} else {
rm(PredictM1, PredictM0, MModel.ranef.sim)
}
et1<-effects.tmp[,,1] ### mediation effect (1)
et2<-effects.tmp[,,2] ### mediation effect (0)
et3<-effects.tmp[,,3] ### direct effect (1)
et4<-effects.tmp[,,4] ### direct effect (0)
delta.1 <- t(as.matrix(apply(et1, 2, weighted.mean, w=weights)))
delta.0 <- t(as.matrix(apply(et2, 2, weighted.mean, w=weights)))
zeta.1 <- t(as.matrix(apply(et3, 2, weighted.mean, w=weights)))
zeta.0 <- t(as.matrix(apply(et4, 2, weighted.mean, w=weights)))
rm(effects.tmp)
tau <- (zeta.1 + delta.0 + zeta.0 + delta.1)/2
nu.0 <- delta.0/tau
nu.1 <- delta.1/tau
delta.avg <- (delta.1 + delta.0)/2
zeta.avg <- (zeta.1 + zeta.0)/2
nu.avg <- (nu.1 + nu.0)/2
d0 <- mean(delta.0) # mediation effect
d1 <- mean(delta.1)
z1 <- mean(zeta.1) # direct effect
z0 <- mean(zeta.0)
tau.coef <- mean(tau) # total effect
n0 <- median(nu.0)
n1 <- median(nu.1)
d.avg <- (d0 + d1)/2
z.avg <- (z0 + z1)/2
n.avg <- (n0 + n1)/2
if(isMer.y | isMer.m){
if(!is.null(group.m) && group.name == group.m){
G<-length(unique(group.id.m))
delta.1.group<-matrix(NA,G,sims)
delta.0.group<-matrix(NA,G,sims)
zeta.1.group<-matrix(NA,G,sims)
zeta.0.group<-matrix(NA,G,sims)
for (g in 1:G){
delta.1.group[g,] <- t(apply(matrix(et1[group.id.m==unique(group.id.m)[g],], ncol=sims), 2, weighted.mean, w=weights[group.id.m==unique(group.id.m)[g]]))
delta.0.group[g,] <- t(apply(matrix(et2[group.id.m==unique(group.id.m)[g],], ncol=sims), 2, weighted.mean, w=weights[group.id.m==unique(group.id.m)[g]]))
zeta.1.group[g,] <- t(apply(matrix(et3[group.id.m==unique(group.id.m)[g],], ncol=sims), 2, weighted.mean, w=weights[group.id.m==unique(group.id.m)[g]]))
zeta.0.group[g,] <- t(apply(matrix(et4[group.id.m==unique(group.id.m)[g],], ncol=sims), 2, weighted.mean, w=weights[group.id.m==unique(group.id.m)[g]]))
}
} else {
G<-length(unique(group.id.y))
delta.1.group<-matrix(NA,G,sims)
delta.0.group<-matrix(NA,G,sims)
zeta.1.group<-matrix(NA,G,sims)
zeta.0.group<-matrix(NA,G,sims)
for (g in 1:G){
delta.1.group[g,] <- t(apply(matrix(et1[group.id.y==unique(group.id.y)[g],], ncol=sims), 2, weighted.mean, w=weights[group.id.y==unique(group.id.y)[g]]))
delta.0.group[g,] <- t(apply(matrix(et2[group.id.y==unique(group.id.y)[g],], ncol=sims), 2, weighted.mean, w=weights[group.id.y==unique(group.id.y)[g]]))
zeta.1.group[g,] <- t(apply(matrix(et3[group.id.y==unique(group.id.y)[g],], ncol=sims), 2, weighted.mean, w=weights[group.id.y==unique(group.id.y)[g]]))
zeta.0.group[g,] <- t(apply(matrix(et4[group.id.y==unique(group.id.y)[g],], ncol=sims), 2, weighted.mean, w=weights[group.id.y==unique(group.id.y)[g]]))
}
}
tau.group <- (zeta.1.group + delta.0.group + zeta.0.group + delta.1.group)/2
nu.0.group <- delta.0.group/tau.group
nu.1.group <- delta.1.group/tau.group
delta.avg.group <- (delta.1.group + delta.0.group)/2
zeta.avg.group <- (zeta.1.group + zeta.0.group)/2
nu.avg.group <- (nu.1.group + nu.0.group)/2
d0.group <- apply(delta.0.group,1,mean) # mediation effect
d1.group <- apply(delta.1.group,1,mean)
z1.group <- apply(zeta.1.group,1,mean) # direct effect
z0.group <- apply(zeta.0.group,1,mean)
tau.coef.group <- apply(tau.group,1,mean) # total effect
n0.group <- apply(nu.0.group,1,median)
n1.group <- apply(nu.1.group,1,median)
d.avg.group <- (d0.group + d1.group)/2
z.avg.group <- (z0.group + z1.group)/2
n.avg.group <- (n0.group + n1.group)/2
}
########################################################################
## Case I-2: Nonparametric Bootstrap
########################################################################
} else {
# Error if lmer or glmer
if(isMer.m | isMer.y){
stop("'boot' must be 'FALSE' for models used")
}
Call.M <- getCall(model.m)
Call.Y <- getCall(model.y)
if (isSurvreg.m){
if (ncol(model.m$y) > 2)
stop("unsupported censoring type")
mname <- names(m.data)[1]
if (substr(mname, 1, 4) != "Surv")
stop("refit the survival model with `Surv' used directly in model formula")
}
if (isSurvreg.y){
if (ncol(model.y$y) > 2)
stop("unsupported censoring type")
yname <- names(y.data)[1]
if (substr(yname, 1, 4) != "Surv")
stop("refit the survival model with `Surv' used directly in model formula")
if (is.null(outcome))
stop("`outcome' must be supplied for survreg outcome with boot")
}
# Bootstrap QoI
message("Running nonparametric bootstrap\n")
# Make objects available to med.fun
environment(med.fun) <- environment()
D <- boot::boot(data = y.data,
statistic = med.fun,
R = sims,
sim = "ordinary",
m.data = m.data,
...)
# drop = F to maintain column as matrix for backward-compatibility
delta.1 <- D$t[, 1, drop = FALSE]
delta.0 <- D$t[, 2, drop = FALSE]
zeta.1 <- D$t[, 3, drop = FALSE]
zeta.0 <- D$t[, 4, drop = FALSE]
# Generate QoIs for actual sample
D <- med.fun(y.data = y.data, m.data = m.data, index = 1:n)
d1 <- D["d1"]
d0 <- D["d0"]
z1 <- D["z1"]
z0 <- D["z0"]
# Unname objects for backward-compatibility
list2env(
lapply(list(d1 = d1, d0 = d0, z1 = z1, z0 = z0,
delta.1 = delta.1, delta.0 = delta.0,
zeta.1 = zeta.1, zeta.0 = zeta.0),
unname),
envir = environment()
)
tau.coef <- (d1 + d0 + z1 + z0)/2
n0 <- d0/tau.coef
n1 <- d1/tau.coef
d.avg <- (d1 + d0)/2
z.avg <- (z1 + z0)/2
n.avg <- (n0 + n1)/2
tau <- (delta.1 + delta.0 + zeta.1 + zeta.0)/2
nu.0 <- delta.0/tau
nu.1 <- delta.1/tau
delta.avg <- (delta.0 + delta.1)/2
zeta.avg <- (zeta.0 + zeta.1)/2
nu.avg <- (nu.0 + nu.1)/2
} # nonpara boot branch ends
########################################################################
## Compute Outputs and Put Them Together
########################################################################
low <- (1 - conf.level)/2
high <- 1 - low
if (boot & boot.ci.type == "bca"){
BC.CI <- function(theta){
z.inv <- length(theta[theta < mean(theta)])/sims
z <- qnorm(z.inv)
U <- (sims - 1) * (mean(theta) - theta)
top <- sum(U^3)
under <- 6 * (sum(U^2))^{3/2}
a <- top / under
lower.inv <- pnorm(z + (z + qnorm(low))/(1 - a * (z + qnorm(low))))
lower2 <- lower <- quantile(theta, lower.inv)
upper.inv <- pnorm(z + (z + qnorm(high))/(1 - a * (z + qnorm(high))))
upper2 <- upper <- quantile(theta, upper.inv)
return(c(lower, upper))
}
d0.ci <- BC.CI(delta.0)
d1.ci <- BC.CI(delta.1)
tau.ci <- BC.CI(tau)
z1.ci <- BC.CI(zeta.1)
z0.ci <- BC.CI(zeta.0)
n0.ci <- BC.CI(nu.0)
n1.ci <- BC.CI(nu.1)
d.avg.ci <- BC.CI(delta.avg)
z.avg.ci <- BC.CI(zeta.avg)
n.avg.ci <- BC.CI(nu.avg)
} else {
d0.ci <- quantile(delta.0, c(low,high), na.rm=TRUE)
d1.ci <- quantile(delta.1, c(low,high), na.rm=TRUE)
tau.ci <- quantile(tau, c(low,high), na.rm=TRUE)
z1.ci <- quantile(zeta.1, c(low,high), na.rm=TRUE)
z0.ci <- quantile(zeta.0, c(low,high), na.rm=TRUE)
n0.ci <- quantile(nu.0, c(low,high), na.rm=TRUE)
n1.ci <- quantile(nu.1, c(low,high), na.rm=TRUE)
d.avg.ci <- quantile(delta.avg, c(low,high), na.rm=TRUE)
z.avg.ci <- quantile(zeta.avg, c(low,high), na.rm=TRUE)
n.avg.ci <- quantile(nu.avg, c(low,high), na.rm=TRUE)
}
# p-values
d0.p <- pval(delta.0, d0)
d1.p <- pval(delta.1, d1)
d.avg.p <- pval(delta.avg, d.avg)
z0.p <- pval(zeta.0, z0)
z1.p <- pval(zeta.1, z1)
z.avg.p <- pval(zeta.avg, z.avg)
n0.p <- pval(nu.0, n0)
n1.p <- pval(nu.1, n1)
n.avg.p <- pval(nu.avg, n.avg)
tau.p <- pval(tau, tau.coef)
if(isMer.y | isMer.m){
QUANT<-function(object){
z<-quantile(object,c(low,high),na.rm=TRUE)
return(z)
}
d0.ci.group <- t(apply(delta.0.group,1,QUANT))
d1.ci.group <- t(apply(delta.1.group,1,QUANT))
tau.ci.group <- t(apply(tau.group,1,QUANT))
z1.ci.group <- t(apply(zeta.1.group,1,QUANT))
z0.ci.group <- t(apply(zeta.0.group,1,QUANT))
n0.ci.group <- t(apply(nu.0.group,1,QUANT))
n1.ci.group <- t(apply(nu.1.group,1,QUANT))
d.avg.ci.group <- t(apply(delta.avg.group,1,QUANT))
z.avg.ci.group <- t(apply(zeta.avg.group,1,QUANT))
n.avg.ci.group <- t(apply(nu.avg.group,1,QUANT))
d0.p.group<-rep(NA,G)
d1.p.group<-rep(NA,G)
d.avg.p.group<-rep(NA,G)
z0.p.group<-rep(NA,G)
z1.p.group<-rep(NA,G)
z.avg.p.group<-rep(NA,G)
n0.p.group<-rep(NA,G)
n1.p.group<-rep(NA,G)
n.avg.p.group<-rep(NA,G)
tau.p.group<-rep(NA,G)
for (g in 1:G){
d0.p.group[g] <- pval(delta.0.group[g,], d0.group[g])
d1.p.group[g] <- pval(delta.1.group[g,], d1.group[g])
d.avg.p.group[g] <- pval(delta.avg.group[g,], d.avg.group[g])
z0.p.group[g] <- pval(zeta.0.group[g,], z0.group[g])
z1.p.group[g] <- pval(zeta.1.group[g,], z1.group[g])
z.avg.p.group[g] <- pval(zeta.avg.group[g,], z.avg.group[g])
n0.p.group[g] <- pval(nu.0.group[g,], n0.group[g])
n1.p.group[g] <- pval(nu.1.group[g,], n1.group[g])
n.avg.p.group[g] <- pval(nu.avg.group[g,], n.avg.group[g])
tau.p.group[g] <- pval(tau.group[g,], tau.coef.group[g])
}
}
# Detect whether models include T-M interaction
INT <- paste(treat,mediator,sep=":") %in% attr(terms(model.y),"term.labels") |
paste(mediator,treat,sep=":") %in% attr(terms(model.y),"term.labels")
if(!INT & isGam.y){
INT <- !isTRUE(all.equal(d0, d1)) # if gam, determine empirically
}
if(long && !isMer.y && !isMer.m) {
out <- list(
d0=d0, d1=d1, d0.ci=d0.ci, d1.ci=d1.ci,
d0.p=d0.p, d1.p=d1.p,
d0.sims=delta.0, d1.sims=delta.1,
z0=z0, z1=z1, z0.ci=z0.ci, z1.ci=z1.ci,
z0.p=z0.p, z1.p=z1.p,
z0.sims=zeta.0, z1.sims=zeta.1,
n0=n0, n1=n1, n0.ci=n0.ci, n1.ci=n1.ci,
n0.p=n0.p, n1.p=n1.p,
n0.sims=nu.0, n1.sims=nu.1,
tau.coef=tau.coef, tau.ci=tau.ci, tau.p=tau.p,
tau.sims=tau,
d.avg=d.avg, d.avg.p=d.avg.p, d.avg.ci=d.avg.ci, d.avg.sims=delta.avg,
z.avg=z.avg, z.avg.p=z.avg.p, z.avg.ci=z.avg.ci, z.avg.sims=zeta.avg,
n.avg=n.avg, n.avg.p=n.avg.p, n.avg.ci=n.avg.ci, n.avg.sims=nu.avg,
boot=boot, boot.ci.type=boot.ci.type,
treat=treat, mediator=mediator,
covariates=covariates,
INT=INT, conf.level=conf.level,
model.y=model.y, model.m=model.m,
control.value=control.value, treat.value=treat.value,
nobs=n, sims=sims, call=cl,
robustSE = robustSE, cluster = cluster
)
class(out) <- "mediate"
}
if(!long && !isMer.y && !isMer.m){
out <- list(d0=d0, d1=d1, d0.ci=d0.ci, d1.ci=d1.ci,
d0.p=d0.p, d1.p=d1.p,
z0=z0, z1=z1, z0.ci=z0.ci, z1.ci=z1.ci,
z0.p=z0.p, z1.p=z1.p,
n0=n0, n1=n1, n0.ci=n0.ci, n1.ci=n1.ci,
n0.p=n0.p, n1.p=n1.p,
tau.coef=tau.coef, tau.ci=tau.ci, tau.p=tau.p,
d.avg=d.avg, d.avg.p=d.avg.p, d.avg.ci=d.avg.ci,
z.avg=z.avg, z.avg.p=z.avg.p, z.avg.ci=z.avg.ci,
n.avg=n.avg, n.avg.p=n.avg.p, n.avg.ci=n.avg.ci,
boot=boot, boot.ci.type=boot.ci.type,
treat=treat, mediator=mediator,
covariates=covariates,
INT=INT, conf.level=conf.level,
model.y=model.y, model.m=model.m,
control.value=control.value, treat.value=treat.value,
nobs=n, sims=sims, call=cl,
robustSE = robustSE, cluster = cluster)
class(out) <- "mediate"
}
if(long && (isMer.y || isMer.m)) {
out <- list(d0=d0, d1=d1, d0.ci=d0.ci, d1.ci=d1.ci,
d0.p=d0.p, d1.p=d1.p,
d0.sims=delta.0, d1.sims=delta.1,
z0=z0, z1=z1, z0.ci=z0.ci, z1.ci=z1.ci,
z0.p=z0.p, z1.p=z1.p,
z0.sims=zeta.0, z1.sims=zeta.1,
n0=n0, n1=n1, n0.ci=n0.ci, n1.ci=n1.ci,
n0.p=n0.p, n1.p=n1.p,
n0.sims=nu.0, n1.sims=nu.1,
tau.coef=tau.coef, tau.ci=tau.ci, tau.p=tau.p,
tau.sims=tau,
d.avg=d.avg, d.avg.p=d.avg.p, d.avg.ci=d.avg.ci, d.avg.sims=delta.avg,
z.avg=z.avg, z.avg.p=z.avg.p, z.avg.ci=z.avg.ci, z.avg.sims=zeta.avg,
n.avg=n.avg, n.avg.p=n.avg.p, n.avg.ci=n.avg.ci, n.avg.sims=nu.avg,
d0.group=d0.group, d1.group=d1.group, d0.ci.group=d0.ci.group, d1.ci.group=d1.ci.group,
d0.p.group=d0.p.group, d1.p.group=d1.p.group,
d0.sims.group=delta.0.group, d1.sims.group=delta.1.group,
z0.group=z0.group, z1.group=z1.group, z0.ci.group=z0.ci.group, z1.ci.group=z1.ci.group,
z0.p.group=z0.p.group, z1.p.group=z1.p.group,
z0.sims.group=zeta.0.group, z1.sims.group=zeta.1.group,
n0.group=n0.group, n1.group=n1.group, n0.ci.group=n0.ci.group, n1.ci.group=n1.ci.group,
n0.p.group=n0.p.group, n1.p.group=n1.p.group,
n0.sims.group=nu.0.group, n1.sims.group=nu.1.group,
tau.coef.group=tau.coef.group, tau.ci.group=tau.ci.group, tau.p.group=tau.p.group,
tau.sims.group=tau.group,
d.avg.group=d.avg.group, d.avg.p.group=d.avg.p.group, d.avg.ci.group=d.avg.ci.group, d.avg.sims.group=delta.avg.group,
z.avg.group=z.avg.group, z.avg.p.group=z.avg.p.group, z.avg.ci.group=z.avg.ci.group, z.avg.sims.group=zeta.avg.group,
n.avg.group=n.avg.group, n.avg.p.group=n.avg.p.group, n.avg.ci.group=n.avg.ci.group, n.avg.sims.group=nu.avg.group,
boot=boot, boot.ci.type=boot.ci.type,
treat=treat, mediator=mediator,
covariates=covariates,
INT=INT, conf.level=conf.level,
model.y=model.y, model.m=model.m,
control.value=control.value, treat.value=treat.value,
nobs=n, sims=sims, call=cl,
group.m=group.m,group.y=group.y,group.name=group.name,
group.id.m=group.id.m,group.id.y=group.id.y,group.id=group.id,
robustSE = robustSE, cluster = cluster)
class(out) <- "mediate.mer"
}
if(!long && (isMer.y || isMer.m)){
out <- list(d0=d0, d1=d1, d0.ci=d0.ci, d1.ci=d1.ci,
d0.p=d0.p, d1.p=d1.p,
z0=z0, z1=z1, z0.ci=z0.ci, z1.ci=z1.ci,
z0.p=z0.p, z1.p=z1.p,
n0=n0, n1=n1, n0.ci=n0.ci, n1.ci=n1.ci,
n0.p=n0.p, n1.p=n1.p,
tau.coef=tau.coef, tau.ci=tau.ci, tau.p=tau.p,
d.avg=d.avg, d.avg.p=d.avg.p, d.avg.ci=d.avg.ci,
z.avg=z.avg, z.avg.p=z.avg.p, z.avg.ci=z.avg.ci,
n.avg=n.avg, n.avg.p=n.avg.p, n.avg.ci=n.avg.ci,
d0.group=d0.group, d1.group=d1.group, d0.ci.group=d0.ci.group, d1.ci.group=d1.ci.group,
d0.p.group=d0.p.group, d1.p.group=d1.p.group,
z0.group=z0.group, z1.group=z1.group, z0.ci.group=z0.ci.group, z1.ci.group=z1.ci.group,
z0.p.group=z0.p.group, z1.p.group=z1.p.group,
n0.group=n0.group, n1.group=n1.group, n0.ci.group=n0.ci.group, n1.ci.group=n1.ci.group,
n0.p.group=n0.p.group, n1.p.group=n1.p.group,
tau.coef.group=tau.coef.group, tau.ci.group=tau.ci.group, tau.p.group=tau.p.group,
d.avg.group=d.avg.group, d.avg.p.group=d.avg.p.group, d.avg.ci.group=d.avg.ci.group,
z.avg.group=z.avg.group, z.avg.p.group=z.avg.p.group, z.avg.ci.group=z.avg.ci.group,
n.avg.group=n.avg.group, n.avg.p.group=n.avg.p.group, n.avg.ci.group=n.avg.ci.group,
boot=boot, boot.ci.type=boot.ci.type,
treat=treat, mediator=mediator,
covariates=covariates,
INT=INT, conf.level=conf.level,
model.y=model.y, model.m=model.m,
control.value=control.value, treat.value=treat.value,
nobs=n, sims=sims, call=cl,
group.m=group.m,group.y=group.y,group.name=group.name,
group.id.m=group.id.m,group.id.y=group.id.y,group.id=group.id,
robustSE = robustSE, cluster = cluster)
class(out) <- "mediate.mer"
}
out
############################################################################
############################################################################
### CASE II: ORDERED OUTCOME
############################################################################
############################################################################
} else {
if(boot != TRUE){
warning("ordered outcome model can only be used with nonparametric bootstrap - option forced")
boot <- TRUE
}
if(isMer.m){
stop("merMod class is not supported for ordered outcome")
}
n.ycat <- length(unique(model.response(y.data)))
# Bootstrap QoI
message("Running nonparametric bootstrap for ordered outcome\n")
# Make objects available to med.fun.ordered
environment(med.fun.ordered) <- environment()
D <- boot::boot(data = y.data,
statistic = med.fun.ordered,
R = sims,
sim = "ordinary",
m.data = m.data,
...)
# Extract estimates from resampling
col_index <- lapply(c("d1", "d0", "z1", "z0"), function(i) {
grep(i, names(D$t0))
})
delta.1 <- D$t[, col_index[[1]]]
delta.0 <- D$t[, col_index[[2]]]
zeta.1 <- D$t[, col_index[[3]]]
zeta.0 <- D$t[, col_index[[4]]]
# Generate QoIs for actual sample
D <- med.fun.ordered(y.data = y.data, m.data = m.data, index = 1:n)
d1 <- D[col_index[[1]]]
d0 <- D[col_index[[2]]]
z1 <- D[col_index[[3]]]
z0 <- D[col_index[[4]]]
tau.coef <- (d1 + d0 + z1 + z0)/2
tau <- (zeta.1 + zeta.0 + delta.0 + delta.1)/2
########################################################################
## Compute Outputs and Put Them Together
########################################################################
low <- (1 - conf.level)/2
high <- 1 - low
if(boot.ci.type == "bca"){
BC.CI <- function(theta){
z.inv <- length(theta[theta < mean(theta)])/sims
z <- qnorm(z.inv)
U <- (sims - 1) * (mean(theta) - theta)
top <- sum(U^3)
under <- 6 * (sum(U^2))^{3/2}
a <- top / under
lower.inv <- pnorm(z + (z + qnorm(low))/(1 - a * (z + qnorm(low))))
lower2 <- lower <- quantile(theta, lower.inv)
upper.inv <- pnorm(z + (z + qnorm(high))/(1 - a * (z + qnorm(high))))
upper2 <- upper <- quantile(theta, upper.inv)
return(c(lower, upper))
}
d0.ci <- BC.CI(delta.0)
d1.ci <- BC.CI(delta.1)
tau.ci <- BC.CI(tau)
z1.ci <- BC.CI(zeta.1)
z0.ci <- BC.CI(zeta.0)
} else {
CI <- function(theta){
return(quantile(theta, c(low, high), na.rm = TRUE))
}
d0.ci <- apply(delta.0, 2, CI)
d1.ci <- apply(delta.1, 2, CI)
tau.ci <- apply(tau, 2, CI)
z1.ci <- apply(zeta.1, 2, CI)
z0.ci <- apply(zeta.0, 2, CI)
}
# p-values
d0.p <- d1.p <- z0.p <- z1.p <- tau.p <- rep(NA, n.ycat)
for(i in 1:n.ycat){
d0.p[i] <- pval(delta.0[,i], d0[i])
d1.p[i] <- pval(delta.1[,i], d1[i])
z0.p[i] <- pval(zeta.0[,i], z0[i])
z1.p[i] <- pval(zeta.1[,i], z1[i])
tau.p[i] <- pval(tau[,i], tau.coef[i])
}
# Detect whether models include T-M interaction
INT <- paste(treat,mediator,sep=":") %in% attr(model.y$terms,"term.labels") |
paste(mediator,treat,sep=":") %in% attr(model.y$terms,"term.labels")
if(long) {
out <- list(d0=d0, d1=d1, d0.ci=d0.ci, d1.ci=d1.ci,
d0.p=d0.p, d1.p=d1.p,
d0.sims=delta.0, d1.sims=delta.1,
tau.coef=tau.coef, tau.ci=tau.ci, tau.p=tau.p,
z0=z0, z1=z1, z0.ci=z0.ci, z1.ci=z1.ci,
z0.p=z0.p, z1.p=z1.p,
z1.sims=zeta.1, z0.sims=zeta.0, tau.sims=tau,
boot=boot, boot.ci.type=boot.ci.type,
treat=treat, mediator=mediator,
covariates=covariates,
INT=INT, conf.level=conf.level,
model.y=model.y, model.m=model.m,
control.value=control.value, treat.value=treat.value,
nobs=n, sims=sims, call=cl,
robustSE = robustSE, cluster = cluster)
} else {
out <- list(d0=d0, d1=d1, d0.ci=d0.ci, d1.ci=d1.ci,
d0.p=d0.p, d1.p=d1.p,
tau.coef=tau.coef, tau.ci=tau.ci, tau.p=tau.p,
z0=z0, z1=z1, z0.ci=z0.ci, z1.ci=z1.ci,
z0.p=z0.p, z1.p=z1.p,
boot=boot, boot.ci.type=boot.ci.type,
treat=treat, mediator=mediator,
covariates=covariates,
INT=INT, conf.level=conf.level,
model.y=model.y, model.m=model.m,
control.value=control.value, treat.value=treat.value,
nobs=n, sims=sims, call=cl,
robustSE = robustSE, cluster = cluster)
}
class(out) <- "mediate.order"
out
}
}
##################################################################
med.fun <- function(y.data, index, m.data) {
if(isSurvreg.m){
mname <- names(m.data)[1]
nc <- nchar(mediator)
eventname <- substr(mname, 5 + nc + 3, nchar(mname) - 1)
if(nchar(eventname) == 0){
m.data.tmp <- data.frame(m.data,
as.numeric(m.data[,1L][,1L]))
names(m.data.tmp)[c(1L, ncol(m.data)+1)] <- c(mname, mediator)
} else {
m.data.tmp <- data.frame(m.data,
as.numeric(m.data[,1L][,1L]),
as.numeric(model.m$y[,2]))
names(m.data.tmp)[c(1L, ncol(m.data)+(1:2))] <- c(mname, mediator, eventname)
}
Call.M$data <- m.data.tmp[index,]
} else {
Call.M$data <- m.data[index,]
}
if(isSurvreg.y){
yname <- names(y.data)[1]
nc <- nchar(outcome)
eventname <- substr(yname, 5 + nc + 3, nchar(yname) - 1)
if(nchar(eventname) == 0){
y.data.tmp <- data.frame(y.data,
as.numeric(y.data[,1L][,1L]))
names(y.data.tmp)[c(1L, ncol(y.data)+1)] <- c(yname, outcome)
} else {
y.data.tmp <- data.frame(y.data,
as.numeric(y.data[,1L][,1L]),
as.numeric(model.y$y[,2]))
names(y.data.tmp)[c(1L, ncol(y.data)+(1:2))] <- c(yname, outcome, eventname)
}
Call.Y$data <- y.data.tmp[index,]
} else {
Call.Y$data <- y.data[index,]
}
Call.M$weights <- m.data[index,"(weights)"]
Call.Y$weights <- y.data[index,"(weights)"]
if(isOrdered.m && length(unique(y.data[index,mediator])) != m){
stop("insufficient variation on mediator")
}
# Refit Models with Resampled Data
new.fit.M <- NULL
new.fit.Y <- NULL
if (use_speed) {
if (isGlm.m)
new.fit.M <- fit_speedglm(Call.M)
else if (isLm.m) {
formula <- Call.M$formula
# ^^ to circumvent eval(call[[2]], parent.frame()) problem.
new.fit.M <- speedglm::speedlm(formula = formula,
data = Call.M$data,
weights = Call.M$weights)
}
if (isGlm.y)
new.fit.Y <- fit_speedglm(Call.Y)
else if (isLm.y) {
formula <- Call.Y$formula
# ^^ See above.
new.fit.Y <- speedglm::speedlm(formula = formula,
data = Call.Y$data,
weights = Call.Y$weights)
}
}
if (is.null(new.fit.M))
new.fit.M <- eval.parent(Call.M)
if (is.null(new.fit.Y))
new.fit.Y <- eval.parent(Call.Y)
#####################################
# Mediator Predictions
#####################################
pred.data.t <- pred.data.c <- m.data
if(isFactorT){
pred.data.t[,treat] <- factor(cat.1, levels = t.levels)
pred.data.c[,treat] <- factor(cat.0, levels = t.levels)
} else {
pred.data.t[,treat] <- cat.1
pred.data.c[,treat] <- cat.0
}
if(!is.null(covariates)){
for(p in 1:length(covariates)){
vl <- names(covariates[p])
if(is.factor(pred.data.t[,vl])){
pred.data.t[,vl] <- pred.data.c[,vl] <- factor(covariates[[p]], levels = levels(m.data[,vl]))
} else {
pred.data.t[,vl] <- pred.data.c[,vl] <- covariates[[p]]
}
}
}
### Case I-2-a: GLM Mediator (including GAMs)
if(isGlm.m){
muM1 <- predict(new.fit.M, type="response", newdata=pred.data.t)
muM0 <- predict(new.fit.M, type="response", newdata=pred.data.c)
if(FamilyM == "poisson"){
PredictM1 <- rpois(n, lambda = muM1)
PredictM0 <- rpois(n, lambda = muM0)
} else if (FamilyM == "Gamma") {
shape <- gamma.shape(new.fit.M)$alpha
PredictM1 <- rgamma(n, shape = shape, scale = muM1/shape)
PredictM0 <- rgamma(n, shape = shape, scale = muM0/shape)
} else if (FamilyM == "binomial"){
PredictM1 <- rbinom(n, size = 1, prob = muM1)
PredictM0 <- rbinom(n, size = 1, prob = muM0)
} else if (FamilyM == "gaussian"){
sigma <- sqrt(summary(new.fit.M)$dispersion)
error <- rnorm(n, mean=0, sd=sigma)
PredictM1 <- muM1 + error
PredictM0 <- muM0 + error
} else if (FamilyM == "inverse.gaussian"){
disp <- summary(new.fit.M)$dispersion
PredictM1 <- SuppDists::rinvGauss(n, nu = muM1, lambda = 1/disp)
PredictM0 <- SuppDists::rinvGauss(n, nu = muM0, lambda = 1/disp)
} else {
stop("unsupported glm family")
}
### Case I-2-b: Ordered Mediator
} else if(isOrdered.m) {
probs_m1 <- predict(new.fit.M, newdata=pred.data.t, type="probs")
probs_m0 <- predict(new.fit.M, newdata=pred.data.c, type="probs")
draws_m1 <- matrix(NA, n, m)
draws_m0 <- matrix(NA, n, m)
for(ii in 1:n){
draws_m1[ii,] <- t(rmultinom(1, 1, prob = probs_m1[ii,]))
draws_m0[ii,] <- t(rmultinom(1, 1, prob = probs_m0[ii,]))
}
PredictM1 <- apply(draws_m1, 1, which.max)
PredictM0 <- apply(draws_m0, 1, which.max)
### Case I-2-c: Quantile Regression for Mediator
} else if(isRq.m){
# Use inverse transform sampling to predict M
call.new <- new.fit.M$call
call.new$tau <- runif(n)
newfits <- eval.parent(call.new)
tt <- delete.response(terms(new.fit.M))
m.t <- model.frame(tt, pred.data.t, xlev = new.fit.M$xlevels)
m.c <- model.frame(tt, pred.data.c, xlev = new.fit.M$xlevels)
X.t <- model.matrix(tt, m.t, contrasts = new.fit.M$contrasts)
X.c <- model.matrix(tt, m.c, contrasts = new.fit.M$contrasts)
rm(tt, m.t, m.c)
PredictM1 <- rowSums(X.t * t(newfits$coefficients))
PredictM0 <- rowSums(X.c * t(newfits$coefficients))
rm(newfits, X.t, X.c)
### Case I-2-d: Linear
} else if(isLm.m){
if (class(new.fit.M) == "speedlm")
sigma <- sqrt(summary(new.fit.M)$var.res)
else
sigma <- summary(new.fit.M)$sigma
error <- rnorm(n, mean=0, sd=sigma)
PredictM1 <- predict(new.fit.M, type="response",
newdata=pred.data.t) + error
PredictM0 <- predict(new.fit.M, type="response",
newdata=pred.data.c) + error
rm(error)
### Case I-2-e: Survreg
} else if(isSurvreg.m){
dd <- survival::survreg.distributions[[new.fit.M$dist]]
if (is.null(dd$itrans)){
itrans <- function(x) x
} else {
itrans <- dd$itrans
}
dname <- dd$dist
if(is.null(dname)){
dname <- new.fit.M$dist
}
scale <- new.fit.M$scale
lpM1 <- predict(new.fit.M, newdata=pred.data.t, type="linear")
lpM0 <- predict(new.fit.M, newdata=pred.data.c, type="linear")
error <- switch(dname,
extreme = log(rweibull(n, shape=1, scale=1)),
gaussian = rnorm(n),
logistic = rlogis(n),
t = rt(n, df=dd$parms))
PredictM1 <- as.numeric(itrans(lpM1 + scale * error))
PredictM0 <- as.numeric(itrans(lpM0 + scale * error))
rm(error)
} else {
stop("mediator model is not yet implemented")
}
#####################################
# Outcome Predictions
#####################################
effects.tmp <- matrix(NA, nrow = n, ncol = 4)
for(e in 1:4){
tt <- switch(e, c(1,1,1,0), c(0,0,1,0), c(1,0,1,1), c(1,0,0,0))
pred.data.t <- pred.data.c <- y.data
if(!is.null(covariates)){
for(p in 1:length(covariates)){
vl <- names(covariates[p])
if(is.factor(pred.data.t[,vl])){
pred.data.t[,vl] <- pred.data.c[,vl] <- factor(covariates[[p]], levels = levels(y.data[,vl]))
} else {
pred.data.t[,vl] <- pred.data.c[,vl] <- covariates[[p]]
}
}
}
# Set treatment values
cat.t <- ifelse(tt[1], cat.1, cat.0)
cat.c <- ifelse(tt[2], cat.1, cat.0)
cat.t.ctrl <- ifelse(tt[1], cat.0, cat.1)
cat.c.ctrl <- ifelse(tt[2], cat.0, cat.1)
if(isFactorT){
pred.data.t[,treat] <- factor(cat.t, levels = t.levels)
pred.data.c[,treat] <- factor(cat.c, levels = t.levels)
if(!is.null(control)){
pred.data.t[,control] <- factor(cat.t.ctrl, levels = t.levels)
pred.data.c[,control] <- factor(cat.c.ctrl, levels = t.levels)
}
} else {
pred.data.t[,treat] <- cat.t
pred.data.c[,treat] <- cat.c
if(!is.null(control)){
pred.data.t[,control] <- cat.t.ctrl
pred.data.c[,control] <- cat.c.ctrl
}
}
# Set mediator values
PredictM1.tmp <- PredictM1
PredictM0.tmp <- PredictM0
PredictMt <- PredictM1 * tt[3] + PredictM0 * (1 - tt[3])
PredictMc <- PredictM1 * tt[4] + PredictM0 * (1 - tt[4])
if(isFactorM) {
pred.data.t[,mediator] <- factor(PredictMt, levels=1:m, labels=m.levels)
pred.data.c[,mediator] <- factor(PredictMc, levels=1:m, labels=m.levels)
} else {
pred.data.t[,mediator] <- PredictMt
pred.data.c[,mediator] <- PredictMc
}
if(isRq.y){
pr.1 <- predict(new.fit.Y, type="response",
newdata=pred.data.t, interval="none")
pr.0 <- predict(new.fit.Y, type="response",
newdata=pred.data.c, interval="none")
} else {
pr.1 <- predict(new.fit.Y, type="response",
newdata=pred.data.t)
pr.0 <- predict(new.fit.Y, type="response",
newdata=pred.data.c)
}
pr.mat <- as.matrix(cbind(pr.1, pr.0))
effects.tmp[,e] <- pr.mat[,1] - pr.mat[,2]
rm(pred.data.t, pred.data.c, pr.1, pr.0, pr.mat)
}
# Compute all QoIs
d1 <- weighted.mean(effects.tmp[,1], weights)
d0 <- weighted.mean(effects.tmp[,2], weights)
z1 <- weighted.mean(effects.tmp[,3], weights)
z0 <- weighted.mean(effects.tmp[,4], weights)
c(d1 = d1, d0 = d0, z1 = z1, z0 = z0)
}
med.fun.ordered <- function(y.data, index, m.data) {
Call.M <- model.m$call
Call.Y <- model.y$call
if(isSurvreg.m){
if(ncol(model.m$y) > 2){
stop("unsupported censoring type")
}
mname <- names(m.data)[1]
if(substr(mname, 1, 4) != "Surv"){
stop("refit the survival model with `Surv' used directly in model formula")
}
nc <- nchar(mediator)
eventname <- substr(mname, 5 + nc + 3, nchar(mname) - 1)
if(nchar(eventname) == 0){
m.data.tmp <- data.frame(m.data,
as.numeric(m.data[,1L][,1L]))
names(m.data.tmp)[c(1L, ncol(m.data)+1)] <- c(mname, mediator)
} else {
m.data.tmp <- data.frame(m.data,
as.numeric(m.data[,1L][,1L]),
as.numeric(model.m$y[,2]))
names(m.data.tmp)[c(1L, ncol(m.data)+(1:2))] <- c(mname, mediator, eventname)
}
Call.M$data <- m.data.tmp[index,]
} else {
Call.M$data <- m.data[index,]
}
Call.Y$data <- y.data[index,]
Call.M$weights <- m.data[index,"(weights)"]
Call.Y$weights <- y.data[index,"(weights)"]
new.fit.M <- eval.parent(Call.M)
new.fit.Y <- eval.parent(Call.Y)
if(isOrdered.m && length(unique(y.data[index,mediator]))!=m){
# Modify the coefficients when mediator has empty cells
coefnames.y <- names(model.y$coefficients)
coefnames.new.y <- names(new.fit.Y$coefficients)
new.fit.Y.coef <- rep(0, length(coefnames.y))
names(new.fit.Y.coef) <- coefnames.y
new.fit.Y.coef[coefnames.new.y] <- new.fit.Y$coefficients
new.fit.Y$coefficients <- new.fit.Y.coef
}
#####################################
# Mediator Predictions
#####################################
pred.data.t <- pred.data.c <- m.data
if(isFactorT){
pred.data.t[,treat] <- factor(cat.1, levels = t.levels)
pred.data.c[,treat] <- factor(cat.0, levels = t.levels)
} else {
pred.data.t[,treat] <- cat.1
pred.data.c[,treat] <- cat.0
}
if(!is.null(covariates)){
for(p in 1:length(covariates)){
vl <- names(covariates[p])
if(is.factor(pred.data.t[,vl])){
pred.data.t[,vl] <- pred.data.c[,vl] <- factor(covariates[[p]], levels = levels(m.data[,vl]))
} else {
pred.data.t[,vl] <- pred.data.c[,vl] <- covariates[[p]]
}
}
}
### Case II-a: GLM Mediator (including GAMs)
if(isGlm.m){
muM1 <- predict(new.fit.M, type="response", newdata=pred.data.t)
muM0 <- predict(new.fit.M, type="response", newdata=pred.data.c)
if(FamilyM == "poisson"){
PredictM1 <- rpois(n, lambda = muM1)
PredictM0 <- rpois(n, lambda = muM0)
} else if (FamilyM == "Gamma") {
shape <- gamma.shape(model.m)$alpha
PredictM1 <- rgamma(n, shape = shape, scale = muM1/shape)
PredictM0 <- rgamma(n, shape = shape, scale = muM0/shape)
} else if (FamilyM == "binomial"){
PredictM1 <- rbinom(n, size = 1, prob = muM1)
PredictM0 <- rbinom(n, size = 1, prob = muM0)
} else if (FamilyM == "gaussian"){
sigma <- sqrt(summary(model.m)$dispersion)
error <- rnorm(n, mean=0, sd=sigma)
PredictM1 <- muM1 + error
PredictM0 <- muM0 + error
} else if (FamilyM == "inverse.gaussian"){
disp <- summary(model.m)$dispersion
PredictM1 <- SuppDists::rinvGauss(n, nu = muM1, lambda = 1/disp)
PredictM0 <- SuppDists::rinvGauss(n, nu = muM0, lambda = 1/disp)
} else {
stop("unsupported glm family")
}
### Case II-b: Ordered Mediator
} else if(isOrdered.m) {
probs_m1 <- predict(new.fit.M, type="probs", newdata=pred.data.t)
probs_m0 <- predict(new.fit.M, type="probs", newdata=pred.data.c)
draws_m1 <- matrix(NA, n, m)
draws_m0 <- matrix(NA, n, m)
for(ii in 1:n){
draws_m1[ii,] <- t(rmultinom(1, 1, prob = probs_m1[ii,]))
draws_m0[ii,] <- t(rmultinom(1, 1, prob = probs_m0[ii,]))
}
PredictM1 <- apply(draws_m1, 1, which.max)
PredictM0 <- apply(draws_m0, 1, which.max)
### Case II-c: Quantile Regression for Mediator
} else if(isRq.m){
# Use inverse transform sampling to predict M
call.new <- new.fit.M$call
call.new$tau <- runif(n)
newfits <- eval.parent(call.new)
tt <- delete.response(terms(new.fit.M))
m.t <- model.frame(tt, pred.data.t, xlev = new.fit.M$xlevels)
m.c <- model.frame(tt, pred.data.c, xlev = new.fit.M$xlevels)
X.t <- model.matrix(tt, m.t, contrasts = new.fit.M$contrasts)
X.c <- model.matrix(tt, m.c, contrasts = new.fit.M$contrasts)
rm(tt, m.t, m.c)
PredictM1 <- rowSums(X.t * t(newfits$coefficients))
PredictM0 <- rowSums(X.c * t(newfits$coefficients))
rm(newfits, X.t, X.c)
### Case II-d: Linear
} else if(isLm.m){
sigma <- summary(new.fit.M)$sigma
error <- rnorm(n, mean=0, sd=sigma)
PredictM1 <- predict(new.fit.M, type="response",
newdata=pred.data.t) + error
PredictM0 <- predict(new.fit.M, type="response",
newdata=pred.data.c) + error
rm(error)
### Case I-2-e: Survreg
} else if(isSurvreg.m){
dd <- survival::survreg.distributions[[new.fit.M$dist]]
if (is.null(dd$itrans)){
itrans <- function(x) x
} else {
itrans <- dd$itrans
}
dname <- dd$dist
if(is.null(dname)){
dname <- new.fit.M$dist
}
scale <- new.fit.M$scale
lpM1 <- predict(new.fit.M, newdata=pred.data.t, type="linear")
lpM0 <- predict(new.fit.M, newdata=pred.data.c, type="linear")
error <- switch(dname,
extreme = log(rweibull(n, shape=1, scale=1)),
gaussian = rnorm(n),
logistic = rlogis(n),
t = rt(n, df=dd$parms))
PredictM1 <- as.numeric(itrans(lpM1 + scale * error))
PredictM0 <- as.numeric(itrans(lpM0 + scale * error))
rm(error)
} else {
stop("mediator model is not yet implemented")
}
#####################################
# Outcome Predictions
#####################################
effects.tmp <- array(NA, dim = c(n, n.ycat, 4))
for(e in 1:4){
tt <- switch(e, c(1,1,1,0), c(0,0,1,0), c(1,0,1,1), c(1,0,0,0))
pred.data.t <- pred.data.c <- y.data
if(!is.null(covariates)){
for(p in 1:length(covariates)){
vl <- names(covariates[p])
if(is.factor(pred.data.t[,vl])){
pred.data.t[,vl] <- pred.data.c[,vl] <- factor(covariates[[p]], levels = levels(y.data[,vl]))
} else {
pred.data.t[,vl] <- pred.data.c[,vl] <- covariates[[p]]
}
}
}
# Set treatment values
cat.t <- ifelse(tt[1], cat.1, cat.0)
cat.c <- ifelse(tt[2], cat.1, cat.0)
cat.t.ctrl <- ifelse(tt[1], cat.0, cat.1)
cat.c.ctrl <- ifelse(tt[2], cat.0, cat.1)
if(isFactorT){
pred.data.t[,treat] <- factor(cat.t, levels = t.levels)
pred.data.c[,treat] <- factor(cat.c, levels = t.levels)
if(!is.null(control)){
pred.data.t[,control] <- factor(cat.t.ctrl, levels = t.levels)
pred.data.c[,control] <- factor(cat.c.ctrl, levels = t.levels)
}
} else {
pred.data.t[,treat] <- cat.t
pred.data.c[,treat] <- cat.c
if(!is.null(control)){
pred.data.t[,control] <- cat.t.ctrl
pred.data.c[,control] <- cat.c.ctrl
}
}
# Set mediator values
PredictM1.tmp <- PredictM1
PredictM0.tmp <- PredictM0
PredictMt <- PredictM1 * tt[3] + PredictM0 * (1 - tt[3])
PredictMc <- PredictM1 * tt[4] + PredictM0 * (1 - tt[4])
if(isFactorM) {
pred.data.t[,mediator] <- factor(PredictMt, levels=1:m, labels=m.levels)
pred.data.c[,mediator] <- factor(PredictMc, levels=1:m, labels=m.levels)
} else {
pred.data.t[,mediator] <- PredictMt
pred.data.c[,mediator] <- PredictMc
}
probs_p1 <- predict(new.fit.Y, newdata=pred.data.t, type="probs")
probs_p0 <- predict(new.fit.Y, newdata=pred.data.c, type="probs")
effects.tmp[,,e] <- probs_p1 - probs_p0
rm(pred.data.t, pred.data.c, probs_p1, probs_p0)
}
# Compute all QoIs
d1 <- apply(effects.tmp[,,1], 2, weighted.mean, w=weights)
d0 <- apply(effects.tmp[,,2], 2, weighted.mean, w=weights)
z1 <- apply(effects.tmp[,,3], 2, weighted.mean, w=weights)
z0 <- apply(effects.tmp[,,4], 2, weighted.mean, w=weights)
c(d1 = d1, d0 = d0, z1 = z1, z0 = z0)
}
##################################################################
##################################################################
#' Summarizing Output from Mediation Analysis
#'
#' Function to report results from mediation analysis. Reported categories are
#' mediation effect, direct effect, total effect, and proportion of total effect
#' mediated. All quantities reported with confidence intervals. If the
#' treatment-mediator interaction is allowed in the mediation analysis, effects
#' are reported separately for the treatment and control conditions as well as
#' the simple averages of these effects are displayed at the bottom of the
#' summary table.
#'
#' @aliases summary.mediate summary.mediate.order print.summary.mediate
#' print.summary.mediate.order
#'
#' @param object output from mediate or mediate_tsls function.
#' @param x output from summary.mediate function.
#' @param ... additional arguments affecting the summary produced.
#'
#' @author Dustin Tingley, Harvard University,
#' \email{dtingley@@gov.harvard.edu}; Teppei Yamamoto, Massachusetts Institute
#' of Technology, \email{teppei@@mit.edu}; Luke Keele, Penn State University,
#' \email{ljk20@@psu.edu}; Kosuke Imai, Princeton University,
#' \email{kimai@@princeton.edu}.
#'
#' @seealso \code{\link{mediate}}, \code{\link{mediate_tsls}},
#' \code{\link{plot.mediate}}, \code{\link{summary}}.
#'
#' @references Tingley, D., Yamamoto, T., Hirose, K., Imai, K. and Keele, L.
#' (2014). "mediation: R package for Causal Mediation Analysis", Journal of
#' Statistical Software, Vol. 59, No. 5, pp. 1-38.
#'
#' Imai, K., Keele, L., Tingley, D. and Yamamoto, T. (2011). Unpacking the
#' Black Box of Causality: Learning about Causal Mechanisms from Experimental
#' and Observational Studies, American Political Science Review, Vol. 105, No.
#' 4 (November), pp. 765-789.
#'
#' Imai, K., Keele, L. and Tingley, D. (2010) A General Approach to Causal
#' Mediation Analysis, Psychological Methods, Vol. 15, No. 4 (December), pp.
#' 309-334.
#'
#' Imai, K., Keele, L. and Yamamoto, T. (2010) Identification, Inference, and
#' Sensitivity Analysis for Causal Mediation Effects, Statistical Science,
#' Vol. 25, No. 1 (February), pp. 51-71.
#'
#' Imai, K., Keele, L., Tingley, D. and Yamamoto, T. (2009) "Causal Mediation
#' Analysis Using R" in Advances in Social Science Research Using R, ed. H. D.
#' Vinod New York: Springer.
#'
#' @export
summary.mediate <- function(object, ...){
structure(object, class = c("summary.mediate", class(object)))
}
#' @rdname summary.mediate
#' @export
print.summary.mediate <- function(x, ...){
clp <- 100 * x$conf.level
cat("\n")
cat(
sprintf(
"Causal Mediation Analysis %s\n\n",
ifelse(inherits(x, "mediate.tsls"), "using Two-Stage Least Squares", "")
)
)
if(x$boot) {
cat(
sprintf(
"Nonparametric Bootstrap Confidence Intervals with the %s Method\n\n",
ifelse(x$boot.ci.type == "perc", "Percentile", "BCa")
)
)
} else {
cat(
sprintf(
"%s Confidence Intervals\n\n",
ifelse(inherits(x, "mediate.tsls"), "Two-Stage Least Squares",
"Quasi-Bayesian")
)
)
}
if(!is.null(x$covariates)){
cat("(Inference Conditional on the Covariate Values Specified in `covariates')\n\n")
}
isLinear.y <- ( (class(x$model.y)[1] %in% c("lm", "rq")) ||
(inherits(x$model.y, "glm") &&
x$model.y$family$family == "gaussian" &&
x$model.y$family$link == "identity") ||
(inherits(x$model.y, "survreg") &&
x$model.y$dist == "gaussian") )
printone <- !x$INT && isLinear.y
if (printone){
# Print only one set of values if lmY/quanY/linear gamY without interaction
smat <- c(x$d1, x$d1.ci, x$d1.p)
smat <- rbind(smat, c(x$z0, x$z0.ci, x$z0.p))
smat <- rbind(smat, c(x$tau.coef, x$tau.ci, x$tau.p))
smat <- rbind(smat, c(x$n0, x$n0.ci, x$n0.p))
rownames(smat) <- c("ACME", "ADE",
"Total Effect", "Prop. Mediated")
} else {
smat <- c(x$d0, x$d0.ci, x$d0.p)
smat <- rbind(smat, c(x$d1, x$d1.ci, x$d1.p))
smat <- rbind(smat, c(x$z0, x$z0.ci, x$z0.p))
smat <- rbind(smat, c(x$z1, x$z1.ci, x$z1.p))
smat <- rbind(smat, c(x$tau.coef, x$tau.ci, x$tau.p))
smat <- rbind(smat, c(x$n0, x$n0.ci, x$n0.p))
smat <- rbind(smat, c(x$n1, x$n1.ci, x$n1.p))
smat <- rbind(smat, c(x$d.avg, x$d.avg.ci, x$d.avg.p))
smat <- rbind(smat, c(x$z.avg, x$z.avg.ci, x$z.avg.p))
smat <- rbind(smat, c(x$n.avg, x$n.avg.ci, x$n.avg.p))
rownames(smat) <- c("ACME (control)", "ACME (treated)",
"ADE (control)", "ADE (treated)",
"Total Effect",
"Prop. Mediated (control)",
"Prop. Mediated (treated)",
"ACME (average)",
"ADE (average)",
"Prop. Mediated (average)")
}
colnames(smat) <- c("Estimate", paste(clp, "% CI Lower", sep=""),
paste(clp, "% CI Upper", sep=""), "p-value")
printCoefmat(smat, digits=3)
cat("\n")
cat("Sample Size Used:", x$nobs,"\n\n")
cat("\n")
cat("Simulations:", x$sims,"\n\n")
invisible(x)
}
#########################################################################
#' Summarizing Output from Mediation Analysis of Multilevel Models
#'
#' Function to report results from mediation analysis of multilevel models.
#' Reported categories are mediation effect, direct effect, total effect, and
#' proportion of total effect mediated. All quantities reported with confidence
#' intervals. Group-specific effects and confidence intervals reported based on
#' the mediator or the outcome group. Group-average quantities reported as
#' default.
#'
#'
#' @aliases summary.mediate.mer print.summary.mediate.mer
#' print.summary.mediate.mer.2 print.summary.mediate.mer.3
#'
#' @param object output from mediate function.
#' @param output group-specific effects organized by effect if output =
#' "byeffect"; group-specific effects organized by group if output =
#' "bygroup"; group-average effects reported as default.
#' @param x output from summary.mediate.mer function.
#' @param ... additional arguments affecting the summary produced.
#'
#' @author Kentaro Hirose, Princeton University, \email{hirose@@princeton.edu}.
#'
#' @seealso \code{\link{mediate}}, \code{\link{plot.mediate.mer}}.
#'
#' @references Tingley, D., Yamamoto, T., Hirose, K., Imai, K. and Keele, L.
#' (2014). "mediation: R package for Causal Mediation Analysis", Journal of
#' Statistical Software, Vol. 59, No. 5, pp. 1-38.
#'
#' Imai, K., Keele, L., Tingley, D. and Yamamoto, T. (2011). Unpacking the
#' Black Box of Causality: Learning about Causal Mechanisms from Experimental
#' and Observational Studies, American Political Science Review, Vol. 105, No.
#' 4 (November), pp. 765-789.
#'
#' Imai, K., Keele, L. and Tingley, D. (2010) A General Approach to Causal
#' Mediation Analysis, Psychological Methods, Vol. 15, No. 4 (December), pp.
#' 309-334.
#'
#' Imai, K., Keele, L. and Yamamoto, T. (2010) Identification, Inference, and
#' Sensitivity Analysis for Causal Mediation Effects, Statistical Science,
#' Vol. 25, No. 1 (February), pp. 51-71.
#'
#' Imai, K., Keele, L., Tingley, D. and Yamamoto, T. (2009) "Causal Mediation
#' Analysis Using R" in Advances in Social Science Research Using R, ed. H. D.
#' Vinod New York: Springer.
#'
#' @examples
#' # Examples with JOBS II Field Experiment
#'
#' # **For illustration purposes a small number of simulations are used**
#' \dontrun{
#' data(jobs)
#' require(lme4)
#'
#' # educ: mediator group
#' # occp: outcome group
#'
#' # Varying intercept for mediator
#' model.m <- glmer(job_dich ~ treat + econ_hard + (1 | educ),
#' family = binomial(link = "probit"), data = jobs)
#'
#' # Varying intercept and slope for outcome
#' model.y <- glmer(work1 ~ treat + job_dich + econ_hard + (1 + treat | occp),
#' family = binomial(link = "probit"), data = jobs)
#'
#' # Output based on mediator group
#' multilevel <- mediate(model.m, model.y, treat = "treat",
#' mediator = "job_dich", sims=50, group.out="educ")
#'
#' # Group-average effects
#' summary(multilevel)
#'
#' # Group-specific effects organized by effect
#' summary(multilevel, output="byeffect")
#'
#' # Group-specific effects organized by group
#' summary(multilevel, output="bygroup")
#' }
#'
#' @export
summary.mediate.mer <- function(object, output=c("default","byeffect","bygroup"),...){
output <- match.arg(output)
switch(output,
default = structure(object, class = c("summary.mediate.mer", class(object))),
byeffect = structure(object, class = c("summary.mediate.mer.2", class(object))),
bygroup = structure(object, class = c("summary.mediate.mer.3", class(object))))
}
#########################################################################
#' @rdname summary.mediate.mer
#' @export
print.summary.mediate.mer <- function(x,...){
clp <- 100 * x$conf.level
cat("\n")
cat("Causal Mediation Analysis \n\n")
if(x$boot){
if(x$boot.ci.type == "perc"){
cat("Nonparametric Bootstrap Confidence Intervals with the Percentile Method\n\n")
} else if(x$boot.ci.type == "bca"){
cat("Nonparametric Bootstrap Confidence Intervals with the BCa Method\n\n")
}
} else {
cat("Quasi-Bayesian Confidence Intervals\n\n")
}
if(!is.null(x$covariates)){
cat("(Inference Conditional on the Covariate Values Specified in `covariates')\n\n")
}
cat("Mediator Groups:", x$group.m,"\n\n")
cat("Outcome Groups:", x$group.y,"\n\n")
cat("Output Based on Overall Averages Across Groups","\n\n")
isLinear.y <- ( (class(x$model.y)[1] %in% c("lm", "rq")) || # lm or quantile
(inherits(x$model.y, "glm") &&
x$model.y$family$family == "gaussian" &&
x$model.y$family$link == "identity") || # glm normal
(inherits(x$model.y, "survreg") &&
x$model.y$dist == "gaussian") || # surv normal
(inherits(x$model.y, "merMod") &&
x$model.y@call[[1]] == "lmer") ) # lmer
printone <- !x$INT && isLinear.y
if(printone){
smat <- c(x$d1, x$d1.ci, x$d1.p)
smat <- rbind(smat, c(x$z0, x$z0.ci, x$z0.p))
smat <- rbind(smat, c(x$tau.coef, x$tau.ci, x$tau.p))
smat <- rbind(smat, c(x$n0, x$n0.ci, x$n0.p))
rownames(smat) <- c("ACME", "ADE",
"Total Effect", "Prop. Mediated")
}else{
smat <- c(x$d0, x$d0.ci, x$d0.p)
smat <- rbind(smat, c(x$d1, x$d1.ci, x$d1.p))
smat <- rbind(smat, c(x$z0, x$z0.ci, x$z0.p))
smat <- rbind(smat, c(x$z1, x$z1.ci, x$z1.p))
smat <- rbind(smat, c(x$tau.coef, x$tau.ci, x$tau.p))
smat <- rbind(smat, c(x$n0, x$n0.ci, x$n0.p))
smat <- rbind(smat, c(x$n1, x$n1.ci, x$n1.p))
smat <- rbind(smat, c(x$d.avg, x$d.avg.ci, x$d.avg.p))
smat <- rbind(smat, c(x$z.avg, x$z.avg.ci, x$z.avg.p))
smat <- rbind(smat, c(x$n.avg, x$n.avg.ci, x$n.avg.p))
rownames(smat) <- c("ACME (control)", "ACME (treated)",
"ADE (control)", "ADE (treated)",
"Total Effect",
"Prop. Mediated (control)",
"Prop. Mediated (treated)",
"ACME (average)",
"ADE (average)",
"Prop. Mediated (average)")
}
colnames(smat) <- c("Estimate", paste(clp, "% CI Lower", sep=""),
paste(clp, "% CI Upper", sep=""), "p-value")
printCoefmat(smat, digits=3)
cat("\n")
cat("Sample Size Used:", x$nobs,"\n\n")
cat("\n")
cat("Simulations:", x$sims,"\n\n")
invisible(x)
}
#########################################################################
#' @rdname summary.mediate.mer
#' @export
print.summary.mediate.mer.2 <- function(x,...){
clp <- 100 * x$conf.level
cat("\n")
cat("Causal Mediation Analysis \n\n")
if(x$boot){
if(x$boot.ci.type == "perc"){
cat("Nonparametric Bootstrap Confidence Intervals with the Percentile Method\n\n")
} else if(x$boot.ci.type == "bca"){
cat("Nonparametric Bootstrap Confidence Intervals with the BCa Method\n\n")
}
} else {
cat("Quasi-Bayesian Confidence Intervals\n\n")
}
if(!is.null(x$covariates)){
cat("(Inference Conditional on the Covariate Values Specified in `covariates')\n\n")
}
cat("Mediator Groups:", x$group.m,"\n\n")
cat("Outcome Groups:", x$group.y,"\n\n")
cat("Output Based on", x$group.name,"\n\n")
if(is.factor(x$group.id)){
gname <- levels(x$group.id)
} else {
gname <- sort(unique(x$group.id))
}
isLinear.y <- ( (class(x$model.y)[1] %in% c("lm", "rq")) || # lm or quantile
(inherits(x$model.y, "glm") &&
x$model.y$family$family == "gaussian" &&
x$model.y$family$link == "identity") || # glm normal
(inherits(x$model.y, "survreg") &&
x$model.y$dist == "gaussian") || # surv normal
(inherits(x$model.y, "merMod") &&
x$model.y@call[[1]] == "lmer") ) # lmer
printone <- !x$INT && isLinear.y
if(printone){
cat("ACME","\n\n")
smat<-cbind(x$d0.group,x$d0.ci.group,x$d0.p.group)
rownames(smat) <- gname
colnames(smat) <- c("Estimate", paste(clp, "% CI Lower", sep=""),
paste(clp, "% CI Upper", sep=""), "p-value")
printCoefmat(smat, digits=3)
cat("\n")
cat("ADE","\n\n")
smat<-cbind(x$z0.group, x$z0.ci.group, x$z0.p.group)
rownames(smat) <- gname
colnames(smat) <- c("Estimate", paste(clp, "% CI Lower", sep=""),
paste(clp, "% CI Upper", sep=""), "p-value")
printCoefmat(smat, digits=3)
cat("\n")
cat("Total Effect","\n\n")
smat<-cbind(x$tau.coef.group, x$tau.ci.group, x$tau.p.group)
rownames(smat) <- gname
colnames(smat) <- c("Estimate", paste(clp, "% CI Lower", sep=""),
paste(clp, "% CI Upper", sep=""), "p-value")
printCoefmat(smat, digits=3)
cat("\n")
cat("Prop. Mediated","\n\n")
smat<-cbind(x$n0.group, x$n0.ci.group, x$n0.p.group)
rownames(smat) <- gname
colnames(smat) <- c("Estimate", paste(clp, "% CI Lower", sep=""),
paste(clp, "% CI Upper", sep=""), "p-value")
printCoefmat(smat, digits=3)
cat("\n")
cat("\n")
cat("Sample Size Used:", x$nobs,"\n\n")
cat("\n")
cat("Simulations:", x$sims,"\n\n")
invisible(x)
}else{
cat("ACME (control)","\n\n")
smat<-cbind(x$d0.group,x$d0.ci.group,x$d0.p.group)
rownames(smat) <- gname
colnames(smat) <- c("Estimate", paste(clp, "% CI Lower", sep=""),
paste(clp, "% CI Upper", sep=""), "p-value")
printCoefmat(smat, digits=3)
cat("\n")
cat("ACME (treated)","\n\n")
smat<-cbind(x$d1.group, x$d1.ci.group, x$d1.p.group)
rownames(smat) <- gname
colnames(smat) <- c("Estimate", paste(clp, "% CI Lower", sep=""),
paste(clp, "% CI Upper", sep=""), "p-value")
printCoefmat(smat, digits=3)
cat("\n")
cat("ADE (control)","\n\n")
smat<-cbind(x$z0.group, x$z0.ci.group, x$z0.p.group)
rownames(smat) <- gname
colnames(smat) <- c("Estimate", paste(clp, "% CI Lower", sep=""),
paste(clp, "% CI Upper", sep=""), "p-value")
printCoefmat(smat, digits=3)
cat("\n")
cat("ADE (treated)","\n\n")
smat<-cbind(x$z1.group, x$z1.ci.group, x$z1.p.group)
rownames(smat) <- gname
colnames(smat) <- c("Estimate", paste(clp, "% CI Lower", sep=""),
paste(clp, "% CI Upper", sep=""), "p-value")
printCoefmat(smat, digits=3)
cat("\n")
cat("Total Effect","\n\n")
smat<-cbind(x$tau.coef.group, x$tau.ci.group, x$tau.p.group)
rownames(smat) <- gname
colnames(smat) <- c("Estimate", paste(clp, "% CI Lower", sep=""),
paste(clp, "% CI Upper", sep=""), "p-value")
printCoefmat(smat, digits=3)
cat("\n")
cat("Prop. Mediated (control)","\n\n")
smat<-cbind(x$n0.group, x$n0.ci.group, x$n0.p.group)
rownames(smat) <- gname
colnames(smat) <- c("Estimate", paste(clp, "% CI Lower", sep=""),
paste(clp, "% CI Upper", sep=""), "p-value")
printCoefmat(smat, digits=3)
cat("\n")
cat("Prop. Mediated (treated)","\n\n")
smat<-cbind(x$n1.group, x$n1.ci.group, x$n1.p.group)
rownames(smat) <- gname
colnames(smat) <- c("Estimate", paste(clp, "% CI Lower", sep=""),
paste(clp, "% CI Upper", sep=""), "p-value")
printCoefmat(smat, digits=3)
cat("\n")
cat("ACME (average)","\n\n")
smat<-cbind(x$d.avg.group, x$d.avg.ci.group, x$d.avg.p.group)
rownames(smat) <- gname
colnames(smat) <- c("Estimate", paste(clp, "% CI Lower", sep=""),
paste(clp, "% CI Upper", sep=""), "p-value")
printCoefmat(smat, digits=3)
cat("\n")
cat("ADE (average)","\n\n")
smat<-cbind(x$z.avg.group, x$z.avg.ci.group, x$z.avg.p.group)
rownames(smat) <- gname
colnames(smat) <- c("Estimate", paste(clp, "% CI Lower", sep=""),
paste(clp, "% CI Upper", sep=""), "p-value")
printCoefmat(smat, digits=3)
cat("\n")
cat("Prop. Mediated (average)","\n\n")
smat<-cbind(x$n.avg.group, x$n.avg.ci.group, x$n.avg.p.group)
rownames(smat) <- gname
colnames(smat) <- c("Estimate", paste(clp, "% CI Lower", sep=""),
paste(clp, "% CI Upper", sep=""), "p-value")
printCoefmat(smat, digits=3)
cat("\n")
cat("\n")
cat("Sample Size Used:", x$nobs,"\n\n")
cat("\n")
cat("Simulations:", x$sims,"\n\n")
invisible(x)
}
}
#########################################################################
#' @rdname summary.mediate.mer
#' @export
print.summary.mediate.mer.3 <- function(x,...){
clp <- 100 * x$conf.level
cat("\n")
cat("Causal Mediation Analysis \n\n")
if(x$boot){
if(x$boot.ci.type == "perc"){
cat("Nonparametric Bootstrap Confidence Intervals with the Percentile Method\n\n")
} else if(x$boot.ci.type == "bca"){
cat("Nonparametric Bootstrap Confidence Intervals with the BCa Method\n\n")
}
} else {
cat("Quasi-Bayesian Confidence Intervals\n\n")
}
if(!is.null(x$covariates)){
cat("(Inference Conditional on the Covariate Values Specified in `covariates')\n\n")
}
cat("Mediator Groups:", x$group.m,"\n\n")
cat("Outcome Groups:", x$group.y,"\n\n")
cat("Output Based on", x$group.name,"\n\n")
if(is.factor(x$group.id)){
gname <- levels(x$group.id)
} else {
gname <- sort(unique(x$group.id))
}
G<-length(gname)
isLinear.y <- ( (class(x$model.y)[1] %in% c("lm", "rq")) || # lm or quantile
(inherits(x$model.y, "glm") &&
x$model.y$family$family == "gaussian" &&
x$model.y$family$link == "identity") || # glm normal
(inherits(x$model.y, "survreg") &&
x$model.y$dist == "gaussian") || # surv normal
(inherits(x$model.y, "merMod") &&
x$model.y@call[[1]] == "lmer") ) # lmer
printone <- !x$INT && isLinear.y
if(printone){
for (g in 1:G){
cat("\n")
cat("Group:",gname[g],"\n")
smat <- c(x$d0.group[g], x$d0.ci.group[g,], x$d0.p.group[g])
smat <- rbind(smat, c(x$z0.group[g], x$z0.ci.group[g,], x$z0.p.group[g]))
smat <- rbind(smat, c(x$tau.coef.group[g], x$tau.ci.group[g,], x$tau.p.group[g]))
smat <- rbind(smat, c(x$n0.group[g], x$n0.ci.group[g,], x$n0.p.group[g]))
rownames(smat) <- c("ACME",
"ADE",
"Total Effect",
"Prop. Mediated")
colnames(smat) <- c("Estimate", paste(clp, "% CI Lower", sep=""),
paste(clp, "% CI Upper", sep=""), "p-value")
printCoefmat(smat, digits=3)
}
cat("\n")
cat("Sample Size Used:", x$nobs,"\n\n")
cat("\n")
cat("Simulations:", x$sims,"\n\n")
invisible(x)
}else{
for (g in 1:G){
cat("\n")
cat("Group:",gname[g],"\n")
smat <- c(x$d0.group[g], x$d0.ci.group[g,], x$d0.p.group[g])
smat <- rbind(smat, c(x$d1.group[g], x$d1.ci.group[g,], x$d1.p.group[g]))
smat <- rbind(smat, c(x$z0.group[g], x$z0.ci.group[g,], x$z0.p.group[g]))
smat <- rbind(smat, c(x$z1.group[g], x$z1.ci.group[g,], x$z1.p.group[g]))
smat <- rbind(smat, c(x$tau.coef.group[g], x$tau.ci.group[g,], x$tau.p.group[g]))
smat <- rbind(smat, c(x$n0.group[g], x$n0.ci.group[g,], x$n0.p.group[g]))
smat <- rbind(smat, c(x$n1.group[g], x$n1.ci.group[g,], x$n1.p.group[g]))
smat <- rbind(smat, c(x$d.avg.group[g], x$d.avg.ci.group[g,], x$d.avg.p.group[g]))
smat <- rbind(smat, c(x$z.avg.group[g], x$z.avg.ci.group[g,], x$z.avg.p.group[g]))
smat <- rbind(smat, c(x$n.avg.group[g], x$n.avg.ci.group[g,], x$n.avg.p.group[g]))
rownames(smat) <- c("ACME (control)", "ACME (treated)",
"ADE (control)", "ADE (treated)",
"Total Effect",
"Prop. Mediated (control)",
"Prop. Mediated (treated)",
"ACME (average)",
"ADE (average)",
"Prop. Mediated (average)")
colnames(smat) <- c("Estimate", paste(clp, "% CI Lower", sep=""),
paste(clp, "% CI Upper", sep=""), "p-value")
printCoefmat(smat, digits=3)
}
cat("\n")
cat("Sample Size Used:", x$nobs,"\n\n")
cat("\n")
cat("Simulations:", x$sims,"\n\n")
invisible(x)
}
}
#########################################################################
#' @export
summary.mediate.order <- function(object, ...){
structure(object, class = c("summary.mediate.order", class(object)))
}
#' @export
print.summary.mediate.order <- function(x, ...){
tab.d0 <- rbind(x$d0, x$d0.ci, x$d0.p)
tab.d1 <- rbind(x$d1, x$d1.ci, x$d1.p)
tab.z0 <- rbind(x$z0, x$z0.ci, x$z0.p)
tab.z1 <- rbind(x$z1, x$z1.ci, x$z1.p)
tab.tau <- rbind(x$tau.coef, x$tau.ci, x$tau.p)
# Outcome Table Labels
y.lab <- sort(unique(levels(model.frame(x$model.y)[,1])))
out.names <- c()
for(i in 1:length(y.lab)){
out.names.tmp <- paste("Pr(Y=",y.lab[i],")",sep="")
out.names <- c(out.names, out.names.tmp)
}
# Label Tables
rownames(tab.d0)[1] <- "ACME (control) "
rownames(tab.d0)[4] <- "p-value "
colnames(tab.d0) <- out.names
rownames(tab.d1)[1] <- "ACME (treated) "
rownames(tab.d1)[4] <- "p-value "
colnames(tab.d1) <- out.names
rownames(tab.z0)[1] <- "ADE (control) "
rownames(tab.z0)[4] <- "p-value "
colnames(tab.z0) <- out.names
rownames(tab.z1)[1] <- "ADE (treated) "
rownames(tab.z1)[4] <- "p-value "
colnames(tab.z1) <- out.names
rownames(tab.tau)[1] <- "Total Effect "
rownames(tab.tau)[4] <- "p-value "
colnames(tab.tau) <- out.names
cat("\n")
cat("Causal Mediation Analysis \n\n")
if(x$boot.ci.type == "perc"){
cat("Nonparametric Bootstrap Confidence Intervals with the Percentile Method\n\n")
} else if(x$boot.ci.type == "bca"){
cat("Nonparametric Bootstrap Confidence Intervals with the BCa Method\n\n")
}
if(!is.null(x$covariates)){
cat("(Inference Conditional on the Covariate Values Specified in `covariates')\n\n")
}
print(tab.d0, digits=3)
cat("\n")
print(tab.d1, digits=3)
cat("\n")
print(tab.z0, digits=3)
cat("\n")
print(tab.z1, digits=3)
cat("\n")
print(tab.tau, digits=3)
cat("\n\n")
cat("Sample Size Used:", x$nobs,"\n\n")
cat("\n\n")
cat("Simulations:", x$sims,"\n\n")
invisible(x)
}
#########################################################################
plot.process <- function(model) {
coef.vec.1 <- c(model$d1, model$z1)
lower.vec.1 <- c(model$d1.ci[1], model$z1.ci[1])
upper.vec.1 <- c(model$d1.ci[2], model$z1.ci[2])
tau.vec <- c(model$tau.coef,model$tau.ci[1],model$tau.ci[2])
range.1 <- range(model$d1.ci[1], model$z1.ci[1],model$tau.ci[1],
model$d1.ci[2], model$z1.ci[2],model$tau.ci[2])
coef.vec.0 <- c(model$d0, model$z0)
lower.vec.0 <- c(model$d0.ci[1], model$z0.ci[1])
upper.vec.0 <- c(model$d0.ci[2], model$z0.ci[2])
range.0 <- range(model$d0.ci[1], model$z0.ci[1],model$tau.ci[1],
model$d0.ci[2], model$z0.ci[2],model$tau.ci[2])
return(list(coef.vec.1=coef.vec.1, lower.vec.1=lower.vec.1,
upper.vec.1=upper.vec.1, coef.vec.0=coef.vec.0,
lower.vec.0=lower.vec.0, upper.vec.0=upper.vec.0, tau.vec=tau.vec,
range.1=range.1, range.0=range.0))
}
#########################################################################
#' Plotting Indirect, Direct, and Total Effects from Mediation Analysis
#'
#' Function to plot results from \code{mediate}. The vertical axis lists
#' indirect, direct, and total effects and the horizontal axis indicates the
#' respective magnitudes. Most standard options for plot function available.
#'
#' @aliases plot.mediate plot.mediate.order
#'
#' @param x object of class \code{mediate} or \code{mediate.order} as produced
#' by \code{mediate}.
#' @param treatment a character string indicating the baseline treatment value
#' of the estimated causal mediation effect and direct effect to plot. Can be
#' either "control", "treated" or "both". If 'NULL' (default), both sets of
#' estimates are plotted if and only if they differ.
#' @param labels a vector of character strings indicating the labels for the
#' estimated effects. The default labels will be used if NULL.
#' @param effect.type a vector indicating which quantities of interest to plot.
#' Default is to plot all three quantities (indirect, direct and total
#' effects).
#' @param xlim range of the horizontal axis.
#' @param ylim range of the vertical axis.
#' @param xlab label of the horizontal axis.
#' @param ylab label of the vertical axis.
#' @param main main title.
#' @param lwd width of the horizontal bars for confidence intervals.
#' @param cex size of the dots for point estimates.
#' @param col color of the dots and horizontal bars for the estimates.
#' @param ... additional parameters passed to 'plot'.
#'
#' @return \code{mediate} returns an object of class "\code{mediate}". The
#' function \code{summary} is used to obtain a table of the results. The
#' \code{plot} function plots these quantities.
#'
#' @author Dustin Tingley, Harvard University,
#' \email{dtingley@@gov.harvard.edu}; Teppei Yamamoto, Massachusetts Institute
#' of Technology, \email{teppei@@mit.edu}.
#'
#' @seealso \code{\link{mediate}}, \code{\link{plot}}
#'
#' @references Tingley, D., Yamamoto, T., Hirose, K., Imai, K. and Keele, L.
#' (2014). "mediation: R package for Causal Mediation Analysis", Journal of
#' Statistical Software, Vol. 59, No. 5, pp. 1-38.
#'
#' Imai, K., Keele, L. and Tingley, D. (2010) A General Approach to Causal
#' Mediation Analysis, Psychological Methods, Vol. 15, No. 4 (December), pp.
#' 309-334.
#'
#' Imai, K., Keele, L. and Yamamoto, T. (2010) Identification, Inference, and
#' Sensitivity Analysis for Causal Mediation Effects, Statistical Science,
#' Vol. 25, No. 1 (February), pp. 51-71.
#'
#' Imai, K., Keele, L., Tingley, D. and Yamamoto, T. (2009) "Causal Mediation
#' Analysis Using R" in Advances in Social Science Research Using R, ed. H. D.
#' Vinod New York: Springer.
#' @export
plot.mediate <- function(x, treatment = NULL, labels = NULL,
effect.type = c("indirect","direct","total"),
xlim = NULL, ylim = NULL, xlab = "", ylab = "",
main = NULL, lwd = 1.5, cex = .85,
col = "black", ...){
# Determine which graph to plot
isLinear.y <- ( (class(x$model.y)[1] %in% c("lm", "rq")) ||
(inherits(x$model.y, "glm") &&
x$model.y$family$family == "gaussian" &&
x$model.y$family$link == "identity") ||
(inherits(x$model.y, "survreg") &&
x$model.y$dist == "gaussian") )
printone <- !x$INT && isLinear.y
effect.type <- match.arg(effect.type, several.ok=TRUE)
IND <- "indirect" %in% effect.type
DIR <- "direct" %in% effect.type
TOT <- "total" %in% effect.type
if(is.null(treatment)){
if(printone){
treatment <- 1
} else {
treatment <- c(0,1)
}
} else {
treatment <- switch(treatment,
control = 0,
treated = 1,
both = c(0,1))
}
param <- plot.process(x)
y.axis <- (IND + DIR + TOT):1
# Set xlim
if(is.null(xlim)){
if(length(treatment) > 1) {
xlim <- range(param$range.1, param$range.0) * 1.2
} else if (treatment == 1){
xlim <- param$range.1 * 1.2
} else {
xlim <- param$range.0 * 1.2
}
}
# Set ylim
if(is.null(ylim)){
ylim <- c(min(y.axis) - 0.5, max(y.axis) + 0.5)
}
# Create blank plot first
plot(rep(0,IND+DIR+TOT), y.axis, type = "n", xlab = xlab, ylab = ylab,
yaxt = "n", xlim = xlim, ylim = ylim, main = main, ...)
# Set offset values depending on number of bars to plot
if(length(treatment) == 1){
adj <- 0
} else {
adj <- 0.05
}
if(1 %in% treatment){
if(IND && DIR) {
points(param$coef.vec.1, y.axis[1:2] + adj, type = "p", pch = 19, cex = cex, col = col)
segments(param$lower.vec.1, y.axis[1:2] + adj, param$upper.vec.1, y.axis[1:2] + adj,
lwd = lwd, col = col)
}
if(IND && !DIR) {
points(param$coef.vec.1[1], y.axis[1] + adj, type = "p", pch = 19, cex = cex, col = col)
segments(param$lower.vec.1[1], y.axis[1] + adj, param$upper.vec.1[1], y.axis[1] + adj,
lwd = lwd, col = col)
}
if(!IND && DIR) {
points(param$coef.vec.1[2], y.axis[1] + adj, type = "p", pch = 19, cex = cex, col = col)
segments(param$lower.vec.1[2], y.axis[1] + adj, param$upper.vec.1[2], y.axis[1] + adj,
lwd = lwd, col = col)
}
}
if(0 %in% treatment) {
if(IND && DIR) {
points(param$coef.vec.0, y.axis[1:2] - adj, type = "p", pch = 1, cex = cex, col = col)
segments(param$lower.vec.0, y.axis[1:2] - adj, param$upper.vec.0, y.axis[1:2] - adj,
lwd = lwd, lty = 3, col = col)
}
if(IND && !DIR) {
points(param$coef.vec.0[1], y.axis[1] - adj, type = "p", pch = 1, cex = cex, col = col)
segments(param$lower.vec.0[1], y.axis[1] - adj, param$upper.vec.0[1], y.axis[1] - adj,
lwd = lwd, lty = 3, col = col)
}
if(!IND && DIR) {
points(param$coef.vec.0[2], y.axis[1] - adj, type = "p", pch = 1, cex = cex, col = col)
segments(param$lower.vec.0[2], y.axis[1] - adj, param$upper.vec.0[2], y.axis[1] - adj,
lwd = lwd, lty = 3, col = col)
}
}
if (TOT) {
points(param$tau.vec[1], 1 , type = "p", pch = 19, cex = cex, col = col)
segments(param$tau.vec[2], 1 , param$tau.vec[3], 1 ,
lwd = lwd, col = col)
}
if(is.null(labels)){
labels <- c("ACME","ADE","Total\nEffect")[c(IND,DIR,TOT)]
}
axis(2, at = y.axis, labels = labels, las = 1, tick = TRUE, ...)
abline(v = 0, lty = 2)
}
#########################################################################
plot.process.mer <- function(model) {
coef.vec.1 <- c(model$d1, model$z1)
lower.vec.1 <- c(model$d1.ci[1], model$z1.ci[1])
upper.vec.1 <- c(model$d1.ci[2], model$z1.ci[2])
tau.vec <- c(model$tau.coef,model$tau.ci[1],model$tau.ci[2])
range.1 <- range(model$d1.ci[1], model$z1.ci[1],model$tau.ci[1],
model$d1.ci[2], model$z1.ci[2],model$tau.ci[2])
coef.vec.0 <- c(model$d0, model$z0)
lower.vec.0 <- c(model$d0.ci[1], model$z0.ci[1])
upper.vec.0 <- c(model$d0.ci[2], model$z0.ci[2])
range.0 <- range(model$d0.ci[1], model$z0.ci[1],model$tau.ci[1],
model$d0.ci[2], model$z0.ci[2],model$tau.ci[2])
coef.vec.0.group <- cbind(model$d0.group, model$z0.group)
lower.vec.0.group <- cbind(model$d0.ci.group[,1], model$z0.ci.group[,1])
upper.vec.0.group <- cbind(model$d0.ci.group[,2], model$z0.ci.group[,2])
coef.vec.1.group <- cbind(model$d1.group, model$z1.group)
lower.vec.1.group <- cbind(model$d1.ci.group[,1], model$z1.ci.group[,1])
upper.vec.1.group <- cbind(model$d1.ci.group[,2], model$z1.ci.group[,2])
tau.vec.group <- cbind(model$tau.coef.group, model$tau.ci.group[,1], model$tau.ci.group[,2])
return(list(coef.vec.1=coef.vec.1, lower.vec.1=lower.vec.1,
upper.vec.1=upper.vec.1, coef.vec.0=coef.vec.0,
lower.vec.0=lower.vec.0, upper.vec.0=upper.vec.0, tau.vec=tau.vec,
range.1=range.1, range.0=range.0,coef.vec.1.group=coef.vec.1.group, lower.vec.1.group=lower.vec.1.group,
upper.vec.1.group=upper.vec.1.group, coef.vec.0.group=coef.vec.0.group,
lower.vec.0.group=lower.vec.0.group, upper.vec.0.group=upper.vec.0.group, tau.vec.group=tau.vec.group))
}
#########################################################################
#' Plotting Indirect, Direct, and Total Effects from Mediation Analysis of
#' Multilevel Models
#'
#' Function to plot group-specific effects derived from causal mediation
#' analysis of multilevel models.
#'
#' @param x object of class 'mediate.mer' produced by 'mediate'.
#' @param treatment a character string indicating the baseline treatment value
#' of the estimated causal mediation effect and direct effect to plot. Can be
#' either "control", "treated", or "both". If 'NULL' (default), both sets of
#' estimates are plotted if and only if they differ.
#' @param group.plots a logical value indicating whether group-specific effects
#' should be plotted in addition to the population-averaged effects.
#' @param ask a logical value. If 'TRUE', the user is asked for input before a
#' new figure is plotted. Default is to ask only if the number of plots on
#' current screen is fewer than necessary.
#' @param xlim range of the horizontal axis.
#' @param ylim range of the vertical axis.
#' @param xlab label of the horizontal axis.
#' @param ylab label of the vertical axis.
#' @param main main title.
#' @param lwd width of the horizontal bars for confidence intervals .
#' @param cex size of the dots for point estimates.
#' @param col color of the dots and horizontal bars for the estimates..
#' @param ... additional parameters passed to 'plot'.
#'
#' @author Kentaro Hirose, Princeton University, \email{hirose@@princeton.edu}.
#'
#' @seealso \code{\link{mediate}}, \code{\link{summary.mediate.mer}}.
#'
#' @references Tingley, D., Yamamoto, T., Hirose, K., Imai, K. and Keele, L.
#' (2014). "mediation: R package for Causal Mediation Analysis", Journal of
#' Statistical Software, Vol. 59, No. 5, pp. 1-38.
#'
#' @examples
#' # Examples with JOBS II Field Experiment
#'
#' # **For illustration purposes a small number of simulations are used**
#' \dontrun{
#' data(jobs)
#' require(lme4)
#'
#' # educ: mediator group
#' # occp: outcome group
#'
#' # Varying intercept for mediator
#' model.m <- glmer(job_dich ~ treat + econ_hard + (1 | educ),
#' family = binomial(link = "probit"), data = jobs)
#'
#' # Varying intercept and slope for outcome
#' model.y <- glmer(work1 ~ treat + job_dich + econ_hard + (1 + treat | occp),
#' family = binomial(link = "probit"), data = jobs)
#'
#' # Output based on mediator group
#' multilevel <- mediate(model.m, model.y, treat = "treat",
#' mediator = "job_dich", sims=50, group.out="educ")
#'
#' #plot(multilevel, group.plots=TRUE)
#' }
#'
#' @export
plot.mediate.mer <- function(x, treatment = NULL, group.plots = FALSE,
ask = prod(par("mfcol")) < nplots,
xlim = NULL, ylim = NULL, xlab = "", ylab = "",
main = NULL, lwd = 1.5, cex = .85,
col = "black", ...){
param <- plot.process.mer(x)
isLinear.y <- ( (class(x$model.y)[1] %in% c("lm", "rq")) || # lm or quantile
(inherits(x$model.y, "glm") &&
x$model.y$family$family == "gaussian" &&
x$model.y$family$link == "identity") || # glm normal
(inherits(x$model.y, "survreg") &&
x$model.y$dist == "gaussian") || # surv normal
(inherits(x$model.y, "merMod") &&
x$model.y@call[[1]] == "lmer") ) # lmer
printone <- !x$INT && isLinear.y
if(is.null(treatment)){
if(printone){
treatment <- 1
} else {
treatment <- c(0,1)
}
} else {
treatment <- switch(treatment,
control = 0,
treated = 1,
both = c(0,1))
}
nplots <- 1 + group.plots * (2 * length(treatment) + 1) # n of plots necessary
if(ask){
oask <- devAskNewPage(TRUE)
on.exit(devAskNewPage(oask))
}
# 1. Summary plot for population effects
labels = c("ACME","ADE","Total\nEffect")
y.axis <- c(length(param$coef.vec.1):.5)
y.axis <- y.axis + 1
if(is.null(xlim)){
if(length(treatment) > 1) {
xlim <- range(param$range.1, param$range.0) * 1.2
} else if (treatment == 1){
xlim <- param$range.1 * 1.2
} else {
xlim <- param$range.0 * 1.2
}
}
if(is.null(ylim)){
ylim <- c(min(y.axis) -1- 0.5, max(y.axis) + 0.5)
}
plot(param$coef.vec.1, y.axis, type = "n", xlab = xlab, ylab = ylab,
yaxt = "n", xlim = xlim, ylim = ylim, main = main, ...)
if(length(treatment) == 1){
adj <- 0
} else {
adj <- 0.05
}
if(1 %in% treatment){
points(param$coef.vec.1, y.axis + adj, type = "p", pch = 19, cex = cex, col = col)
segments(param$lower.vec.1, y.axis + adj, param$upper.vec.1, y.axis + adj,
lwd = lwd, col = col)
points(param$tau.vec[1], 1, type = "p", pch = 19, cex = cex, col = col)
segments(param$tau.vec[2], 1 , param$tau.vec[3], 1 ,
lwd = lwd, col = col)
}
if(0 %in% treatment) {
points(param$coef.vec.0, y.axis - adj, type = "p", pch = 1, cex = cex, col = col)
segments(param$lower.vec.0, y.axis - adj, param$upper.vec.0, y.axis - adj,
lwd = lwd, lty = 3, col = col)
}
y.axis.new <- c(3,2,1)
axis(2, at = y.axis.new, labels = labels, las = 1, tick = TRUE, ...)
abline(v = 0, lty = 2)
# 2. Group effects
if(group.plots){
#########################################################################
if(is.factor(x$group.id)){
labels <- levels(x$group.id)
} else {
labels = sort(unique(x$group.id))
}
#########################################################################
if(0 %in% treatment){
y.axis <- c(length(param$coef.vec.0.group[,1]):.5)
y.axis <- y.axis + 1
xlim <- c(param$lower.vec.0.group[,1], param$coef.vec.0.group[,1], param$upper.vec.0.group[,1])
MIN <- ifelse(min(xlim)>0, min(xlim)*0.9, min(xlim)*1.1)
MAX <- ifelse(max(xlim)>0, max(xlim)*1.1, max(xlim)*0.9)
xlim <- c(MIN, MAX)
ylim <- c(min(y.axis), max(y.axis))
plot(param$coef.vec.0.group[,1], y.axis, type = "n", xlab = xlab, ylab = ylab,
yaxt = "n", xlim = xlim, ylim = ylim, main = "ACME (control)", ...)
points(param$coef.vec.0.group[,1], y.axis, type = "p", pch = 1, cex = cex, col = col)
segments(param$lower.vec.0.group[,1], y.axis, param$upper.vec.0.group[,1], y.axis,
lwd = lwd, col = col)
axis(2, at = y.axis, labels = labels, las = 1, tick = TRUE, ...)
abline(v = 0, lty = 2)
}
#########################################################################
if(1 %in% treatment){
y.axis <- c(length(param$coef.vec.1.group[,1]):.5)
y.axis <- y.axis + 1
xlim <- c(param$lower.vec.1.group[,1], param$coef.vec.1.group[,1], param$upper.vec.1.group[,1])
MIN <- ifelse(min(xlim)>0, min(xlim)*0.9, min(xlim)*1.1)
MAX <- ifelse(max(xlim)>0, max(xlim)*1.1, max(xlim)*0.9)
xlim <- c(MIN, MAX)
ylim <- c(min(y.axis), max(y.axis))
plot(param$coef.vec.1.group[,1], y.axis, type = "n", xlab = xlab, ylab = ylab,
yaxt = "n", xlim = xlim, ylim = ylim, main = ifelse(printone, "ACME", "ACME (treated)"), ...)
points(param$coef.vec.1.group[,1], y.axis, type = "p", pch = 19, cex = cex, col = col)
segments(param$lower.vec.1.group[,1], y.axis, param$upper.vec.1.group[,1], y.axis,
lwd = lwd, col = col)
axis(2, at = y.axis, labels = labels, las = 1, tick = TRUE, ...)
abline(v = 0, lty = 2)
}
#########################################################################
if(0 %in% treatment){
y.axis <- c(length(param$coef.vec.0.group[,2]):.5)
y.axis <- y.axis + 1
xlim <- c(param$lower.vec.0.group[,2], param$coef.vec.0.group[,2], param$upper.vec.0.group[,2])
MIN <- ifelse(min(xlim)>0, min(xlim)*0.9, min(xlim)*1.1)
MAX <- ifelse(max(xlim)>0, max(xlim)*1.1, max(xlim)*0.9)
xlim <- c(MIN, MAX)
ylim <- c(min(y.axis), max(y.axis))
plot(param$coef.vec.0.group[,2], y.axis, type = "n", xlab = xlab, ylab = ylab,
yaxt = "n", xlim = xlim, ylim = ylim, main = "ADE (control)", ...)
points(param$coef.vec.0.group[,2], y.axis, type = "p", pch = 1, cex = cex, col = col)
segments(param$lower.vec.0.group[,2], y.axis, param$upper.vec.0.group[,2], y.axis,
lwd = lwd, lty = 3, col = col)
axis(2, at = y.axis, labels = labels, las = 1, tick = TRUE, ...)
abline(v = 0, lty = 2)
}
#########################################################################
if(1 %in% treatment){
y.axis <- c(length(param$coef.vec.1.group[,2]):.5)
y.axis <- y.axis + 1
xlim <- c(param$lower.vec.1.group[,2], param$coef.vec.1.group[,2], param$upper.vec.1.group[,2])
MIN <- ifelse(min(xlim)>0, min(xlim)*0.9, min(xlim)*1.1)
MAX <- ifelse(max(xlim)>0, max(xlim)*1.1, max(xlim)*0.9)
xlim <- c(MIN, MAX)
ylim <- c(min(y.axis), max(y.axis))
plot(param$coef.vec.1.group[,2], y.axis, type = "n", xlab = xlab, ylab = ylab,
yaxt = "n", xlim = xlim, ylim = ylim, main = ifelse(printone, "ADE", "ADE (treated)"), ...)
points(param$coef.vec.1.group[,2], y.axis, type = "p", pch = 19, cex = cex, col = col)
segments(param$lower.vec.1.group[,2], y.axis, param$upper.vec.1.group[,2], y.axis,
lwd = lwd, lty = 3, col = col)
axis(2, at = y.axis, labels = labels, las = 1, tick = TRUE, ...)
abline(v = 0, lty = 2)
}
#########################################################################
y.axis <- c(length(param$tau.vec.group[,1]):.5)
y.axis <- y.axis + 1
xlim <- c(param$tau.vec.group[,1], param$tau.vec.group[,2], param$tau.vec.group[,3])
MIN <- ifelse(min(xlim)>0, min(xlim)*0.9, min(xlim)*1.1)
MAX <- ifelse(max(xlim)>0, max(xlim)*1.1, max(xlim)*0.9)
xlim <- c(MIN, MAX)
ylim <- c(min(y.axis), max(y.axis))
plot(param$tau.vec.group[,1], y.axis, type = "n", xlab = xlab, ylab = ylab,
yaxt = "n", xlim = xlim, ylim = ylim, main = "Total\nEffect", ...)
points(param$tau.vec.group[,1], y.axis , type = "p", pch = 19, cex = cex, col = col)
segments(param$tau.vec.group[,2], y.axis , param$tau.vec.group[,3], y.axis ,
lwd = lwd, col = col)
axis(2, at = y.axis, labels = labels, las = 1, tick = TRUE, ...)
abline(v = 0, lty = 2)
}
}
#########################################################################
plot.process.order <- function(model){
length <- length(model$d1)
coef.vec.1 <- lower.vec.1 <- upper.vec.1 <-
coef.vec.0 <- lower.vec.0 <- upper.vec.0 <- matrix(NA,ncol=2,nrow=length)
tau.vec<-matrix(NA,ncol=3,nrow=length)
for(j in 1:length){
coef.vec.1[j,] <- c(model$d1[j], model$z1[j])
lower.vec.1[j,] <- c(model$d1.ci[1,j], model$z1.ci[1,j])
upper.vec.1[j,] <- c(model$d1.ci[2,j], model$z1.ci[2,j])
coef.vec.0[j,] <- c(model$d0[j], model$z0[j])
lower.vec.0[j,] <- c(model$d0.ci[1,j], model$z0.ci[1,j])
upper.vec.0[j,] <- c(model$d0.ci[2,j], model$z0.ci[2,j])
tau.vec[j,] <- c(model$tau.coef[j], model$tau.ci[1,j], model$tau.ci[2,j])
}
range.1 <- range(model$d1.ci[1,], model$z1.ci[1,],model$tau.ci[1,],
model$d1.ci[2,], model$z1.ci[2,],model$tau.ci[2,])
range.0 <- range(model$d0.ci[1,], model$z0.ci[1,],model$tau.ci[1,],
model$d0.ci[2,], model$z0.ci[2,],model$tau.ci[2,])
return(list(coef.vec.1=coef.vec.1, lower.vec.1=lower.vec.1,
upper.vec.1=upper.vec.1, coef.vec.0=coef.vec.0,
lower.vec.0=lower.vec.0, upper.vec.0=upper.vec.0,
tau.vec=tau.vec,
range.1=range.1, range.0=range.0, length=length))
}
#########################################################################
#' @export
plot.mediate.order <- function(x, treatment = NULL,
labels = c("ACME","ADE","Total\nEffect"),
xlim = NULL, ylim = NULL, xlab = "", ylab = "",
main = NULL, lwd = 1.5, cex = .85,
col = "black", ...){
# Determine which graph to plot
if(is.null(treatment)){
if(x$INT){
treatment <- c(0,1)
} else {
treatment <- 1
}
} else {
treatment <- switch(treatment,
control = 0,
treated = 1,
both = c(0,1))
}
param <- plot.process.order(x)
y.axis <- c(ncol(param$coef.vec.1):.5)
y.axis <- y.axis + 1
# create indicator for y.axis, descending so labels go from top to bottom
# Set xlim
if(is.null(xlim)){
if(length(treatment) > 1) {
xlim <- range(param$range.1, param$range.0) * 1.2
} else if (treatment == 1){
xlim <- param$range.1 * 1.2
} else {
xlim <- param$range.0 * 1.2
}
}
# Set ylim
if(is.null(ylim)){
ylim <- c(min(y.axis) - 1 - 0.5, max(y.axis) + 0.5)
}
# Plot
plot(param$coef.vec.1[1,], y.axis, type = "n", xlab = xlab, ylab = ylab,
yaxt = "n", xlim = xlim, ylim = ylim, main = main, ...)
# Set offset values depending on number of bars to plot
if(length(treatment) == 1){
adj <- 0
} else {
adj <- 0.05
}
if(1 %in% treatment){
adj.1 <- adj * nrow(param$coef.vec.1)
for(z in 1:nrow(param$coef.vec.1)){
points(param$coef.vec.1[z,], y.axis + adj.1,
type = "p", pch = 19, cex = cex, col = col)
segments(param$lower.vec.1[z,], y.axis + adj.1,
param$upper.vec.1[z,], y.axis + adj.1,
lwd = lwd, col = col)
points(param$tau.vec[z,1], 1 + adj.1 ,
type = "p", pch = 19, cex = cex, col = col)
segments(param$tau.vec[z,2], 1 + adj.1 ,
param$tau.vec[z,3], 1 + adj.1 ,
lwd = lwd, col = col)
adj.1 <- adj.1 - 0.05
}
}
if(0 %in% treatment) {
adj.0 <- adj
for(z in 1:nrow(param$coef.vec.0)){
points(param$coef.vec.0[z,], y.axis - adj.0,
type = "p", pch = 1, cex = cex, col = col)
segments(param$lower.vec.0[z,], y.axis - adj.0,
param$upper.vec.0[z,], y.axis - adj.0,
lwd = lwd, lty = 3, col = col)
adj.0 <- adj.0 + 0.05
}
}
if (treatment[1]==0 & length(treatment)==1){
print("test")
adj.1 <- adj * nrow(param$coef.vec.1)
for(z in 1:nrow(param$tau.vec)){
points(param$tau.vec[z,1], 1 + adj.1 ,
type = "p", pch = 19, cex = cex, col = col)
segments(param$tau.vec[z,2], 1 + adj.1 ,
param$tau.vec[z,3], 1 +adj.1 ,
lwd = lwd, col = col)
adj.1 <- adj.1 - 0.05
}
}
y.axis.new <- c(3,2,1)
axis(2, at = y.axis.new, labels = labels, las = 1, tick = TRUE, ...)
abline(v = 0, lty = 2)
}
pval <- function(x, xhat){
## Compute p-values
if (xhat == 0) out <- 1
else {
out <- 2 * min(sum(x > 0), sum(x < 0)) / length(x)
}
return(min(out, 1))
}
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Defines functions mediate med.fun med.fun.ordered summary.mediate print.summary.mediate summary.mediate.mer print.summary.mediate.mer print.summary.mediate.mer.2 print.summary.mediate.mer.3 summary.mediate.order print.summary.mediate.order plot.process plot.mediate plot.process.mer plot.mediate.mer plot.process.order plot.mediate.order pval
Documented in mediate plot.mediate plot.mediate.mer plot.mediate.order print.summary.mediate print.summary.mediate.mer print.summary.mediate.mer.2 print.summary.mediate.mer.3 print.summary.mediate.order summary.mediate summary.mediate.mer summary.mediate.order
#' Causal Mediation Analysis
#'
#' 'mediate' is used to estimate various quantities for causal mediation
#' analysis, including average causal mediation effects (indirect effect),
#' average direct effects, proportions mediated, and total effect.
#'
#' @details This is the workhorse function for estimating causal mediation
#' effects for a variety of data types. The average causal mediation effect
#' (ACME) represents the expected difference in the potential outcome when the
#' mediator took the value that would realize under the treatment condition as
#' opposed to the control condition, while the treatment status itself is held
#' constant. That is,
#' \deqn{\delta(t) \ = \ E\{Y(t, M(t_1)) - Y(t, M(t_0))\},}{%
#' \delta(t) = E[Y(t, M(t1)) - Y(t, M(t0))],}
#' where \eqn{t, t_1, t_0}{t, t1, t0} are particular values of the treatment
#' \eqn{T} such that \eqn{t_1 \neq t_0}{t1 != t0}, \eqn{M(t)} is the potential
#' mediator, and \eqn{Y(t,m)} is the potential outcome variable. The average
#' direct effect (ADE) is defined similarly as,
#' \deqn{\zeta(t) \ = \ E\{Y(t_1, M(t)) - Y(t_0, M(t))\},}{%
#' \zeta(t) = E[Y(t1, M(t)) - Y(t0, M(t))],}
#' which represents the expected difference in the potential outcome when the
#' treatment is changed but the mediator is held constant at the value that
#' would realize if the treatment equals \eqn{t}. The two quantities on
#' average add up to the total effect of the treatment on the outcome,
#' \eqn{\tau}. See the references for more details.
#'
#' When both the mediator model ('model.m') and outcome model ('model.y') are
#' normal linear regressions, the results will be identical to the usual LSEM
#' method by Baron and Kenny (1986). The function can, however, accommodate
#' other data types including binary, ordered and count outcomes and mediators
#' as well as censored outcomes. Variables can also be modeled
#' nonparametrically, semiparametrically, or using quantile regression.
#'
#' If it is desired that inference be made conditional on specific values of
#' the pre-treatment covariates included in the model, the `covariates'
#' argument can be used to set those values as a list or data frame. The list
#' may contain either the entire set or any strict subset of the covariates in
#' the model; in the latter case, the effects will be averaged over the other
#' covariates. The `covariates' argument will be particularly useful when the
#' models contain interactions between the covariates and the treatment and/or
#' mediator (known as ``moderated mediation'').
#'
#' The prior weights in the mediator and outcome models are taken as sampling
#' weights and the estimated effects will be weighted averages when non-NULL
#' weights are used in fitting 'model.m' and 'model.y'. This will be useful
#' when data does not come from a simple random sample, for example.
#'
#' As of version 4.0, the mediator model can be of either 'lm', 'glm' (or
#' `bayesglm'), 'polr' (or `bayespolr'), 'gam', 'rq', `survreg', or `merMod'
#' class, corresponding respectively to the linear regression models,
#' generalized linear models, ordered response models, generalized additive
#' models, quantile regression models, parametric duration models, or
#' multilevel models.. For binary response models, the 'mediator' must be a
#' numeric variable with values 0 or 1 as opposed to a factor.
#' Quasi-likelihood-based inferences are not allowed for the mediator model
#' because the functional form must be exactly specified for the estimation
#' algorithm to work. The 'binomial' family can only be used for binary
#' response mediators and cannot be used for multiple-trial responses. This
#' is due to conflicts between how the latter type of models are implemented
#' in \code{\link{glm}} and how 'mediate' is currently written.
#'
#' For the outcome model, the censored regression model fitted via package
#' \code{VGAM} (of class 'vglm' with 'family@vfamily' equal to "tobit") can be
#' used in addition to the models listed above for the mediator. The
#' 'mediate' function is not compatible with censored regression models fitted
#' via other packages. When the quantile regression is used for the outcome
#' model ('rq'), the estimated quantities are quantile causal mediation
#' effects, quantile direct effects and etc., instead of the average effects.
#' If the outcome model is of class 'survreg', the name of the outcome
#' variable must be explicitly supplied in the `outcome' argument. This is due
#' to the fact that 'survreg' objects do not contain that information in an
#' easily extractable form. It should also be noted that for
#' \code{\link{survreg}} models, the \code{\link{Surv}} function must be
#' directly used in the model formula in the call to the survreg function, and
#' that censoring types requiring more than two arguments to Surv (e.g.,
#' interval censoring) are not currently supported by 'mediate'.
#'
#' The quasi-Bayesian approximation (King et al. 2000) cannot be used if
#' 'model.m' is of class 'rq' or 'gam', or if 'model.y' is of class 'gam',
#' 'polr' or 'bayespolr'. In these cases, either an error message is returned
#' or use of the nonparametric bootstrap is forced. Users should note that use
#' of the nonparametric bootstrap often requires significant computing time,
#' especially when 'sims' is set to a large value.
#'
#' The 'control' argument must be provided when 'gam' is used for the outcome
#' model and user wants to allow ACME and ADE to vary as functions of the
#' treatment (i.e., to relax the "no interaction" assumption). Note that the
#' outcome model must be fitted via package \code{\link{mgcv}} with
#' appropriate formula using \code{\link{s}} constructs (see Imai et al. 2009
#' in the references). For other model types, the interaction can be allowed
#' by including an interaction term between \eqn{T} and \eqn{M} in the linear
#' predictor of the outcome model. As of version 3.0, the 'INT' argument is
#' deprecated and the existence of the interaction term is automatically
#' detected (except for 'gam' outcome models).
#'
#' When the treatment variable is continuous or a factor with multiple levels,
#' user must specify the values of \eqn{t_1}{t1} and \eqn{t_0}{t0} using the
#' 'treat.value' and 'control.value' arguments, respectively. The value of
#' \eqn{t} in the above expressions is set to \eqn{t_0}{t0} for 'd0', 'z0',
#' etc. and to \eqn{t_1}{t1} for 'd1', 'z1', etc.
#'
#' @param model.m a fitted model object for mediator. Can be of class 'lm',
#' 'polr', 'bayespolr', 'glm', 'bayesglm', 'gam', 'rq', 'survreg', or
#' 'merMod'.
#' @param model.y a fitted model object for outcome. Can be of class 'lm',
#' 'polr', 'bayespolr', 'glm', 'bayesglm', 'gam', 'vglm', 'rq', 'survreg', or
#' 'merMod'.
#' @param sims number of Monte Carlo draws for nonparametric bootstrap or
#' quasi-Bayesian approximation.
#' @param boot a logical value. if 'FALSE' a quasi-Bayesian approximation is
#' used for confidence intervals; if 'TRUE' nonparametric bootstrap will be
#' used. Default is 'FALSE'.
#' @param boot.ci.type a character string indicating the type of bootstrap
#' confidence intervals. If "bca" and boot = TRUE, bias-corrected and
#' accelerated (BCa) confidence intervals will be estimated. If "perc" and
#' boot = TRUE, percentile confidence intervals will be estimated. Default is
#' "perc".
#' @param conf.level level of the returned two-sided confidence intervals.
#' Default is to return the 2.5 and 97.5 percentiles of the simulated
#' quantities.
#' @param treat a character string indicating the name of the treatment variable
#' used in the models. The treatment can be either binary (integer or a
#' two-valued factor) or continuous (numeric).
#' @param mediator a character string indicating the name of the mediator
#' variable used in the models.
#' @param covariates a list or data frame containing values for a subset of the
#' pre-treatment covariates in 'model.m' and 'model.y'. If provided, the
#' function will return the estimates conditional on those covariate values.
#' @param outcome a character string indicating the name of the outcome variable
#' in `model.y'. Only necessary if 'model.y' is of class 'survreg'; otherwise
#' ignored.
#' @param control a character string indicating the name of the control group
#' indicator. Only relevant if 'model.y' is of class 'gam'. If provided, 'd0',
#' 'z0' and 'n0' are allowed to differ from 'd1', 'z1' and 'n1', respectively.
#' @param control.value value of the treatment variable used as the control
#' condition. Default is 0.
#' @param treat.value value of the treatment variable used as the treatment
#' condition. Default is 1.
#' @param long a logical value. If 'TRUE', the output will contain the entire
#' sets of simulation draws of the the average causal mediation effects,
#' direct effects, proportions mediated, and total effect. Default is 'TRUE'.
#' @param dropobs a logical value indicating the behavior when the model frames
#' of 'model.m' and 'model.y' (and the 'cluster' variable if included) are
#' composed of different observations. If 'TRUE', models will be re-fitted
#' using common data rows. If 'FALSE', error is returned. Default is 'FALSE'.
#' @param robustSE a logical value. If 'TRUE', heteroskedasticity-consistent
#' standard errors will be used in quasi-Bayesian simulations. Ignored if
#' 'boot' is 'TRUE' or neither 'model.m' nor 'model.y' has a method for
#' \code{vcovHC} in the \code{sandwich} package. Default is 'FALSE'.
#' @param cluster a variable indicating clusters for standard errors. Note that
#' this should be a vector of cluster indicators itself, not a character
#' string for the name of the variable.
#' @param group.out a character string indicating the name of the lmer/glmer
#' group on which the mediate output is based. Can be used even when a merMod
#' function is applied to only one of the mediator or the outcome. If merMod
#' functions are applied to both the mediator and the outcome, default is the
#' group name used in the outcome model; if the mediator group and the outcome
#' group are different and the user is interested in the mediate output based
#' on the mediator group, then set group.out to the group name used in the
#' mediator merMod model. If a merMod function is applied to only one of the
#' mediator or the outcome, group.out is automatically set to the group name
#' used in the merMod model.
#' @param use_speed a logical value indicating whether, if nonparametric
#' bootstrap is used, \code{lm} and \code{glm} models should be re-fit using
#' functions from the \code{speedglm} package. Ignored if 'boot' is 'FALSE' or
#' if neither 'model.m' nor 'model.y' is of class 'lm' or 'glm'. Default is
#' 'FALSE'.
#' @param ... other arguments passed to \code{vcovHC} in the \code{sandwich}
#' package: typically the 'type' argument, which is ignored if 'robustSE' is
#' 'FALSE'. Arguments to the \code{boot} in the \code{boot} package may also
#' be passed, e.g. 'parallel' and 'ncpus'.
#'
#' @return \code{mediate} returns an object of class "\code{mediate}",
#' "\code{mediate.order}" if the outcome model used is 'polr' or 'bayespolr',
#' or "\code{mediate.mer}" if 'lmer' or 'glmer' is used for the outcome or the
#' mediator model, a list that contains the components listed below. Some of
#' these elements are not available if 'long' is set to 'FALSE' by the user.
#'
#' The function \code{summary} (i.e., \code{summary.mediate},
#' \code{summary.mediate.order}, or \code{summary.mediate.mer}) can be used to
#' obtain a table of the results. The function \code{plot} (i.e.,
#' \code{plot.mediate}, \code{plot.mediate.order}, or \code{plot.mediate.mer})
#' can be used to produce a plot of the estimated average causal mediation,
#' average direct, and total effects along with their confidence intervals.
#'
#' \item{d0, d1}{point estimates for average causal mediation effects under
#' the control and treatment conditions.}
#' \item{d0.ci, d1.ci}{confidence intervals for average causal mediation
#' effects. The confidence level is set at the value specified in
#' 'conf.level'.}
#' \item{d0.p, d1.p}{two-sided p-values for average causal mediation effects.}
#' \item{d0.sims, d1.sims}{vectors of length 'sims' containing simulation
#' draws of average causal mediation effects.}
#' \item{z0, z1}{point estimates for average direct effect under the control
#' and treatment conditions.}
#' \item{z0.ci, z1.ci}{confidence intervals for average direct effects.}
#' \item{z0.p, z1.p}{two-sided p-values for average causal direct effects.}
#' \item{z0.sims, z1.sims}{vectors of length 'sims' containing simulation
#' draws of average direct effects.}
#' \item{n0, n1}{the "proportions mediated", or the size of the average causal
#' mediation effects relative to the total effect.}
#' \item{n0.ci, n1.ci}{confidence intervals for the proportions mediated.}
#' \item{n0.p, n1.p}{two-sided p-values for proportions mediated.}
#' \item{n0.sims, n1.sims}{vectors of length 'sims' containing simulation
#' draws of the proportions mediated.}
#' \item{tau.coef}{point estimate for total effect.}
#' \item{tau.ci}{confidence interval for total effect.}
#' \item{tau.p}{two-sided p-values for total effect.}
#' \item{tau.sims}{a vector of length 'sims' containing simulation draws of
#' the total effect.}
#' \item{d.avg, z.avg, n.avg}{simple averages of d0 and d1, z0 and z1, n0 and
#' n1, respectively, which users may want to use as summary values when those
#' quantities differ.}
#' \item{d.avg.ci, z.avg.ci, n.avg.ci}{confidence intervals for the above.}
#' \item{d.avg.p, z.avg.p, n.avg.p}{two-sided p-values for the above.}
#' \item{d.avg.sims, z.avg.sims, n.avg.sims}{vectors of length 'sims'
#' containing simulation draws of d.avg, z.avg and n.avg, respectively.}
#' \item{d0.group, d1.group}{group-specific point estimates for average
#' causal mediation effects under the control and treatment conditions.}
#' \item{d0.ci.group, d1.ci.group}{group-specific confidence intervals for
#' average causal mediation effects. The confidence level is set at the value
#' specified in 'conf.level'.}
#' \item{d0.p.group, d1.p.group}{group-specific two-sided p-values for average
#' causal mediation effects.}
#' \item{d0.sims.group, d1.sims.group}{group-specific vectors of length 'sims'
#' containing simulation draws of average causal mediation effects.}
#' \item{z0.group, z1.group}{group-specific point estimates for average direct
#' effect under the control and treatment conditions.}
#' \item{z0.ci.group, z1.ci.group}{group-specific confidence intervals for
#' average direct effects.}
#' \item{z0.p.group, z1.p.group}{group-specific two-sided p-values for average
#' causal direct effects.}
#' \item{z0.sims.group, z1.sims.group}{group-specific vectors of length 'sims'
#' containing simulation draws of average direct effects.}
#' \item{n0.group, n1.group}{the group-specific "proportions mediated", or the
#' size of the group-specific average causal mediation effects relative to the
#' total effect.}
#' \item{n0.ci.group, n1.ci.group}{group-specific confidence intervals for the
#' proportions mediated.}
#' \item{n0.p.group, n1.p.group}{group-specific two-sided p-values for
#' proportions mediated.}
#' \item{n0.sims.group, n1.sims.group}{group-specific vectors of length 'sims'
#' containing simulation draws of the proportions mediated.}
#' \item{tau.coef.group}{group-specific point estimate for total effect.}
#' \item{tau.ci.group}{group-specific confidence interval for total effect.}
#' \item{tau.p.group}{group-specific two-sided p-values for total effect.}
#' \item{tau.sims.group}{a group-specific vector of length 'sims' containing
#' simulation draws of the total effect.}
#' \item{d.avg.group, z.avg.group, n.avg.group}{group-specific simple averages
#' of d0 and d1, z0 and z1, n0 and n1, respectively, which users may want to
#' use as summary values when those quantities differ.}
#' \item{d.avg.ci.group, z.avg.ci.group, n.avg.ci.group}{group-specific
#' confidence intervals for the above.}
#' \item{d.avg.p.group, z.avg.p.group, n.avg.p.group}{group-specific two-sided
#' p-values for the above.}
#' \item{d.avg.sims.group, z.avg.sims.group, n.avg.sims.group}{group-specific
#' vectors of length 'sims' containing simulation draws of d.avg, z.avg and
#' n.avg, respectively.}
#' \item{boot}{logical, the 'boot' argument used.}
#' \item{treat}{a character string indicating the name of the 'treat' variable
#' used.}
#' \item{mediator}{a character string indicating the name of the 'mediator'
#' variable used.}
#' \item{INT}{a logical value indicating whether the model specification
#' allows the effects to differ between the treatment and control conditions.}
#' \item{conf.level}{the confidence level used. }
#' \item{model.y}{the outcome model used.}
#' \item{model.m}{the mediator model used.}
#' \item{group.m}{the name of the mediator group used.}
#' \item{group.y}{the name of the outcome group used.}
#' \item{group.name}{the name of the group on which the output is based.}
#' \item{group.id.m}{the data on the mediator group.}
#' \item{group.id.y}{the data on the outcome group.}
#' \item{group.id}{the data on the group on which the output is based.}
#' \item{control.value}{value of the treatment variable used as the control
#' condition.}
#' \item{treat.value}{value of the treatment variable used as the treatment
#' condition.}
#' \item{nobs}{number of observations in the model frame for 'model.m' and
#' 'model.y'. May differ from the numbers in the original models input to
#' 'mediate' if 'dropobs' was 'TRUE'.}
#' \item{robustSE}{`TRUE' or `FALSE'.}
#' \item{cluster}{the clusters used.}
#'
#' @author Dustin Tingley, Harvard University,
#' \email{dtingley@@gov.harvard.edu}; Teppei Yamamoto, Massachusetts Institute
#' of Technology, \email{teppei@@mit.edu}; Luke Keele, Penn State University,
#' \email{ljk20@@psu.edu}; Kosuke Imai, Princeton University,
#' \email{kimai@@princeton.edu}; Kentaro Hirose, Princeton University,
#' \email{hirose@@princeton.edu}.
#'
#' @seealso \code{\link{medsens}}, \code{\link{plot.mediate}},
#' \code{\link{summary.mediate}}, \code{\link{summary.mediate.mer}},
#' \code{\link{plot.mediate.mer}}, \code{\link{mediations}}, \code{vcovHC}
#'
#' @references Tingley, D., Yamamoto, T., Hirose, K., Imai, K. and Keele, L.
#' (2014). "mediation: R package for Causal Mediation Analysis", Journal of
#' Statistical Software, Vol. 59, No. 5, pp. 1-38.
#'
#' Imai, K., Keele, L., Tingley, D. and Yamamoto, T. (2011). Unpacking the
#' Black Box of Causality: Learning about Causal Mechanisms from Experimental
#' and Observational Studies, American Political Science Review, Vol. 105, No.
#' 4 (November), pp. 765-789.
#'
#' Imai, K., Keele, L. and Tingley, D. (2010) A General Approach to Causal
#' Mediation Analysis, Psychological Methods, Vol. 15, No. 4 (December), pp.
#' 309-334.
#'
#' Imai, K., Keele, L. and Yamamoto, T. (2010) Identification, Inference, and
#' Sensitivity Analysis for Causal Mediation Effects, Statistical Science,
#' Vol. 25, No. 1 (February), pp. 51-71.
#'
#' Imai, K., Keele, L., Tingley, D. and Yamamoto, T. (2009) "Causal Mediation
#' Analysis Using R" in Advances in Social Science Research Using R, ed. H. D.
#' Vinod New York: Springer.
#'
#' @export
#' @examples
#' # Examples with JOBS II Field Experiment
#'
#' # **For illustration purposes a small number of simulations are used**
#'
#' data(jobs)
#'
#' ####################################################
#' # Example 1: Linear Outcome and Mediator Models
#' ####################################################
#' b <- lm(job_seek ~ treat + econ_hard + sex + age, data=jobs)
#' c <- lm(depress2 ~ treat + job_seek + econ_hard + sex + age, data=jobs)
#'
#' # Estimation via quasi-Bayesian approximation
#' contcont <- mediate(b, c, sims=50, treat="treat", mediator="job_seek")
#' summary(contcont)
#' plot(contcont)
#'
#' \dontrun{
#' # Estimation via nonparametric bootstrap
#' contcont.boot <- mediate(b, c, boot=TRUE, sims=50, treat="treat", mediator="job_seek")
#' summary(contcont.boot)
#' }
#'
#' # Allowing treatment-mediator interaction
#' d <- lm(depress2 ~ treat + job_seek + treat:job_seek + econ_hard + sex + age, data=jobs)
#' contcont.int <- mediate(b, d, sims=50, treat="treat", mediator="job_seek")
#' summary(contcont.int)
#'
#' # Allowing ``moderated mediation'' with respect to age
#' b.int <- lm(job_seek ~ treat*age + econ_hard + sex, data=jobs)
#' d.int <- lm(depress2 ~ treat*job_seek*age + econ_hard + sex, data=jobs)
#' contcont.age20 <- mediate(b.int, d.int, sims=50, treat="treat", mediator="job_seek",
#' covariates = list(age = 20))
#' contcont.age70 <- mediate(b.int, d.int, sims=50, treat="treat", mediator="job_seek",
#' covariates = list(age = 70))
#' summary(contcont.age20)
#' summary(contcont.age70)
#'
#' # Continuous treatment
#' jobs$treat_cont <- jobs$treat + rnorm(nrow(jobs)) # (hypothetical) continuous treatment
#' b.contT <- lm(job_seek ~ treat_cont + econ_hard + sex + age, data=jobs)
#' c.contT <- lm(depress2 ~ treat_cont + job_seek + econ_hard + sex + age, data=jobs)
#' contcont.cont <- mediate(b.contT, c.contT, sims=50,
#' treat="treat_cont", mediator="job_seek",
#' treat.value = 4, control.value = -2)
#' summary(contcont.cont)
#'
#' # Categorical treatment
#' \dontrun{
#' b <- lm(job_seek ~ educ + sex, data=jobs)
#' c <- lm(depress2 ~ educ + job_seek + sex, data=jobs)
#'
#' # compare two categories of educ --- gradwk and somcol
#' model.cat <- mediate(b, c, treat="educ", mediator="job_seek", sims=50,
#' control.value = "gradwk", treat.value = "somcol")
#' summary(model.cat)
#' }
#'
#' ######################################################
#' # Example 2: Binary Outcome and Ordered Mediator
#' ######################################################
#' \dontrun{
#' jobs$job_disc <- as.factor(jobs$job_disc)
#' b.ord <- polr(job_disc ~ treat + econ_hard + sex + age, data=jobs,
#' method="probit", Hess=TRUE)
#' d.bin <- glm(work1 ~ treat + job_disc + econ_hard + sex + age, data=jobs,
#' family=binomial(link="probit"))
#' ordbin <- mediate(b.ord, d.bin, sims=50, treat="treat", mediator="job_disc")
#' summary(ordbin)
#'
#' # Using heteroskedasticity-consistent standard errors
#' ordbin.rb <- mediate(b.ord, d.bin, sims=50, treat="treat", mediator="job_disc",
#' robustSE=TRUE)
#' summary(ordbin.rb)
#'
#' # Using non-parametric bootstrap
#' ordbin.boot <- mediate(b.ord, d.bin, sims=50, treat="treat", mediator="job_disc",
#' boot=TRUE)
#' summary(ordbin.boot)
#' }
#'
#' ######################################################
#' # Example 3: Quantile Causal Mediation Effect
#' ######################################################
#' require(quantreg)
#' c.quan <- rq(depress2 ~ treat + job_seek + econ_hard + sex + age, data=jobs,
#' tau = 0.5) # median
#' contquan <- mediate(b, c.quan, sims=50, treat="treat", mediator="job_seek")
#' summary(contquan)
#'
#' ######################################################
#' # Example 4: GAM Outcome
#' ######################################################
#' \dontrun{
#' require(mgcv)
#' c.gam <- gam(depress2 ~ treat + s(job_seek, bs="cr") +
#' econ_hard + sex + age, data=jobs)
#' contgam <- mediate(b, c.gam, sims=10, treat="treat",
#' mediator="job_seek", boot=TRUE)
#' summary(contgam)
#'
#' # With interaction
#' d.gam <- gam(depress2 ~ treat + s(job_seek, by = treat) +
#' s(job_seek, by = control) + econ_hard + sex + age, data=jobs)
#' contgam.int <- mediate(b, d.gam, sims=10, treat="treat", mediator="job_seek",
#' control = "control", boot=TRUE)
#' summary(contgam.int)
#' }
#' ######################################################
#' # Example 5: Multilevel Outcome and Mediator Models
#' ######################################################
#' \dontrun{
#' require(lme4)
#'
#' # educ: mediator group
#' # occp: outcome group
#'
#' # Varying intercept for mediator
#' model.m <- glmer(job_dich ~ treat + econ_hard + (1 | educ),
#' family = binomial(link = "probit"), data = jobs)
#'
#' # Varying intercept and slope for outcome
#' model.y <- glmer(work1 ~ treat + job_dich + econ_hard + (1 + treat | occp),
#' family = binomial(link = "probit"), data = jobs)
#'
#' # Output based on mediator group ("educ")
#' multilevel <- mediate(model.m, model.y, treat = "treat",
#' mediator = "job_dich", sims=50, group.out="educ")
#'
#' # Output based on outcome group ("occp")
#' # multilevel <- mediate(model.m, model.y, treat = "treat",
#' mediator = "job_dich", sims=50)
#'
#' # Group-average effects
#' summary(multilevel)
#'
#' # Group-specific effects organized by effect
#' summary(multilevel, output="byeffect")
#' # plot(multilevel, group.plots=TRUE)
#' # See summary.mediate.mer and plot.mediate.mer for detailed explanations
#'
#' # Group-specific effects organized by group
#' summary(multilevel, output="bygroup")
#' # See summary.mediate.mer for detailed explanations
#' }
mediate <- function(model.m, model.y, sims = 1000,
boot = FALSE, boot.ci.type = "perc",
treat = "treat.name", mediator = "med.name",
covariates = NULL, outcome = NULL,
control = NULL, conf.level = .95,
control.value = 0, treat.value = 1,
long = TRUE, dropobs = FALSE,
robustSE = FALSE, cluster = NULL, group.out = NULL,
use_speed = FALSE, ...){
cl <- match.call()
# Warn users who still use INT option
if(match("INT", names(cl), 0L)){
warning("'INT' is deprecated - existence of interaction terms is now automatically detected from model formulas")
}
# Warning for robustSE and cluster used with boot
if(robustSE && boot){
warning("'robustSE' is ignored for nonparametric bootstrap")
}
if(!is.null(cluster) && boot){
warning("'cluster' is ignored for nonparametric bootstrap")
}
if(robustSE & !is.null(cluster)){
stop("choose either `robustSE' or `cluster' option, not both")
}
if(boot.ci.type != "bca" & boot.ci.type != "perc"){
stop("choose either `bca' or `perc' for boot.ci.type")
}
# Drop observations not common to both mediator and outcome models
if(dropobs){
odata.m <- model.frame(model.m)
odata.y <- model.frame(model.y)
if(!is.null(cluster)){
if(is.null(row.names(cluster)) &
(nrow(odata.m)!=length(cluster) | nrow(odata.y)!=length(cluster))
){
warning("cluster IDs may not correctly match original observations due to missing data")
}
odata.y <- merge(odata.y, as.data.frame(cluster), sort=FALSE,
by="row.names")
rownames(odata.y) <- odata.y$Row.names
odata.y <- odata.y[,-1L]
}
newdata <- merge(odata.m, odata.y, sort=FALSE,
by=c("row.names", intersect(names(odata.m), names(odata.y))))
rownames(newdata) <- newdata$Row.names
newdata <- newdata[,-1L]
rm(odata.m, odata.y)
call.m <- getCall(model.m)
call.y <- getCall(model.y)
call.m$data <- call.y$data <- newdata
if(c("(weights)") %in% names(newdata)){
call.m$weights <- call.y$weights <- model.weights(newdata)
}
model.m <- eval.parent(call.m)
model.y <- eval.parent(call.y)
if(!is.null(cluster)){
cluster <- factor(newdata[, ncol(newdata)]) # factor drops missing levels
}
}
# Model type indicators
isGam.y <- inherits(model.y, "gam")
isGam.m <- inherits(model.m, "gam")
isGlm.y <- inherits(model.y, "glm") # Note gam and bayesglm also inherits "glm"
isGlm.m <- inherits(model.m, "glm") # Note gam and bayesglm also inherits "glm"
isLm.y <- inherits(model.y, "lm") # Note gam, glm and bayesglm also inherit "lm"
isLm.m <- inherits(model.m, "lm") # Note gam, glm and bayesglm also inherit "lm"
isVglm.y <- inherits(model.y, "vglm")
isRq.y <- inherits(model.y, "rq")
isRq.m <- inherits(model.m, "rq")
isOrdered.y <- inherits(model.y, "polr") # Note bayespolr also inherits "polr"
isOrdered.m <- inherits(model.m, "polr") # Note bayespolr also inherits "polr"
isSurvreg.y <- inherits(model.y, "survreg")
isSurvreg.m <- inherits(model.m, "survreg")
isMer.y <- inherits(model.y, "merMod") # Note lmer and glmer do not inherit "lm" and "glm"
isMer.m <- inherits(model.m, "merMod") # Note lmer and glmer do not inherit "lm" and "glm"
# Record family and link of model.m if glmer
if(isMer.m && class(model.m)[[1]] == "glmerMod"){
m.family <- as.character(model.m@call$family)
if(m.family[1] == "binomial" && (is.na(m.family[2]) || m.family[2] == "logit")){
M.fun <- binomial(link = "logit")
} else if(m.family[1] == "binomial" && m.family[2] == "probit"){
M.fun <- binomial(link = "probit")
} else if(m.family[1] == "binomial" && m.family[2] == "cloglog"){
M.fun <- binomial(link = "cloglog")
} else if(m.family[1] == "poisson" && (is.na(m.family[2]) || m.family[2] == "log")){
M.fun <- poisson(link = "log")
} else if(m.family[1] == "poisson" && m.family[2] == "identity"){
M.fun <- poisson(link = "identity")
} else if(m.family[1] == "poisson" && m.family[2] == "sqrt"){
M.fun <- poisson(link = "sqrt")
} else {
stop("glmer family for the mediation model not supported")
} ### gamma & inverse gaussian excluded (no function to estimate parameters of S4 glmer vs. S3 glm)
}
# Record family and link of model.y if glmer
if(isMer.y && class(model.y)[[1]] == "glmerMod"){
y.family <- as.character(model.y@call$family)
if(y.family[1] == "binomial" && (is.na(y.family[2]) || y.family[2] == "logit")){
Y.fun <- binomial(link = "logit")
} else if(y.family[1] == "binomial" && y.family[2] == "probit"){
Y.fun <- binomial(link = "probit")
} else if(y.family[1] == "binomial" && y.family[2] == "cloglog"){
Y.fun <- binomial(link = "cloglog")
} else if(y.family[1] == "poisson" && (is.na(y.family[2]) || y.family[2] == "log")){
Y.fun <- poisson(link = "log")
} else if(y.family[1] == "poisson" && y.family[2] == "identity"){
Y.fun <- poisson(link = "identity")
} else if(y.family[1] == "poisson" && y.family[2] == "sqrt"){
Y.fun <- poisson(link = "sqrt")
} else {
stop("glmer family for the outcome model not supported")
} ### gamma & inverse gaussian excluded (no function to estimate parameters of S4 glmer vs. S3 glm)
}
# Record family of model.m if glm
if(isGlm.m){
FamilyM <- model.m$family$family
}
# Record family of model.m if glmer
if(isMer.m && class(model.m)[[1]] == "glmerMod"){
FamilyM <- M.fun$family
}
# Record vfamily of model.y if vglm (currently only tobit)
if(isVglm.y){
VfamilyY <- model.y@family@vfamily
}
# Warning for unused options
if(!is.null(control) && !isGam.y){
warning("'control' is only used for GAM outcome models - ignored")
control <- NULL
}
if(!is.null(outcome) && !(isSurvreg.y && boot)){
warning("'outcome' is only relevant for survival outcome models with bootstrap - ignored")
}
# Model frames for M and Y models
m.data <- model.frame(model.m) # Call.M$data
y.data <- model.frame(model.y) # Call.Y$data
if(!is.null(cluster)){
row.names(m.data) <- 1:nrow(m.data)
row.names(y.data) <- 1:nrow(y.data)
if(!is.null(model.m$weights)){
m.weights <- as.data.frame(model.m$weights)
m.name <- as.character(model.m$call$weights)
names(m.weights) <- m.name
m.data <- cbind(m.data, m.weights)
}
if(!is.null(model.y$weights)){
y.weights <- as.data.frame(model.y$weights)
y.name <- as.character(model.y$call$weights)
names(y.weights) <- y.name
y.data <- cbind(y.data, y.weights)
}
}
# group-level mediator
if(isMer.y & !isMer.m){
m.data <- eval(model.m$call$data, environment(formula(model.m))) ### add group ID to m.data
m.data <- na.omit(m.data)
y.data <- na.omit(y.data)
}
# Specify group names
if(isMer.m && isMer.y){
med.group <- names(model.m@flist)
out.group <- names(model.y@flist)
n.med <- length(med.group)
n.out <- length(out.group)
if(n.med > 1 || n.out > 1){
stop("mediate does not support more than two levels per model")
} else {
group.m <- med.group
group.y <- out.group
if(!is.null(group.out) && !(group.out %in% c(group.m, group.y))){
warning("group.out does not match group names used in merMod")
} else if(is.null(group.out)){
group.out <- group.y
}
}
} else if(!isMer.m && isMer.y){
out.group <- names(model.y@flist)
n.out <- length(out.group)
if(n.out > 1){
stop("mediate does not support more than two levels per model")
} else {
group.m <- NULL
group.y <- out.group
group.out <- group.y
}
} else if(isMer.m && !isMer.y){
med.group <- names(model.m@flist)
n.med <- length(med.group)
if(n.med > 1){
stop("mediate does not support more than two levels per model")
} else {
group.m <- med.group
group.y <- NULL
group.out <- group.m
}
} else {
group.m <- NULL
group.y <- NULL
group.out <- NULL
}
# group data if lmer or glmer
if(isMer.m){
group.id.m <- m.data[,group.m]
} else {
group.id.m <- NULL
}
if(isMer.y){
group.id.y <- y.data[,group.y]
} else {
group.id.y <- NULL
}
# group data to be output in summary and plot if lmer or glmer
if(isMer.y && isMer.m){
if(group.out == group.m){
group.id <- m.data[,group.m]
group.name <- group.m
} else {
group.id <- y.data[,group.y]
group.name <- group.y
}
} else if(!isMer.y && isMer.m){
group.id <- m.data[,group.m]
group.name <- group.m
} else if(isMer.y && !isMer.m){ ### group-level mediator
if(!(group.y %in% names(m.data))){
stop("specify group-level variable in mediator data")
} else {
group.id <- y.data[,group.y]
group.name <- group.y
Y.ID<- sort(unique(group.id))
if(is.character(m.data[,group.y])){
M.ID <- sort(as.factor(m.data[,group.y]))
} else {
M.ID <- sort(as.vector(data.matrix(m.data[group.y])))
}
if(length(Y.ID) != length(M.ID)){
stop("groups do not match between mediator and outcome models")
} else {
if(FALSE %in% unique(Y.ID == M.ID)){
stop("groups do not match between mediator and outcome models")
}
}
}
} else {
group.id <- NULL
group.name <- NULL
}
# Numbers of observations and categories
n.m <- nrow(m.data)
n.y <- nrow(y.data)
if(!(isMer.y & !isMer.m)){ ### n.y and n.m are different when group-level mediator is used
if(n.m != n.y){
stop("number of observations do not match between mediator and outcome models")
} else{
n <- n.m
}
m <- length(sort(unique(model.frame(model.m)[,1])))
}
# Extracting weights from models
weights.m <- model.weights(m.data)
weights.y <- model.weights(y.data)
if(!is.null(weights.m) && isGlm.m && FamilyM == "binomial"){
message("weights taken as sampling weights, not total number of trials")
}
if(!is.null(weights.m) && isMer.m && class(model.m)[[1]] == "glmerMod" && FamilyM == "binomial"){
message("weights taken as sampling weights, not total number of trials")
}
if(is.null(weights.m)){
weights.m <- rep(1,nrow(m.data))
}
if(is.null(weights.y)){
weights.y <- rep(1,nrow(y.data))
}
if(!(isMer.y & !isMer.m)){
if(!all(weights.m == weights.y)) {
stop("weights on outcome and mediator models not identical")
} else {
weights <- weights.m
}
} else{
weights <- weights.y ### group-level mediator
}
# Convert character treatment to factor
if(is.character(m.data[,treat])){
m.data[,treat] <- factor(m.data[,treat])
}
if(is.character(y.data[,treat])){
y.data[,treat] <- factor(y.data[,treat])
}
# Convert character mediator to factor
if(is.character(y.data[,mediator])){
y.data[,mediator] <- factor(y.data[,mediator])
}
# Factor treatment indicator
isFactorT.m <- is.factor(m.data[,treat])
isFactorT.y <- is.factor(y.data[,treat])
if(isFactorT.m != isFactorT.y){
stop("treatment variable types differ in mediator and outcome models")
} else {
isFactorT <- isFactorT.y
}
if(isFactorT){
t.levels <- levels(y.data[,treat])
if(treat.value %in% t.levels & control.value %in% t.levels){
cat.0 <- control.value
cat.1 <- treat.value
} else {
cat.0 <- t.levels[1]
cat.1 <- t.levels[2]
warning("treatment and control values do not match factor levels; using ", cat.0, " and ", cat.1, " as control and treatment, respectively")
}
} else {
cat.0 <- control.value
cat.1 <- treat.value
}
# Factor mediator indicator
isFactorM <- is.factor(y.data[,mediator])
if(isFactorM){
m.levels <- levels(y.data[,mediator])
}
# Eventually, we want to use only objects collected in K,
# passing K into intermediate functions, and clean up all stray objects.
K <- as.list(environment())
# rm(list = ls())
############################################################################
############################################################################
### CASE I: EVERYTHING EXCEPT ORDERED OUTCOME
############################################################################
############################################################################
if (!isOrdered.y) {
########################################################################
## Case I-1: Quasi-Bayesian Monte Carlo
########################################################################
if(!boot){
# Error if gam outcome or quantile mediator
if(isGam.m | isGam.y | isRq.m){
stop("'boot' must be 'TRUE' for models used")
}
# Get mean and variance parameters for mediator simulations
if(isSurvreg.m && is.null(survival::survreg.distributions[[model.m$dist]]$scale)){
MModel.coef <- c(coef(model.m), log(model.m$scale))
scalesim.m <- TRUE
} else if(isMer.m){
MModel.fixef <- lme4::fixef(model.m)
MModel.ranef <- lme4::ranef(model.m)
scalesim.m <- FALSE
} else {
MModel.coef <- coef(model.m)
scalesim.m <- FALSE
}
if(isOrdered.m){
if(is.null(model.m$Hess)){
cat("Mediator model object does not contain 'Hessian';")
}
k <- length(MModel.coef)
MModel.var.cov <- vcov(model.m)[(1:k),(1:k)]
} else if(isSurvreg.m){
MModel.var.cov <- vcov(model.m)
} else {
if(robustSE & !isMer.m){
MModel.var.cov <- vcovHC(model.m, ...)
} else if(robustSE & isMer.m){
MModel.var.cov <- vcov(model.m)
warning("robustSE does not support mer class: non-robust SEs are computed for model.m")
} else if(!is.null(cluster)){
if(nrow(m.data)!=length(cluster)){
warning("length of cluster vector differs from # of obs for mediator model")
}
dta <- merge(m.data, as.data.frame(cluster), sort=FALSE,
by="row.names")
fm <- update(model.m, data=dta)
MModel.var.cov <- sandwich::vcovCL(fm, dta[,ncol(dta)])
} else {
MModel.var.cov <- vcov(model.m)
}
}
# Get mean and variance parameters for outcome simulations
if(isSurvreg.y && is.null(survival::survreg.distributions[[model.y$dist]]$scale)){
YModel.coef <- c(coef(model.y), log(model.y$scale))
scalesim.y <- TRUE # indicates if survreg scale parameter is simulated
} else if(isMer.y){
YModel.fixef <- lme4::fixef(model.y)
YModel.ranef <- lme4::ranef(model.y)
scalesim.y <- FALSE
} else {
YModel.coef <- coef(model.y)
scalesim.y <- FALSE
}
if(isRq.y){
YModel.var.cov <- summary(model.y, covariance=TRUE)$cov
} else if(isSurvreg.y){
YModel.var.cov <- vcov(model.y)
} else {
if(robustSE & !isMer.y){
YModel.var.cov <- vcovHC(model.y, ...)
} else if(robustSE & isMer.y){
YModel.var.cov <- vcov(model.y)
warning("robustSE does not support mer class: non-robust SEs are computed for model.y")
} else if(!is.null(cluster)){
if(nrow(y.data)!=length(cluster)){
warning("length of cluster vector differs from # of obs for outcome model")
}
dta <- merge(y.data, as.data.frame(cluster), sort=FALSE,
by="row.names")
fm <- update(model.y, data=dta)
YModel.var.cov <- sandwich::vcovCL(fm, dta[,ncol(dta)])
} else {
YModel.var.cov <- vcov(model.y)
}
}
# Draw model coefficients from normal
se.ranef.new <- function (object) {
se.bygroup <- lme4::ranef(object, condVar = TRUE)
n.groupings <- length(se.bygroup)
for (m in 1:n.groupings) {
vars.m <- attr(se.bygroup[[m]], "postVar")
K <- dim(vars.m)[1]
J <- dim(vars.m)[3]
names.full <- dimnames(se.bygroup[[m]])
se.bygroup[[m]] <- array(NA, c(J, K))
for (j in 1:J) {
se.bygroup[[m]][j, ] <- sqrt(diag(as.matrix(vars.m[,
, j])))
}
dimnames(se.bygroup[[m]]) <- list(names.full[[1]], names.full[[2]])
}
return(se.bygroup)
}
if(isMer.m){
MModel.fixef.vcov <- as.matrix(vcov(model.m))
MModel.fixef.sim <- rmvnorm(sims,mean=MModel.fixef,sigma=MModel.fixef.vcov)
Nm.ranef <- ncol(lme4::ranef(model.m)[[1]])
MModel.ranef.sim <- vector("list",Nm.ranef)
for (d in 1:Nm.ranef){
MModel.ranef.sim[[d]] <- matrix(rnorm(sims*nrow(lme4::ranef(model.m)[[1]]), mean = lme4::ranef(model.m)[[1]][,d], sd = se.ranef.new(model.m)[[1]][,d]), nrow = sims, byrow = TRUE)
}
} else {
if(sum(is.na(MModel.coef)) > 0){
stop("NA in model coefficients; rerun models with nonsingular design matrix")
}
MModel <- rmvnorm(sims, mean=MModel.coef, sigma=MModel.var.cov)
}
if(isMer.y){
YModel.fixef.vcov <- as.matrix(vcov(model.y))
YModel.fixef.sim <- rmvnorm(sims,mean=YModel.fixef,sigma=YModel.fixef.vcov)
Ny.ranef <- ncol(lme4::ranef(model.y)[[1]])
YModel.ranef.sim <- vector("list",Ny.ranef)
for (d in 1:Ny.ranef){
YModel.ranef.sim[[d]] <- matrix(rnorm(sims*nrow(lme4::ranef(model.y)[[1]]), mean = lme4::ranef(model.y)[[1]][,d], sd = se.ranef.new(model.y)[[1]][,d]), nrow = sims, byrow = TRUE)
}
} else {
if(sum(is.na(YModel.coef)) > 0){
stop("NA in model coefficients; rerun models with nonsingular design matrix")
}
YModel <- rmvnorm(sims, mean=YModel.coef, sigma=YModel.var.cov)
}
if(robustSE && (isSurvreg.m | isSurvreg.y)){
warning("`robustSE' ignored for survival models; fit the model with `robust' option instead\n")
}
if(!is.null(cluster) && (isSurvreg.m | isSurvreg.y)){
warning("`cluster' ignored for survival models; fit the model with 'cluster()' term in the formula\n")
}
#####################################
## Mediator Predictions
#####################################
### number of observations are different when group-level mediator is used
if(isMer.y & !isMer.m){
n <- n.m
}
pred.data.t <- pred.data.c <- m.data
if(isFactorT){
pred.data.t[,treat] <- factor(cat.1, levels = t.levels)
pred.data.c[,treat] <- factor(cat.0, levels = t.levels)
} else {
pred.data.t[,treat] <- cat.1
pred.data.c[,treat] <- cat.0
}
if(!is.null(covariates)){
for(p in 1:length(covariates)){
vl <- names(covariates[p])
if(is.factor(pred.data.t[,vl])){
pred.data.t[,vl] <- pred.data.c[,vl] <- factor(covariates[[p]], levels = levels(m.data[,vl]))
} else {
pred.data.t[,vl] <- pred.data.c[,vl] <- covariates[[p]]
}
}
}
mmat.t <- model.matrix(terms(model.m), data=pred.data.t)
mmat.c <- model.matrix(terms(model.m), data=pred.data.c)
### Case I-1-a: GLM Mediator
if(isGlm.m){
muM1 <- model.m$family$linkinv(tcrossprod(MModel, mmat.t))
muM0 <- model.m$family$linkinv(tcrossprod(MModel, mmat.c))
if(FamilyM == "poisson"){
PredictM1 <- matrix(rpois(sims*n, lambda = muM1), nrow = sims)
PredictM0 <- matrix(rpois(sims*n, lambda = muM0), nrow = sims)
} else if (FamilyM == "Gamma") {
shape <- gamma.shape(model.m)$alpha
PredictM1 <- matrix(rgamma(n*sims, shape = shape,
scale = muM1/shape), nrow = sims)
PredictM0 <- matrix(rgamma(n*sims, shape = shape,
scale = muM0/shape), nrow = sims)
} else if (FamilyM == "binomial"){
PredictM1 <- matrix(rbinom(n*sims, size = 1,
prob = muM1), nrow = sims)
PredictM0 <- matrix(rbinom(n*sims, size = 1,
prob = muM0), nrow = sims)
} else if (FamilyM == "gaussian"){
sigma <- sqrt(summary(model.m)$dispersion)
error <- rnorm(sims*n, mean=0, sd=sigma)
PredictM1 <- muM1 + matrix(error, nrow=sims)
PredictM0 <- muM0 + matrix(error, nrow=sims)
} else if (FamilyM == "inverse.gaussian"){
disp <- summary(model.m)$dispersion
PredictM1 <- matrix(SuppDists::rinvGauss(n*sims, nu = muM1,
lambda = 1/disp), nrow = sims)
PredictM0 <- matrix(SuppDists::rinvGauss(n*sims, nu = muM0,
lambda = 1/disp), nrow = sims)
} else {
stop("unsupported glm family")
}
### Case I-1-b: Ordered mediator
} else if(isOrdered.m){
if(model.m$method=="logistic"){
linkfn <- plogis
} else if(model.m$method=="probit") {
linkfn <- pnorm
} else {
stop("unsupported polr method; use 'logistic' or 'probit'")
}
m.cat <- sort(unique(model.frame(model.m)[,1]))
lambda <- model.m$zeta
mmat.t <- mmat.t[,-1]
mmat.c <- mmat.c[,-1]
ystar_m1 <- tcrossprod(MModel, mmat.t)
ystar_m0 <- tcrossprod(MModel, mmat.c)
PredictM1 <- matrix(,nrow=sims, ncol=n)
PredictM0 <- matrix(,nrow=sims, ncol=n)
for(i in 1:sims){
cprobs_m1 <- matrix(NA,n,m)
cprobs_m0 <- matrix(NA,n,m)
probs_m1 <- matrix(NA,n,m)
probs_m0 <- matrix(NA,n,m)
for (j in 1:(m-1)) { # loop to get category-specific probabilities
cprobs_m1[,j] <- linkfn(lambda[j]-ystar_m1[i,])
cprobs_m0[,j] <- linkfn(lambda[j]-ystar_m0[i,])
# cumulative probabilities
probs_m1[,m] <- 1-cprobs_m1[,m-1] # top category
probs_m0[,m] <- 1-cprobs_m0[,m-1] # top category
probs_m1[,1] <- cprobs_m1[,1] # bottom category
probs_m0[,1] <- cprobs_m0[,1] # bottom category
}
for (j in 2:(m-1)){ # middle categories
probs_m1[,j] <- cprobs_m1[,j]-cprobs_m1[,j-1]
probs_m0[,j] <- cprobs_m0[,j]-cprobs_m0[,j-1]
}
draws_m1 <- matrix(NA, n, m)
draws_m0 <- matrix(NA, n, m)
for(ii in 1:n){
draws_m1[ii,] <- t(rmultinom(1, 1, prob = probs_m1[ii,]))
draws_m0[ii,] <- t(rmultinom(1, 1, prob = probs_m0[ii,]))
}
PredictM1[i,] <- apply(draws_m1, 1, which.max)
PredictM0[i,] <- apply(draws_m0, 1, which.max)
}
### Case I-1-c: Linear
} else if(isLm.m){
sigma <- summary(model.m)$sigma
error <- rnorm(sims*n, mean=0, sd=sigma)
muM1 <- tcrossprod(MModel, mmat.t)
muM0 <- tcrossprod(MModel, mmat.c)
PredictM1 <- muM1 + matrix(error, nrow=sims)
PredictM0 <- muM0 + matrix(error, nrow=sims)
rm(error)
### Case I-1-d: Survreg
} else if(isSurvreg.m){
dd <- survival::survreg.distributions[[model.m$dist]]
if (is.null(dd$itrans)){
itrans <- function(x) x
} else {
itrans <- dd$itrans
}
dname <- dd$dist
if(is.null(dname)){
dname <- model.m$dist
}
if(scalesim.m){
scale <- exp(MModel[,ncol(MModel)])
lpM1 <- tcrossprod(MModel[,1:(ncol(MModel)-1)], mmat.t)
lpM0 <- tcrossprod(MModel[,1:(ncol(MModel)-1)], mmat.c)
} else {
scale <- dd$scale
lpM1 <- tcrossprod(MModel, mmat.t)
lpM0 <- tcrossprod(MModel, mmat.c)
}
error <- switch(dname,
extreme = log(rweibull(sims*n, shape=1, scale=1)),
gaussian = rnorm(sims*n),
logistic = rlogis(sims*n),
t = rt(sims*n, df=dd$parms))
PredictM1 <- itrans(lpM1 + scale * matrix(error, nrow=sims))
PredictM0 <- itrans(lpM0 + scale * matrix(error, nrow=sims))
rm(error)
### Case I-1-e: Linear Mixed Effect
} else if(isMer.m && class(model.m)[[1]]=="lmerMod"){
M.RANEF1 <- M.RANEF0 <- 0
for (d in 1:Nm.ranef){
name <- colnames(lme4::ranef(model.m)[[1]])[d]
if(name == "(Intercept)"){
var1 <- var0 <- matrix(1,sims,n) ### RE intercept
} else if(name == treat){ ### RE slope of treat
var1 <- matrix(1,sims,n) ### T = 1
var0 <- matrix(0,sims,n) ### T = 0
}
else {
var1 <- var0 <- matrix(data.matrix(m.data[name]),sims,n,byrow=T) ### RE slope of other variables
}
M.ranef<-matrix(NA,sims,n)
MModel.ranef.sim.d <- MModel.ranef.sim[[d]]
Z <- data.frame(MModel.ranef.sim.d)
if(is.factor(group.id.m)){
colnames(Z) <- levels(group.id.m)
for (i in 1:n){
M.ranef[,i]<-Z[,group.id.m[i]==levels(group.id.m)]
}
} else {
colnames(Z) <- sort(unique(group.id.m))
for (i in 1:n){
M.ranef[,i]<-Z[,group.id.m[i]==sort(unique(group.id.m))]
}
}
M.RANEF1 <- M.ranef*var1 + M.RANEF1 # sum of (random effects*corresponding covarites)
M.RANEF0 <- M.ranef*var0 + M.RANEF0
}
sigma <- attr(lme4::VarCorr(model.m), "sc")
error <- rnorm(sims*n, mean=0, sd=sigma)
muM1 <- tcrossprod(MModel.fixef.sim, mmat.t) + M.RANEF1
muM0 <- tcrossprod(MModel.fixef.sim, mmat.c) + M.RANEF0
PredictM1 <- muM1 + matrix(error, nrow=sims)
PredictM0 <- muM0 + matrix(error, nrow=sims)
rm(error)
### Case I-1-f: Generalized Linear Mixed Effect
} else if(isMer.m && class(model.m)[[1]]=="glmerMod"){
M.RANEF1 <-M.RANEF0 <- 0 ### 1=RE for M(1); 0=RE for M(0)
for (d in 1:Nm.ranef){
name <- colnames(lme4::ranef(model.m)[[1]])[d]
if(name == "(Intercept)"){
var1 <- var0 <- matrix(1,sims,n) ### RE intercept
} else if(name == treat){ ### RE slope of treat
var1 <- matrix(1,sims,n) ### T = 1
var0 <- matrix(0,sims,n) ### T = 0
} else {
var1 <- var0 <- matrix(data.matrix(m.data[name]),sims,n,byrow=T) ### RE slope of other variables
}
M.ranef<-matrix(NA,sims,n)
MModel.ranef.sim.d <- MModel.ranef.sim[[d]]
Z <- data.frame(MModel.ranef.sim.d)
if(is.factor(group.id.m)){
colnames(Z) <- levels(group.id.m)
for (i in 1:n){
M.ranef[,i]<-Z[,group.id.m[i]==levels(group.id.m)]
}
} else {
colnames(Z) <- sort(unique(group.id.m))
for (i in 1:n){
M.ranef[,i]<-Z[,group.id.m[i]==sort(unique(group.id.m))]
}
}
M.RANEF1 <- M.ranef*var1 + M.RANEF1 # sum of (random effects*corresponding covarites)
M.RANEF0 <- M.ranef*var0 + M.RANEF0
}
muM1 <- M.fun$linkinv(tcrossprod(MModel.fixef.sim,mmat.t) + M.RANEF1)
muM0 <- M.fun$linkinv(tcrossprod(MModel.fixef.sim,mmat.c) + M.RANEF0)
FamilyM <- M.fun$family
if(FamilyM == "poisson"){
PredictM1 <- matrix(rpois(sims*n, lambda = muM1), nrow = sims)
PredictM0 <- matrix(rpois(sims*n, lambda = muM0), nrow = sims)
} else if (FamilyM == "binomial"){
PredictM1 <- matrix(rbinom(n*sims, size = 1,
prob = muM1), nrow = sims)
PredictM0 <- matrix(rbinom(n*sims, size = 1,
prob = muM0), nrow = sims)
}
} else {
stop("mediator model is not yet implemented")
}
### group-level mediator : J -> NJ
if(isMer.y & !isMer.m){
J <- nrow(m.data)
if(is.character(m.data[,group.y])){
group.id.m <- as.factor(m.data[,group.y])
} else {
group.id.m <- as.vector(data.matrix(m.data[group.y]))
}
v1 <- v0 <- matrix(NA, sims, length(group.id.y))
num.m <- 1:J
num.y <- 1:length(group.id.y)
for (j in 1:J){
id.y <- unique(group.id.y)[j]
NUM.M <- num.m[group.id.m == id.y]
NUM.Y <- num.y[group.id.y == id.y]
v1[, NUM.Y] <- PredictM1[, NUM.M]
v0[, NUM.Y] <- PredictM0[, NUM.M]
}
PredictM1 <- v1
PredictM0 <- v0
}
rm(mmat.t, mmat.c)
#####################################
## Outcome Predictions
#####################################
### number of observations are different when group-level mediator is used
if(isMer.y & !isMer.m){
n <- n.y
}
effects.tmp <- array(NA, dim = c(n, sims, 4))
if(isMer.y){
Y.RANEF1 <- Y.RANEF2 <- Y.RANEF3 <- Y.RANEF4 <- 0
### 1=RE for Y(1,M(1)); 2=RE for Y(1,M(0)); 3=RE for Y(0,M(1)); 4=RE for Y(0,M(0))
for (d in 1:Ny.ranef){
name <- colnames(lme4::ranef(model.y)[[1]])[d]
if(name == "(Intercept)"){
var1 <- var2 <- var3 <- var4 <- matrix(1,sims,n)
} else if(name == treat){
var1 <- matrix(1,sims,n)
var2 <- matrix(1,sims,n)
var3 <- matrix(0,sims,n)
var4 <- matrix(0,sims,n)
} else if(name == mediator){
var1 <- PredictM1
var2 <- PredictM0
var3 <- PredictM1
var4 <- PredictM0
} else {
if(name %in% colnames(y.data)){
var1 <- var2 <- var3 <- var4 <- matrix(data.matrix(y.data[name]),sims,n,byrow=T)
} else {
int.term.name <- strsplit(name, ":")[[1]]
int.term <- rep(1, nrow(y.data))
for (p in 1:length(int.term.name)){
int.term <- y.data[int.term.name[p]][[1]] * int.term
}
var1 <- var2 <- var3 <- var4 <- matrix(int.term,sims,n,byrow=T)
}
}
Y.ranef<-matrix(NA,sims,n)
YModel.ranef.sim.d <- YModel.ranef.sim[[d]]
Z <- data.frame(YModel.ranef.sim.d)
if(is.factor(group.id.y)){
colnames(Z) <- levels(group.id.y)
for (i in 1:n){
Y.ranef[,i]<-Z[,group.id.y[i]==levels(group.id.y)]
}
} else {
colnames(Z) <- sort(unique(group.id.y))
for (i in 1:n){
Y.ranef[,i]<-Z[,group.id.y[i]==sort(unique(group.id.y))]
}
}
Y.RANEF1 <- Y.ranef*var1 + Y.RANEF1 # sum of (random effects*corresponding covarites)
Y.RANEF2 <- Y.ranef*var2 + Y.RANEF2
Y.RANEF3 <- Y.ranef*var3 + Y.RANEF3
Y.RANEF4 <- Y.ranef*var4 + Y.RANEF4
}
}
for(e in 1:4){
tt <- switch(e, c(1,1,1,0), c(0,0,1,0), c(1,0,1,1), c(1,0,0,0))
Pr1 <- matrix(, nrow=n, ncol=sims)
Pr0 <- matrix(, nrow=n, ncol=sims)
for(j in 1:sims){
pred.data.t <- pred.data.c <- y.data
if(!is.null(covariates)){
for(p in 1:length(covariates)){
vl <- names(covariates[p])
if(is.factor(pred.data.t[,vl])){
pred.data.t[,vl] <- pred.data.c[,vl] <- factor(covariates[[p]], levels = levels(y.data[,vl]))
} else {
pred.data.t[,vl] <- pred.data.c[,vl] <- covariates[[p]]
}
}
}
# Set treatment values
cat.t <- ifelse(tt[1], cat.1, cat.0)
cat.c <- ifelse(tt[2], cat.1, cat.0)
cat.t.ctrl <- ifelse(tt[1], cat.0, cat.1)
cat.c.ctrl <- ifelse(tt[2], cat.0, cat.1)
if(isFactorT){
pred.data.t[,treat] <- factor(cat.t, levels = t.levels)
pred.data.c[,treat] <- factor(cat.c, levels = t.levels)
if(!is.null(control)){
pred.data.t[,control] <- factor(cat.t.ctrl, levels = t.levels)
pred.data.c[,control] <- factor(cat.c.ctrl, levels = t.levels)
}
} else {
pred.data.t[,treat] <- cat.t
pred.data.c[,treat] <- cat.c
if(!is.null(control)){
pred.data.t[,control] <- cat.t.ctrl
pred.data.c[,control] <- cat.c.ctrl
}
}
# Set mediator values
PredictMt <- PredictM1[j,] * tt[3] + PredictM0[j,] * (1 - tt[3])
PredictMc <- PredictM1[j,] * tt[4] + PredictM0[j,] * (1 - tt[4])
if(isFactorM) {
pred.data.t[,mediator] <- factor(PredictMt, levels=1:m, labels=m.levels)
pred.data.c[,mediator] <- factor(PredictMc, levels=1:m, labels=m.levels)
} else {
pred.data.t[,mediator] <- PredictMt
pred.data.c[,mediator] <- PredictMc
}
ymat.t <- model.matrix(terms(model.y), data=pred.data.t)
ymat.c <- model.matrix(terms(model.y), data=pred.data.c)
if(isVglm.y){
if(VfamilyY=="tobit") {
Pr1.tmp <- ymat.t %*% YModel[j,-2]
Pr0.tmp <- ymat.c %*% YModel[j,-2]
Pr1[,j] <- pmin(pmax(Pr1.tmp, model.y@misc$Lower), model.y@misc$Upper)
Pr0[,j] <- pmin(pmax(Pr0.tmp, model.y@misc$Lower), model.y@misc$Upper)
} else {
stop("outcome model is in unsupported vglm family")
}
} else if(scalesim.y){
Pr1[,j] <- t(as.matrix(YModel[j,1:(ncol(YModel)-1)])) %*% t(ymat.t)
Pr0[,j] <- t(as.matrix(YModel[j,1:(ncol(YModel)-1)])) %*% t(ymat.c)
} else if(isMer.y){
if(e == 1){ ### mediation(1)
Y.RANEF.A <- Y.RANEF1
Y.RANEF.B <- Y.RANEF2
} else if(e == 2){ ### mediation(0)
Y.RANEF.A <- Y.RANEF3
Y.RANEF.B <- Y.RANEF4
} else if(e == 3){ ### direct(1)
Y.RANEF.A <- Y.RANEF1
Y.RANEF.B <- Y.RANEF3
} else { ### direct(0)
Y.RANEF.A <- Y.RANEF2
Y.RANEF.B <- Y.RANEF4
}
Pr1[,j] <- t(as.matrix(YModel.fixef.sim[j,])) %*% t(ymat.t) + Y.RANEF.A[j,]
Pr0[,j] <- t(as.matrix(YModel.fixef.sim[j,])) %*% t(ymat.c) + Y.RANEF.B[j,]
} else {
Pr1[,j] <- t(as.matrix(YModel[j,])) %*% t(ymat.t)
Pr0[,j] <- t(as.matrix(YModel[j,])) %*% t(ymat.c)
}
rm(ymat.t, ymat.c, pred.data.t, pred.data.c)
}
if(isGlm.y){
Pr1 <- apply(Pr1, 2, model.y$family$linkinv)
Pr0 <- apply(Pr0, 2, model.y$family$linkinv)
} else if(isSurvreg.y){
dd <- survival::survreg.distributions[[model.y$dist]]
if (is.null(dd$itrans)){
itrans <- function(x) x
} else {
itrans <- dd$itrans
}
Pr1 <- apply(Pr1, 2, itrans)
Pr0 <- apply(Pr0, 2, itrans)
} else if(isMer.y && class(model.y)[[1]] == "glmerMod"){
Pr1 <- apply(Pr1, 2, Y.fun$linkinv)
Pr0 <- apply(Pr0, 2, Y.fun$linkinv)
}
effects.tmp[,,e] <- Pr1 - Pr0 ### e=1:mediation(1); e=2:mediation(0); e=3:direct(1); e=4:direct(0)
rm(Pr1, Pr0)
}
if(!isMer.m && !isMer.y){
rm(PredictM1, PredictM0, YModel, MModel)
} else if(!isMer.m && isMer.y){
rm(PredictM1, PredictM0, YModel.ranef.sim)
} else {
rm(PredictM1, PredictM0, MModel.ranef.sim)
}
et1<-effects.tmp[,,1] ### mediation effect (1)
et2<-effects.tmp[,,2] ### mediation effect (0)
et3<-effects.tmp[,,3] ### direct effect (1)
et4<-effects.tmp[,,4] ### direct effect (0)
delta.1 <- t(as.matrix(apply(et1, 2, weighted.mean, w=weights)))
delta.0 <- t(as.matrix(apply(et2, 2, weighted.mean, w=weights)))
zeta.1 <- t(as.matrix(apply(et3, 2, weighted.mean, w=weights)))
zeta.0 <- t(as.matrix(apply(et4, 2, weighted.mean, w=weights)))
rm(effects.tmp)
tau <- (zeta.1 + delta.0 + zeta.0 + delta.1)/2
nu.0 <- delta.0/tau
nu.1 <- delta.1/tau
delta.avg <- (delta.1 + delta.0)/2
zeta.avg <- (zeta.1 + zeta.0)/2
nu.avg <- (nu.1 + nu.0)/2
d0 <- mean(delta.0) # mediation effect
d1 <- mean(delta.1)
z1 <- mean(zeta.1) # direct effect
z0 <- mean(zeta.0)
tau.coef <- mean(tau) # total effect
n0 <- median(nu.0)
n1 <- median(nu.1)
d.avg <- (d0 + d1)/2
z.avg <- (z0 + z1)/2
n.avg <- (n0 + n1)/2
if(isMer.y | isMer.m){
if(!is.null(group.m) && group.name == group.m){
G<-length(unique(group.id.m))
delta.1.group<-matrix(NA,G,sims)
delta.0.group<-matrix(NA,G,sims)
zeta.1.group<-matrix(NA,G,sims)
zeta.0.group<-matrix(NA,G,sims)
for (g in 1:G){
delta.1.group[g,] <- t(apply(matrix(et1[group.id.m==unique(group.id.m)[g],], ncol=sims), 2, weighted.mean, w=weights[group.id.m==unique(group.id.m)[g]]))
delta.0.group[g,] <- t(apply(matrix(et2[group.id.m==unique(group.id.m)[g],], ncol=sims), 2, weighted.mean, w=weights[group.id.m==unique(group.id.m)[g]]))
zeta.1.group[g,] <- t(apply(matrix(et3[group.id.m==unique(group.id.m)[g],], ncol=sims), 2, weighted.mean, w=weights[group.id.m==unique(group.id.m)[g]]))
zeta.0.group[g,] <- t(apply(matrix(et4[group.id.m==unique(group.id.m)[g],], ncol=sims), 2, weighted.mean, w=weights[group.id.m==unique(group.id.m)[g]]))
}
} else {
G<-length(unique(group.id.y))
delta.1.group<-matrix(NA,G,sims)
delta.0.group<-matrix(NA,G,sims)
zeta.1.group<-matrix(NA,G,sims)
zeta.0.group<-matrix(NA,G,sims)
for (g in 1:G){
delta.1.group[g,] <- t(apply(matrix(et1[group.id.y==unique(group.id.y)[g],], ncol=sims), 2, weighted.mean, w=weights[group.id.y==unique(group.id.y)[g]]))
delta.0.group[g,] <- t(apply(matrix(et2[group.id.y==unique(group.id.y)[g],], ncol=sims), 2, weighted.mean, w=weights[group.id.y==unique(group.id.y)[g]]))
zeta.1.group[g,] <- t(apply(matrix(et3[group.id.y==unique(group.id.y)[g],], ncol=sims), 2, weighted.mean, w=weights[group.id.y==unique(group.id.y)[g]]))
zeta.0.group[g,] <- t(apply(matrix(et4[group.id.y==unique(group.id.y)[g],], ncol=sims), 2, weighted.mean, w=weights[group.id.y==unique(group.id.y)[g]]))
}
}
tau.group <- (zeta.1.group + delta.0.group + zeta.0.group + delta.1.group)/2
nu.0.group <- delta.0.group/tau.group
nu.1.group <- delta.1.group/tau.group
delta.avg.group <- (delta.1.group + delta.0.group)/2
zeta.avg.group <- (zeta.1.group + zeta.0.group)/2
nu.avg.group <- (nu.1.group + nu.0.group)/2
d0.group <- apply(delta.0.group,1,mean) # mediation effect
d1.group <- apply(delta.1.group,1,mean)
z1.group <- apply(zeta.1.group,1,mean) # direct effect
z0.group <- apply(zeta.0.group,1,mean)
tau.coef.group <- apply(tau.group,1,mean) # total effect
n0.group <- apply(nu.0.group,1,median)
n1.group <- apply(nu.1.group,1,median)
d.avg.group <- (d0.group + d1.group)/2
z.avg.group <- (z0.group + z1.group)/2
n.avg.group <- (n0.group + n1.group)/2
}
########################################################################
## Case I-2: Nonparametric Bootstrap
########################################################################
} else {
# Error if lmer or glmer
if(isMer.m | isMer.y){
stop("'boot' must be 'FALSE' for models used")
}
Call.M <- getCall(model.m)
Call.Y <- getCall(model.y)
if (isSurvreg.m){
if (ncol(model.m$y) > 2)
stop("unsupported censoring type")
mname <- names(m.data)[1]
if (substr(mname, 1, 4) != "Surv")
stop("refit the survival model with `Surv' used directly in model formula")
}
if (isSurvreg.y){
if (ncol(model.y$y) > 2)
stop("unsupported censoring type")
yname <- names(y.data)[1]
if (substr(yname, 1, 4) != "Surv")
stop("refit the survival model with `Surv' used directly in model formula")
if (is.null(outcome))
stop("`outcome' must be supplied for survreg outcome with boot")
}
# Bootstrap QoI
message("Running nonparametric bootstrap\n")
# Make objects available to med.fun
environment(med.fun) <- environment()
D <- boot::boot(data = y.data,
statistic = med.fun,
R = sims,
sim = "ordinary",
m.data = m.data,
...)
# drop = F to maintain column as matrix for backward-compatibility
delta.1 <- D$t[, 1, drop = FALSE]
delta.0 <- D$t[, 2, drop = FALSE]
zeta.1 <- D$t[, 3, drop = FALSE]
zeta.0 <- D$t[, 4, drop = FALSE]
# Generate QoIs for actual sample
D <- med.fun(y.data = y.data, m.data = m.data, index = 1:n)
d1 <- D["d1"]
d0 <- D["d0"]
z1 <- D["z1"]
z0 <- D["z0"]
# Unname objects for backward-compatibility
list2env(
lapply(list(d1 = d1, d0 = d0, z1 = z1, z0 = z0,
delta.1 = delta.1, delta.0 = delta.0,
zeta.1 = zeta.1, zeta.0 = zeta.0),
unname),
envir = environment()
)
tau.coef <- (d1 + d0 + z1 + z0)/2
n0 <- d0/tau.coef
n1 <- d1/tau.coef
d.avg <- (d1 + d0)/2
z.avg <- (z1 + z0)/2
n.avg <- (n0 + n1)/2
tau <- (delta.1 + delta.0 + zeta.1 + zeta.0)/2
nu.0 <- delta.0/tau
nu.1 <- delta.1/tau
delta.avg <- (delta.0 + delta.1)/2
zeta.avg <- (zeta.0 + zeta.1)/2
nu.avg <- (nu.0 + nu.1)/2
} # nonpara boot branch ends
########################################################################
## Compute Outputs and Put Them Together
########################################################################
low <- (1 - conf.level)/2
high <- 1 - low
if (boot & boot.ci.type == "bca"){
BC.CI <- function(theta){
z.inv <- length(theta[theta < mean(theta)])/sims
z <- qnorm(z.inv)
U <- (sims - 1) * (mean(theta) - theta)
top <- sum(U^3)
under <- 6 * (sum(U^2))^{3/2}
a <- top / under
lower.inv <- pnorm(z + (z + qnorm(low))/(1 - a * (z + qnorm(low))))
lower2 <- lower <- quantile(theta, lower.inv)
upper.inv <- pnorm(z + (z + qnorm(high))/(1 - a * (z + qnorm(high))))
upper2 <- upper <- quantile(theta, upper.inv)
return(c(lower, upper))
}
d0.ci <- BC.CI(delta.0)
d1.ci <- BC.CI(delta.1)
tau.ci <- BC.CI(tau)
z1.ci <- BC.CI(zeta.1)
z0.ci <- BC.CI(zeta.0)
n0.ci <- BC.CI(nu.0)
n1.ci <- BC.CI(nu.1)
d.avg.ci <- BC.CI(delta.avg)
z.avg.ci <- BC.CI(zeta.avg)
n.avg.ci <- BC.CI(nu.avg)
} else {
d0.ci <- quantile(delta.0, c(low,high), na.rm=TRUE)
d1.ci <- quantile(delta.1, c(low,high), na.rm=TRUE)
tau.ci <- quantile(tau, c(low,high), na.rm=TRUE)
z1.ci <- quantile(zeta.1, c(low,high), na.rm=TRUE)
z0.ci <- quantile(zeta.0, c(low,high), na.rm=TRUE)
n0.ci <- quantile(nu.0, c(low,high), na.rm=TRUE)
n1.ci <- quantile(nu.1, c(low,high), na.rm=TRUE)
d.avg.ci <- quantile(delta.avg, c(low,high), na.rm=TRUE)
z.avg.ci <- quantile(zeta.avg, c(low,high), na.rm=TRUE)
n.avg.ci <- quantile(nu.avg, c(low,high), na.rm=TRUE)
}
# p-values
d0.p <- pval(delta.0, d0)
d1.p <- pval(delta.1, d1)
d.avg.p <- pval(delta.avg, d.avg)
z0.p <- pval(zeta.0, z0)
z1.p <- pval(zeta.1, z1)
z.avg.p <- pval(zeta.avg, z.avg)
n0.p <- pval(nu.0, n0)
n1.p <- pval(nu.1, n1)
n.avg.p <- pval(nu.avg, n.avg)
tau.p <- pval(tau, tau.coef)
if(isMer.y | isMer.m){
QUANT<-function(object){
z<-quantile(object,c(low,high),na.rm=TRUE)
return(z)
}
d0.ci.group <- t(apply(delta.0.group,1,QUANT))
d1.ci.group <- t(apply(delta.1.group,1,QUANT))
tau.ci.group <- t(apply(tau.group,1,QUANT))
z1.ci.group <- t(apply(zeta.1.group,1,QUANT))
z0.ci.group <- t(apply(zeta.0.group,1,QUANT))
n0.ci.group <- t(apply(nu.0.group,1,QUANT))
n1.ci.group <- t(apply(nu.1.group,1,QUANT))
d.avg.ci.group <- t(apply(delta.avg.group,1,QUANT))
z.avg.ci.group <- t(apply(zeta.avg.group,1,QUANT))
n.avg.ci.group <- t(apply(nu.avg.group,1,QUANT))
d0.p.group<-rep(NA,G)
d1.p.group<-rep(NA,G)
d.avg.p.group<-rep(NA,G)
z0.p.group<-rep(NA,G)
z1.p.group<-rep(NA,G)
z.avg.p.group<-rep(NA,G)
n0.p.group<-rep(NA,G)
n1.p.group<-rep(NA,G)
n.avg.p.group<-rep(NA,G)
tau.p.group<-rep(NA,G)
for (g in 1:G){
d0.p.group[g] <- pval(delta.0.group[g,], d0.group[g])
d1.p.group[g] <- pval(delta.1.group[g,], d1.group[g])
d.avg.p.group[g] <- pval(delta.avg.group[g,], d.avg.group[g])
z0.p.group[g] <- pval(zeta.0.group[g,], z0.group[g])
z1.p.group[g] <- pval(zeta.1.group[g,], z1.group[g])
z.avg.p.group[g] <- pval(zeta.avg.group[g,], z.avg.group[g])
n0.p.group[g] <- pval(nu.0.group[g,], n0.group[g])
n1.p.group[g] <- pval(nu.1.group[g,], n1.group[g])
n.avg.p.group[g] <- pval(nu.avg.group[g,], n.avg.group[g])
tau.p.group[g] <- pval(tau.group[g,], tau.coef.group[g])
}
}
# Detect whether models include T-M interaction
INT <- paste(treat,mediator,sep=":") %in% attr(terms(model.y),"term.labels") |
paste(mediator,treat,sep=":") %in% attr(terms(model.y),"term.labels")
if(!INT & isGam.y){
INT <- !isTRUE(all.equal(d0, d1)) # if gam, determine empirically
}
if(long && !isMer.y && !isMer.m) {
out <- list(
d0=d0, d1=d1, d0.ci=d0.ci, d1.ci=d1.ci,
d0.p=d0.p, d1.p=d1.p,
d0.sims=delta.0, d1.sims=delta.1,
z0=z0, z1=z1, z0.ci=z0.ci, z1.ci=z1.ci,
z0.p=z0.p, z1.p=z1.p,
z0.sims=zeta.0, z1.sims=zeta.1,
n0=n0, n1=n1, n0.ci=n0.ci, n1.ci=n1.ci,
n0.p=n0.p, n1.p=n1.p,
n0.sims=nu.0, n1.sims=nu.1,
tau.coef=tau.coef, tau.ci=tau.ci, tau.p=tau.p,
tau.sims=tau,
d.avg=d.avg, d.avg.p=d.avg.p, d.avg.ci=d.avg.ci, d.avg.sims=delta.avg,
z.avg=z.avg, z.avg.p=z.avg.p, z.avg.ci=z.avg.ci, z.avg.sims=zeta.avg,
n.avg=n.avg, n.avg.p=n.avg.p, n.avg.ci=n.avg.ci, n.avg.sims=nu.avg,
boot=boot, boot.ci.type=boot.ci.type,
treat=treat, mediator=mediator,
covariates=covariates,
INT=INT, conf.level=conf.level,
model.y=model.y, model.m=model.m,
control.value=control.value, treat.value=treat.value,
nobs=n, sims=sims, call=cl,
robustSE = robustSE, cluster = cluster
)
class(out) <- "mediate"
}
if(!long && !isMer.y && !isMer.m){
out <- list(d0=d0, d1=d1, d0.ci=d0.ci, d1.ci=d1.ci,
d0.p=d0.p, d1.p=d1.p,
z0=z0, z1=z1, z0.ci=z0.ci, z1.ci=z1.ci,
z0.p=z0.p, z1.p=z1.p,
n0=n0, n1=n1, n0.ci=n0.ci, n1.ci=n1.ci,
n0.p=n0.p, n1.p=n1.p,
tau.coef=tau.coef, tau.ci=tau.ci, tau.p=tau.p,
d.avg=d.avg, d.avg.p=d.avg.p, d.avg.ci=d.avg.ci,
z.avg=z.avg, z.avg.p=z.avg.p, z.avg.ci=z.avg.ci,
n.avg=n.avg, n.avg.p=n.avg.p, n.avg.ci=n.avg.ci,
boot=boot, boot.ci.type=boot.ci.type,
treat=treat, mediator=mediator,
covariates=covariates,
INT=INT, conf.level=conf.level,
model.y=model.y, model.m=model.m,
control.value=control.value, treat.value=treat.value,
nobs=n, sims=sims, call=cl,
robustSE = robustSE, cluster = cluster)
class(out) <- "mediate"
}
if(long && (isMer.y || isMer.m)) {
out <- list(d0=d0, d1=d1, d0.ci=d0.ci, d1.ci=d1.ci,
d0.p=d0.p, d1.p=d1.p,
d0.sims=delta.0, d1.sims=delta.1,
z0=z0, z1=z1, z0.ci=z0.ci, z1.ci=z1.ci,
z0.p=z0.p, z1.p=z1.p,
z0.sims=zeta.0, z1.sims=zeta.1,
n0=n0, n1=n1, n0.ci=n0.ci, n1.ci=n1.ci,
n0.p=n0.p, n1.p=n1.p,
n0.sims=nu.0, n1.sims=nu.1,
tau.coef=tau.coef, tau.ci=tau.ci, tau.p=tau.p,
tau.sims=tau,
d.avg=d.avg, d.avg.p=d.avg.p, d.avg.ci=d.avg.ci, d.avg.sims=delta.avg,
z.avg=z.avg, z.avg.p=z.avg.p, z.avg.ci=z.avg.ci, z.avg.sims=zeta.avg,
n.avg=n.avg, n.avg.p=n.avg.p, n.avg.ci=n.avg.ci, n.avg.sims=nu.avg,
d0.group=d0.group, d1.group=d1.group, d0.ci.group=d0.ci.group, d1.ci.group=d1.ci.group,
d0.p.group=d0.p.group, d1.p.group=d1.p.group,
d0.sims.group=delta.0.group, d1.sims.group=delta.1.group,
z0.group=z0.group, z1.group=z1.group, z0.ci.group=z0.ci.group, z1.ci.group=z1.ci.group,
z0.p.group=z0.p.group, z1.p.group=z1.p.group,
z0.sims.group=zeta.0.group, z1.sims.group=zeta.1.group,
n0.group=n0.group, n1.group=n1.group, n0.ci.group=n0.ci.group, n1.ci.group=n1.ci.group,
n0.p.group=n0.p.group, n1.p.group=n1.p.group,
n0.sims.group=nu.0.group, n1.sims.group=nu.1.group,
tau.coef.group=tau.coef.group, tau.ci.group=tau.ci.group, tau.p.group=tau.p.group,
tau.sims.group=tau.group,
d.avg.group=d.avg.group, d.avg.p.group=d.avg.p.group, d.avg.ci.group=d.avg.ci.group, d.avg.sims.group=delta.avg.group,
z.avg.group=z.avg.group, z.avg.p.group=z.avg.p.group, z.avg.ci.group=z.avg.ci.group, z.avg.sims.group=zeta.avg.group,
n.avg.group=n.avg.group, n.avg.p.group=n.avg.p.group, n.avg.ci.group=n.avg.ci.group, n.avg.sims.group=nu.avg.group,
boot=boot, boot.ci.type=boot.ci.type,
treat=treat, mediator=mediator,
covariates=covariates,
INT=INT, conf.level=conf.level,
model.y=model.y, model.m=model.m,
control.value=control.value, treat.value=treat.value,
nobs=n, sims=sims, call=cl,
group.m=group.m,group.y=group.y,group.name=group.name,
group.id.m=group.id.m,group.id.y=group.id.y,group.id=group.id,
robustSE = robustSE, cluster = cluster)
class(out) <- "mediate.mer"
}
if(!long && (isMer.y || isMer.m)){
out <- list(d0=d0, d1=d1, d0.ci=d0.ci, d1.ci=d1.ci,
d0.p=d0.p, d1.p=d1.p,
z0=z0, z1=z1, z0.ci=z0.ci, z1.ci=z1.ci,
z0.p=z0.p, z1.p=z1.p,
n0=n0, n1=n1, n0.ci=n0.ci, n1.ci=n1.ci,
n0.p=n0.p, n1.p=n1.p,
tau.coef=tau.coef, tau.ci=tau.ci, tau.p=tau.p,
d.avg=d.avg, d.avg.p=d.avg.p, d.avg.ci=d.avg.ci,
z.avg=z.avg, z.avg.p=z.avg.p, z.avg.ci=z.avg.ci,
n.avg=n.avg, n.avg.p=n.avg.p, n.avg.ci=n.avg.ci,
d0.group=d0.group, d1.group=d1.group, d0.ci.group=d0.ci.group, d1.ci.group=d1.ci.group,
d0.p.group=d0.p.group, d1.p.group=d1.p.group,
z0.group=z0.group, z1.group=z1.group, z0.ci.group=z0.ci.group, z1.ci.group=z1.ci.group,
z0.p.group=z0.p.group, z1.p.group=z1.p.group,
n0.group=n0.group, n1.group=n1.group, n0.ci.group=n0.ci.group, n1.ci.group=n1.ci.group,
n0.p.group=n0.p.group, n1.p.group=n1.p.group,
tau.coef.group=tau.coef.group, tau.ci.group=tau.ci.group, tau.p.group=tau.p.group,
d.avg.group=d.avg.group, d.avg.p.group=d.avg.p.group, d.avg.ci.group=d.avg.ci.group,
z.avg.group=z.avg.group, z.avg.p.group=z.avg.p.group, z.avg.ci.group=z.avg.ci.group,
n.avg.group=n.avg.group, n.avg.p.group=n.avg.p.group, n.avg.ci.group=n.avg.ci.group,
boot=boot, boot.ci.type=boot.ci.type,
treat=treat, mediator=mediator,
covariates=covariates,
INT=INT, conf.level=conf.level,
model.y=model.y, model.m=model.m,
control.value=control.value, treat.value=treat.value,
nobs=n, sims=sims, call=cl,
group.m=group.m,group.y=group.y,group.name=group.name,
group.id.m=group.id.m,group.id.y=group.id.y,group.id=group.id,
robustSE = robustSE, cluster = cluster)
class(out) <- "mediate.mer"
}
out
############################################################################
############################################################################
### CASE II: ORDERED OUTCOME
############################################################################
############################################################################
} else {
if(boot != TRUE){
warning("ordered outcome model can only be used with nonparametric bootstrap - option forced")
boot <- TRUE
}
if(isMer.m){
stop("merMod class is not supported for ordered outcome")
}
n.ycat <- length(unique(model.response(y.data)))
# Bootstrap QoI
message("Running nonparametric bootstrap for ordered outcome\n")
# Make objects available to med.fun.ordered
environment(med.fun.ordered) <- environment()
D <- boot::boot(data = y.data,
statistic = med.fun.ordered,
R = sims,
sim = "ordinary",
m.data = m.data,
...)
# Extract estimates from resampling
col_index <- lapply(c("d1", "d0", "z1", "z0"), function(i) {
grep(i, names(D$t0))
})
delta.1 <- D$t[, col_index[[1]]]
delta.0 <- D$t[, col_index[[2]]]
zeta.1 <- D$t[, col_index[[3]]]
zeta.0 <- D$t[, col_index[[4]]]
# Generate QoIs for actual sample
D <- med.fun.ordered(y.data = y.data, m.data = m.data, index = 1:n)
d1 <- D[col_index[[1]]]
d0 <- D[col_index[[2]]]
z1 <- D[col_index[[3]]]
z0 <- D[col_index[[4]]]
tau.coef <- (d1 + d0 + z1 + z0)/2
tau <- (zeta.1 + zeta.0 + delta.0 + delta.1)/2
########################################################################
## Compute Outputs and Put Them Together
########################################################################
low <- (1 - conf.level)/2
high <- 1 - low
if(boot.ci.type == "bca"){
BC.CI <- function(theta){
z.inv <- length(theta[theta < mean(theta)])/sims
z <- qnorm(z.inv)
U <- (sims - 1) * (mean(theta) - theta)
top <- sum(U^3)
under <- 6 * (sum(U^2))^{3/2}
a <- top / under
lower.inv <- pnorm(z + (z + qnorm(low))/(1 - a * (z + qnorm(low))))
lower2 <- lower <- quantile(theta, lower.inv)
upper.inv <- pnorm(z + (z + qnorm(high))/(1 - a * (z + qnorm(high))))
upper2 <- upper <- quantile(theta, upper.inv)
return(c(lower, upper))
}
d0.ci <- BC.CI(delta.0)
d1.ci <- BC.CI(delta.1)
tau.ci <- BC.CI(tau)
z1.ci <- BC.CI(zeta.1)
z0.ci <- BC.CI(zeta.0)
} else {
CI <- function(theta){
return(quantile(theta, c(low, high), na.rm = TRUE))
}
d0.ci <- apply(delta.0, 2, CI)
d1.ci <- apply(delta.1, 2, CI)
tau.ci <- apply(tau, 2, CI)
z1.ci <- apply(zeta.1, 2, CI)
z0.ci <- apply(zeta.0, 2, CI)
}
# p-values
d0.p <- d1.p <- z0.p <- z1.p <- tau.p <- rep(NA, n.ycat)
for(i in 1:n.ycat){
d0.p[i] <- pval(delta.0[,i], d0[i])
d1.p[i] <- pval(delta.1[,i], d1[i])
z0.p[i] <- pval(zeta.0[,i], z0[i])
z1.p[i] <- pval(zeta.1[,i], z1[i])
tau.p[i] <- pval(tau[,i], tau.coef[i])
}
# Detect whether models include T-M interaction
INT <- paste(treat,mediator,sep=":") %in% attr(model.y$terms,"term.labels") |
paste(mediator,treat,sep=":") %in% attr(model.y$terms,"term.labels")
if(long) {
out <- list(d0=d0, d1=d1, d0.ci=d0.ci, d1.ci=d1.ci,
d0.p=d0.p, d1.p=d1.p,
d0.sims=delta.0, d1.sims=delta.1,
tau.coef=tau.coef, tau.ci=tau.ci, tau.p=tau.p,
z0=z0, z1=z1, z0.ci=z0.ci, z1.ci=z1.ci,
z0.p=z0.p, z1.p=z1.p,
z1.sims=zeta.1, z0.sims=zeta.0, tau.sims=tau,
boot=boot, boot.ci.type=boot.ci.type,
treat=treat, mediator=mediator,
covariates=covariates,
INT=INT, conf.level=conf.level,
model.y=model.y, model.m=model.m,
control.value=control.value, treat.value=treat.value,
nobs=n, sims=sims, call=cl,
robustSE = robustSE, cluster = cluster)
} else {
out <- list(d0=d0, d1=d1, d0.ci=d0.ci, d1.ci=d1.ci,
d0.p=d0.p, d1.p=d1.p,
tau.coef=tau.coef, tau.ci=tau.ci, tau.p=tau.p,
z0=z0, z1=z1, z0.ci=z0.ci, z1.ci=z1.ci,
z0.p=z0.p, z1.p=z1.p,
boot=boot, boot.ci.type=boot.ci.type,
treat=treat, mediator=mediator,
covariates=covariates,
INT=INT, conf.level=conf.level,
model.y=model.y, model.m=model.m,
control.value=control.value, treat.value=treat.value,
nobs=n, sims=sims, call=cl,
robustSE = robustSE, cluster = cluster)
}
class(out) <- "mediate.order"
out
}
}
##################################################################
med.fun <- function(y.data, index, m.data) {
if(isSurvreg.m){
mname <- names(m.data)[1]
nc <- nchar(mediator)
eventname <- substr(mname, 5 + nc + 3, nchar(mname) - 1)
if(nchar(eventname) == 0){
m.data.tmp <- data.frame(m.data,
as.numeric(m.data[,1L][,1L]))
names(m.data.tmp)[c(1L, ncol(m.data)+1)] <- c(mname, mediator)
} else {
m.data.tmp <- data.frame(m.data,
as.numeric(m.data[,1L][,1L]),
as.numeric(model.m$y[,2]))
names(m.data.tmp)[c(1L, ncol(m.data)+(1:2))] <- c(mname, mediator, eventname)
}
Call.M$data <- m.data.tmp[index,]
} else {
Call.M$data <- m.data[index,]
}
if(isSurvreg.y){
yname <- names(y.data)[1]
nc <- nchar(outcome)
eventname <- substr(yname, 5 + nc + 3, nchar(yname) - 1)
if(nchar(eventname) == 0){
y.data.tmp <- data.frame(y.data,
as.numeric(y.data[,1L][,1L]))
names(y.data.tmp)[c(1L, ncol(y.data)+1)] <- c(yname, outcome)
} else {
y.data.tmp <- data.frame(y.data,
as.numeric(y.data[,1L][,1L]),
as.numeric(model.y$y[,2]))
names(y.data.tmp)[c(1L, ncol(y.data)+(1:2))] <- c(yname, outcome, eventname)
}
Call.Y$data <- y.data.tmp[index,]
} else {
Call.Y$data <- y.data[index,]
}
Call.M$weights <- m.data[index,"(weights)"]
Call.Y$weights <- y.data[index,"(weights)"]
if(isOrdered.m && length(unique(y.data[index,mediator])) != m){
stop("insufficient variation on mediator")
}
# Refit Models with Resampled Data
new.fit.M <- NULL
new.fit.Y <- NULL
if (use_speed) {
if (isGlm.m)
new.fit.M <- fit_speedglm(Call.M)
else if (isLm.m) {
formula <- Call.M$formula
# ^^ to circumvent eval(call[[2]], parent.frame()) problem.
new.fit.M <- speedglm::speedlm(formula = formula,
data = Call.M$data,
weights = Call.M$weights)
}
if (isGlm.y)
new.fit.Y <- fit_speedglm(Call.Y)
else if (isLm.y) {
formula <- Call.Y$formula
# ^^ See above.
new.fit.Y <- speedglm::speedlm(formula = formula,
data = Call.Y$data,
weights = Call.Y$weights)
}
}
if (is.null(new.fit.M))
new.fit.M <- eval.parent(Call.M)
if (is.null(new.fit.Y))
new.fit.Y <- eval.parent(Call.Y)
#####################################
# Mediator Predictions
#####################################
pred.data.t <- pred.data.c <- m.data
if(isFactorT){
pred.data.t[,treat] <- factor(cat.1, levels = t.levels)
pred.data.c[,treat] <- factor(cat.0, levels = t.levels)
} else {
pred.data.t[,treat] <- cat.1
pred.data.c[,treat] <- cat.0
}
if(!is.null(covariates)){
for(p in 1:length(covariates)){
vl <- names(covariates[p])
if(is.factor(pred.data.t[,vl])){
pred.data.t[,vl] <- pred.data.c[,vl] <- factor(covariates[[p]], levels = levels(m.data[,vl]))
} else {
pred.data.t[,vl] <- pred.data.c[,vl] <- covariates[[p]]
}
}
}
### Case I-2-a: GLM Mediator (including GAMs)
if(isGlm.m){
muM1 <- predict(new.fit.M, type="response", newdata=pred.data.t)
muM0 <- predict(new.fit.M, type="response", newdata=pred.data.c)
if(FamilyM == "poisson"){
PredictM1 <- rpois(n, lambda = muM1)
PredictM0 <- rpois(n, lambda = muM0)
} else if (FamilyM == "Gamma") {
shape <- gamma.shape(new.fit.M)$alpha
PredictM1 <- rgamma(n, shape = shape, scale = muM1/shape)
PredictM0 <- rgamma(n, shape = shape, scale = muM0/shape)
} else if (FamilyM == "binomial"){
PredictM1 <- rbinom(n, size = 1, prob = muM1)
PredictM0 <- rbinom(n, size = 1, prob = muM0)
} else if (FamilyM == "gaussian"){
sigma <- sqrt(summary(new.fit.M)$dispersion)
error <- rnorm(n, mean=0, sd=sigma)
PredictM1 <- muM1 + error
PredictM0 <- muM0 + error
} else if (FamilyM == "inverse.gaussian"){
disp <- summary(new.fit.M)$dispersion
PredictM1 <- SuppDists::rinvGauss(n, nu = muM1, lambda = 1/disp)
PredictM0 <- SuppDists::rinvGauss(n, nu = muM0, lambda = 1/disp)
} else {
stop("unsupported glm family")
}
### Case I-2-b: Ordered Mediator
} else if(isOrdered.m) {
probs_m1 <- predict(new.fit.M, newdata=pred.data.t, type="probs")
probs_m0 <- predict(new.fit.M, newdata=pred.data.c, type="probs")
draws_m1 <- matrix(NA, n, m)
draws_m0 <- matrix(NA, n, m)
for(ii in 1:n){
draws_m1[ii,] <- t(rmultinom(1, 1, prob = probs_m1[ii,]))
draws_m0[ii,] <- t(rmultinom(1, 1, prob = probs_m0[ii,]))
}
PredictM1 <- apply(draws_m1, 1, which.max)
PredictM0 <- apply(draws_m0, 1, which.max)
### Case I-2-c: Quantile Regression for Mediator
} else if(isRq.m){
# Use inverse transform sampling to predict M
call.new <- new.fit.M$call
call.new$tau <- runif(n)
newfits <- eval.parent(call.new)
tt <- delete.response(terms(new.fit.M))
m.t <- model.frame(tt, pred.data.t, xlev = new.fit.M$xlevels)
m.c <- model.frame(tt, pred.data.c, xlev = new.fit.M$xlevels)
X.t <- model.matrix(tt, m.t, contrasts = new.fit.M$contrasts)
X.c <- model.matrix(tt, m.c, contrasts = new.fit.M$contrasts)
rm(tt, m.t, m.c)
PredictM1 <- rowSums(X.t * t(newfits$coefficients))
PredictM0 <- rowSums(X.c * t(newfits$coefficients))
rm(newfits, X.t, X.c)
### Case I-2-d: Linear
} else if(isLm.m){
if (class(new.fit.M) == "speedlm")
sigma <- sqrt(summary(new.fit.M)$var.res)
else
sigma <- summary(new.fit.M)$sigma
error <- rnorm(n, mean=0, sd=sigma)
PredictM1 <- predict(new.fit.M, type="response",
newdata=pred.data.t) + error
PredictM0 <- predict(new.fit.M, type="response",
newdata=pred.data.c) + error
rm(error)
### Case I-2-e: Survreg
} else if(isSurvreg.m){
dd <- survival::survreg.distributions[[new.fit.M$dist]]
if (is.null(dd$itrans)){
itrans <- function(x) x
} else {
itrans <- dd$itrans
}
dname <- dd$dist
if(is.null(dname)){
dname <- new.fit.M$dist
}
scale <- new.fit.M$scale
lpM1 <- predict(new.fit.M, newdata=pred.data.t, type="linear")
lpM0 <- predict(new.fit.M, newdata=pred.data.c, type="linear")
error <- switch(dname,
extreme = log(rweibull(n, shape=1, scale=1)),
gaussian = rnorm(n),
logistic = rlogis(n),
t = rt(n, df=dd$parms))
PredictM1 <- as.numeric(itrans(lpM1 + scale * error))
PredictM0 <- as.numeric(itrans(lpM0 + scale * error))
rm(error)
} else {
stop("mediator model is not yet implemented")
}
#####################################
# Outcome Predictions
#####################################
effects.tmp <- matrix(NA, nrow = n, ncol = 4)
for(e in 1:4){
tt <- switch(e, c(1,1,1,0), c(0,0,1,0), c(1,0,1,1), c(1,0,0,0))
pred.data.t <- pred.data.c <- y.data
if(!is.null(covariates)){
for(p in 1:length(covariates)){
vl <- names(covariates[p])
if(is.factor(pred.data.t[,vl])){
pred.data.t[,vl] <- pred.data.c[,vl] <- factor(covariates[[p]], levels = levels(y.data[,vl]))
} else {
pred.data.t[,vl] <- pred.data.c[,vl] <- covariates[[p]]
}
}
}
# Set treatment values
cat.t <- ifelse(tt[1], cat.1, cat.0)
cat.c <- ifelse(tt[2], cat.1, cat.0)
cat.t.ctrl <- ifelse(tt[1], cat.0, cat.1)
cat.c.ctrl <- ifelse(tt[2], cat.0, cat.1)
if(isFactorT){
pred.data.t[,treat] <- factor(cat.t, levels = t.levels)
pred.data.c[,treat] <- factor(cat.c, levels = t.levels)
if(!is.null(control)){
pred.data.t[,control] <- factor(cat.t.ctrl, levels = t.levels)
pred.data.c[,control] <- factor(cat.c.ctrl, levels = t.levels)
}
} else {
pred.data.t[,treat] <- cat.t
pred.data.c[,treat] <- cat.c
if(!is.null(control)){
pred.data.t[,control] <- cat.t.ctrl
pred.data.c[,control] <- cat.c.ctrl
}
}
# Set mediator values
PredictM1.tmp <- PredictM1
PredictM0.tmp <- PredictM0
PredictMt <- PredictM1 * tt[3] + PredictM0 * (1 - tt[3])
PredictMc <- PredictM1 * tt[4] + PredictM0 * (1 - tt[4])
if(isFactorM) {
pred.data.t[,mediator] <- factor(PredictMt, levels=1:m, labels=m.levels)
pred.data.c[,mediator] <- factor(PredictMc, levels=1:m, labels=m.levels)
} else {
pred.data.t[,mediator] <- PredictMt
pred.data.c[,mediator] <- PredictMc
}
if(isRq.y){
pr.1 <- predict(new.fit.Y, type="response",
newdata=pred.data.t, interval="none")
pr.0 <- predict(new.fit.Y, type="response",
newdata=pred.data.c, interval="none")
} else {
pr.1 <- predict(new.fit.Y, type="response",
newdata=pred.data.t)
pr.0 <- predict(new.fit.Y, type="response",
newdata=pred.data.c)
}
pr.mat <- as.matrix(cbind(pr.1, pr.0))
effects.tmp[,e] <- pr.mat[,1] - pr.mat[,2]
rm(pred.data.t, pred.data.c, pr.1, pr.0, pr.mat)
}
# Compute all QoIs
d1 <- weighted.mean(effects.tmp[,1], weights)
d0 <- weighted.mean(effects.tmp[,2], weights)
z1 <- weighted.mean(effects.tmp[,3], weights)
z0 <- weighted.mean(effects.tmp[,4], weights)
c(d1 = d1, d0 = d0, z1 = z1, z0 = z0)
}
med.fun.ordered <- function(y.data, index, m.data) {
Call.M <- model.m$call
Call.Y <- model.y$call
if(isSurvreg.m){
if(ncol(model.m$y) > 2){
stop("unsupported censoring type")
}
mname <- names(m.data)[1]
if(substr(mname, 1, 4) != "Surv"){
stop("refit the survival model with `Surv' used directly in model formula")
}
nc <- nchar(mediator)
eventname <- substr(mname, 5 + nc + 3, nchar(mname) - 1)
if(nchar(eventname) == 0){
m.data.tmp <- data.frame(m.data,
as.numeric(m.data[,1L][,1L]))
names(m.data.tmp)[c(1L, ncol(m.data)+1)] <- c(mname, mediator)
} else {
m.data.tmp <- data.frame(m.data,
as.numeric(m.data[,1L][,1L]),
as.numeric(model.m$y[,2]))
names(m.data.tmp)[c(1L, ncol(m.data)+(1:2))] <- c(mname, mediator, eventname)
}
Call.M$data <- m.data.tmp[index,]
} else {
Call.M$data <- m.data[index,]
}
Call.Y$data <- y.data[index,]
Call.M$weights <- m.data[index,"(weights)"]
Call.Y$weights <- y.data[index,"(weights)"]
new.fit.M <- eval.parent(Call.M)
new.fit.Y <- eval.parent(Call.Y)
if(isOrdered.m && length(unique(y.data[index,mediator]))!=m){
# Modify the coefficients when mediator has empty cells
coefnames.y <- names(model.y$coefficients)
coefnames.new.y <- names(new.fit.Y$coefficients)
new.fit.Y.coef <- rep(0, length(coefnames.y))
names(new.fit.Y.coef) <- coefnames.y
new.fit.Y.coef[coefnames.new.y] <- new.fit.Y$coefficients
new.fit.Y$coefficients <- new.fit.Y.coef
}
#####################################
# Mediator Predictions
#####################################
pred.data.t <- pred.data.c <- m.data
if(isFactorT){
pred.data.t[,treat] <- factor(cat.1, levels = t.levels)
pred.data.c[,treat] <- factor(cat.0, levels = t.levels)
} else {
pred.data.t[,treat] <- cat.1
pred.data.c[,treat] <- cat.0
}
if(!is.null(covariates)){
for(p in 1:length(covariates)){
vl <- names(covariates[p])
if(is.factor(pred.data.t[,vl])){
pred.data.t[,vl] <- pred.data.c[,vl] <- factor(covariates[[p]], levels = levels(m.data[,vl]))
} else {
pred.data.t[,vl] <- pred.data.c[,vl] <- covariates[[p]]
}
}
}
### Case II-a: GLM Mediator (including GAMs)
if(isGlm.m){
muM1 <- predict(new.fit.M, type="response", newdata=pred.data.t)
muM0 <- predict(new.fit.M, type="response", newdata=pred.data.c)
if(FamilyM == "poisson"){
PredictM1 <- rpois(n, lambda = muM1)
PredictM0 <- rpois(n, lambda = muM0)
} else if (FamilyM == "Gamma") {
shape <- gamma.shape(model.m)$alpha
PredictM1 <- rgamma(n, shape = shape, scale = muM1/shape)
PredictM0 <- rgamma(n, shape = shape, scale = muM0/shape)
} else if (FamilyM == "binomial"){
PredictM1 <- rbinom(n, size = 1, prob = muM1)
PredictM0 <- rbinom(n, size = 1, prob = muM0)
} else if (FamilyM == "gaussian"){
sigma <- sqrt(summary(model.m)$dispersion)
error <- rnorm(n, mean=0, sd=sigma)
PredictM1 <- muM1 + error
PredictM0 <- muM0 + error
} else if (FamilyM == "inverse.gaussian"){
disp <- summary(model.m)$dispersion
PredictM1 <- SuppDists::rinvGauss(n, nu = muM1, lambda = 1/disp)
PredictM0 <- SuppDists::rinvGauss(n, nu = muM0, lambda = 1/disp)
} else {
stop("unsupported glm family")
}
### Case II-b: Ordered Mediator
} else if(isOrdered.m) {
probs_m1 <- predict(new.fit.M, type="probs", newdata=pred.data.t)
probs_m0 <- predict(new.fit.M, type="probs", newdata=pred.data.c)
draws_m1 <- matrix(NA, n, m)
draws_m0 <- matrix(NA, n, m)
for(ii in 1:n){
draws_m1[ii,] <- t(rmultinom(1, 1, prob = probs_m1[ii,]))
draws_m0[ii,] <- t(rmultinom(1, 1, prob = probs_m0[ii,]))
}
PredictM1 <- apply(draws_m1, 1, which.max)
PredictM0 <- apply(draws_m0, 1, which.max)
### Case II-c: Quantile Regression for Mediator
} else if(isRq.m){
# Use inverse transform sampling to predict M
call.new <- new.fit.M$call
call.new$tau <- runif(n)
newfits <- eval.parent(call.new)
tt <- delete.response(terms(new.fit.M))
m.t <- model.frame(tt, pred.data.t, xlev = new.fit.M$xlevels)
m.c <- model.frame(tt, pred.data.c, xlev = new.fit.M$xlevels)
X.t <- model.matrix(tt, m.t, contrasts = new.fit.M$contrasts)
X.c <- model.matrix(tt, m.c, contrasts = new.fit.M$contrasts)
rm(tt, m.t, m.c)
PredictM1 <- rowSums(X.t * t(newfits$coefficients))
PredictM0 <- rowSums(X.c * t(newfits$coefficients))
rm(newfits, X.t, X.c)
### Case II-d: Linear
} else if(isLm.m){
sigma <- summary(new.fit.M)$sigma
error <- rnorm(n, mean=0, sd=sigma)
PredictM1 <- predict(new.fit.M, type="response",
newdata=pred.data.t) + error
PredictM0 <- predict(new.fit.M, type="response",
newdata=pred.data.c) + error
rm(error)
### Case I-2-e: Survreg
} else if(isSurvreg.m){
dd <- survival::survreg.distributions[[new.fit.M$dist]]
if (is.null(dd$itrans)){
itrans <- function(x) x
} else {
itrans <- dd$itrans
}
dname <- dd$dist
if(is.null(dname)){
dname <- new.fit.M$dist
}
scale <- new.fit.M$scale
lpM1 <- predict(new.fit.M, newdata=pred.data.t, type="linear")
lpM0 <- predict(new.fit.M, newdata=pred.data.c, type="linear")
error <- switch(dname,
extreme = log(rweibull(n, shape=1, scale=1)),
gaussian = rnorm(n),
logistic = rlogis(n),
t = rt(n, df=dd$parms))
PredictM1 <- as.numeric(itrans(lpM1 + scale * error))
PredictM0 <- as.numeric(itrans(lpM0 + scale * error))
rm(error)
} else {
stop("mediator model is not yet implemented")
}
#####################################
# Outcome Predictions
#####################################
effects.tmp <- array(NA, dim = c(n, n.ycat, 4))
for(e in 1:4){
tt <- switch(e, c(1,1,1,0), c(0,0,1,0), c(1,0,1,1), c(1,0,0,0))
pred.data.t <- pred.data.c <- y.data
if(!is.null(covariates)){
for(p in 1:length(covariates)){
vl <- names(covariates[p])
if(is.factor(pred.data.t[,vl])){
pred.data.t[,vl] <- pred.data.c[,vl] <- factor(covariates[[p]], levels = levels(y.data[,vl]))
} else {
pred.data.t[,vl] <- pred.data.c[,vl] <- covariates[[p]]
}
}
}
# Set treatment values
cat.t <- ifelse(tt[1], cat.1, cat.0)
cat.c <- ifelse(tt[2], cat.1, cat.0)
cat.t.ctrl <- ifelse(tt[1], cat.0, cat.1)
cat.c.ctrl <- ifelse(tt[2], cat.0, cat.1)
if(isFactorT){
pred.data.t[,treat] <- factor(cat.t, levels = t.levels)
pred.data.c[,treat] <- factor(cat.c, levels = t.levels)
if(!is.null(control)){
pred.data.t[,control] <- factor(cat.t.ctrl, levels = t.levels)
pred.data.c[,control] <- factor(cat.c.ctrl, levels = t.levels)
}
} else {
pred.data.t[,treat] <- cat.t
pred.data.c[,treat] <- cat.c
if(!is.null(control)){
pred.data.t[,control] <- cat.t.ctrl
pred.data.c[,control] <- cat.c.ctrl
}
}
# Set mediator values
PredictM1.tmp <- PredictM1
PredictM0.tmp <- PredictM0
PredictMt <- PredictM1 * tt[3] + PredictM0 * (1 - tt[3])
PredictMc <- PredictM1 * tt[4] + PredictM0 * (1 - tt[4])
if(isFactorM) {
pred.data.t[,mediator] <- factor(PredictMt, levels=1:m, labels=m.levels)
pred.data.c[,mediator] <- factor(PredictMc, levels=1:m, labels=m.levels)
} else {
pred.data.t[,mediator] <- PredictMt
pred.data.c[,mediator] <- PredictMc
}
probs_p1 <- predict(new.fit.Y, newdata=pred.data.t, type="probs")
probs_p0 <- predict(new.fit.Y, newdata=pred.data.c, type="probs")
effects.tmp[,,e] <- probs_p1 - probs_p0
rm(pred.data.t, pred.data.c, probs_p1, probs_p0)
}
# Compute all QoIs
d1 <- apply(effects.tmp[,,1], 2, weighted.mean, w=weights)
d0 <- apply(effects.tmp[,,2], 2, weighted.mean, w=weights)
z1 <- apply(effects.tmp[,,3], 2, weighted.mean, w=weights)
z0 <- apply(effects.tmp[,,4], 2, weighted.mean, w=weights)
c(d1 = d1, d0 = d0, z1 = z1, z0 = z0)
}
##################################################################
##################################################################
#' Summarizing Output from Mediation Analysis
#'
#' Function to report results from mediation analysis. Reported categories are
#' mediation effect, direct effect, total effect, and proportion of total effect
#' mediated. All quantities reported with confidence intervals. If the
#' treatment-mediator interaction is allowed in the mediation analysis, effects
#' are reported separately for the treatment and control conditions as well as
#' the simple averages of these effects are displayed at the bottom of the
#' summary table.
#'
#' @aliases summary.mediate summary.mediate.order print.summary.mediate
#' print.summary.mediate.order
#'
#' @param object output from mediate or mediate_tsls function.
#' @param x output from summary.mediate function.
#' @param ... additional arguments affecting the summary produced.
#'
#' @author Dustin Tingley, Harvard University,
#' \email{dtingley@@gov.harvard.edu}; Teppei Yamamoto, Massachusetts Institute
#' of Technology, \email{teppei@@mit.edu}; Luke Keele, Penn State University,
#' \email{ljk20@@psu.edu}; Kosuke Imai, Princeton University,
#' \email{kimai@@princeton.edu}.
#'
#' @seealso \code{\link{mediate}}, \code{\link{mediate_tsls}},
#' \code{\link{plot.mediate}}, \code{\link{summary}}.
#'
#' @references Tingley, D., Yamamoto, T., Hirose, K., Imai, K. and Keele, L.
#' (2014). "mediation: R package for Causal Mediation Analysis", Journal of
#' Statistical Software, Vol. 59, No. 5, pp. 1-38.
#'
#' Imai, K., Keele, L., Tingley, D. and Yamamoto, T. (2011). Unpacking the
#' Black Box of Causality: Learning about Causal Mechanisms from Experimental
#' and Observational Studies, American Political Science Review, Vol. 105, No.
#' 4 (November), pp. 765-789.
#'
#' Imai, K., Keele, L. and Tingley, D. (2010) A General Approach to Causal
#' Mediation Analysis, Psychological Methods, Vol. 15, No. 4 (December), pp.
#' 309-334.
#'
#' Imai, K., Keele, L. and Yamamoto, T. (2010) Identification, Inference, and
#' Sensitivity Analysis for Causal Mediation Effects, Statistical Science,
#' Vol. 25, No. 1 (February), pp. 51-71.
#'
#' Imai, K., Keele, L., Tingley, D. and Yamamoto, T. (2009) "Causal Mediation
#' Analysis Using R" in Advances in Social Science Research Using R, ed. H. D.
#' Vinod New York: Springer.
#'
#' @export
summary.mediate <- function(object, ...){
structure(object, class = c("summary.mediate", class(object)))
}
#' @rdname summary.mediate
#' @export
print.summary.mediate <- function(x, ...){
clp <- 100 * x$conf.level
cat("\n")
cat(
sprintf(
"Causal Mediation Analysis %s\n\n",
ifelse(inherits(x, "mediate.tsls"), "using Two-Stage Least Squares", "")
)
)
if(x$boot) {
cat(
sprintf(
"Nonparametric Bootstrap Confidence Intervals with the %s Method\n\n",
ifelse(x$boot.ci.type == "perc", "Percentile", "BCa")
)
)
} else {
cat(
sprintf(
"%s Confidence Intervals\n\n",
ifelse(inherits(x, "mediate.tsls"), "Two-Stage Least Squares",
"Quasi-Bayesian")
)
)
}
if(!is.null(x$covariates)){
cat("(Inference Conditional on the Covariate Values Specified in `covariates')\n\n")
}
isLinear.y <- ( (class(x$model.y)[1] %in% c("lm", "rq")) ||
(inherits(x$model.y, "glm") &&
x$model.y$family$family == "gaussian" &&
x$model.y$family$link == "identity") ||
(inherits(x$model.y, "survreg") &&
x$model.y$dist == "gaussian") )
printone <- !x$INT && isLinear.y
if (printone){
# Print only one set of values if lmY/quanY/linear gamY without interaction
smat <- c(x$d1, x$d1.ci, x$d1.p)
smat <- rbind(smat, c(x$z0, x$z0.ci, x$z0.p))
smat <- rbind(smat, c(x$tau.coef, x$tau.ci, x$tau.p))
smat <- rbind(smat, c(x$n0, x$n0.ci, x$n0.p))
rownames(smat) <- c("ACME", "ADE",
"Total Effect", "Prop. Mediated")
} else {
smat <- c(x$d0, x$d0.ci, x$d0.p)
smat <- rbind(smat, c(x$d1, x$d1.ci, x$d1.p))
smat <- rbind(smat, c(x$z0, x$z0.ci, x$z0.p))
smat <- rbind(smat, c(x$z1, x$z1.ci, x$z1.p))
smat <- rbind(smat, c(x$tau.coef, x$tau.ci, x$tau.p))
smat <- rbind(smat, c(x$n0, x$n0.ci, x$n0.p))
smat <- rbind(smat, c(x$n1, x$n1.ci, x$n1.p))
smat <- rbind(smat, c(x$d.avg, x$d.avg.ci, x$d.avg.p))
smat <- rbind(smat, c(x$z.avg, x$z.avg.ci, x$z.avg.p))
smat <- rbind(smat, c(x$n.avg, x$n.avg.ci, x$n.avg.p))
rownames(smat) <- c("ACME (control)", "ACME (treated)",
"ADE (control)", "ADE (treated)",
"Total Effect",
"Prop. Mediated (control)",
"Prop. Mediated (treated)",
"ACME (average)",
"ADE (average)",
"Prop. Mediated (average)")
}
colnames(smat) <- c("Estimate", paste(clp, "% CI Lower", sep=""),
paste(clp, "% CI Upper", sep=""), "p-value")
printCoefmat(smat, digits=3)
cat("\n")
cat("Sample Size Used:", x$nobs,"\n\n")
cat("\n")
cat("Simulations:", x$sims,"\n\n")
invisible(x)
}
#########################################################################
#' Summarizing Output from Mediation Analysis of Multilevel Models
#'
#' Function to report results from mediation analysis of multilevel models.
#' Reported categories are mediation effect, direct effect, total effect, and
#' proportion of total effect mediated. All quantities reported with confidence
#' intervals. Group-specific effects and confidence intervals reported based on
#' the mediator or the outcome group. Group-average quantities reported as
#' default.
#'
#'
#' @aliases summary.mediate.mer print.summary.mediate.mer
#' print.summary.mediate.mer.2 print.summary.mediate.mer.3
#'
#' @param object output from mediate function.
#' @param output group-specific effects organized by effect if output =
#' "byeffect"; group-specific effects organized by group if output =
#' "bygroup"; group-average effects reported as default.
#' @param x output from summary.mediate.mer function.
#' @param ... additional arguments affecting the summary produced.
#'
#' @author Kentaro Hirose, Princeton University, \email{hirose@@princeton.edu}.
#'
#' @seealso \code{\link{mediate}}, \code{\link{plot.mediate.mer}}.
#'
#' @references Tingley, D., Yamamoto, T., Hirose, K., Imai, K. and Keele, L.
#' (2014). "mediation: R package for Causal Mediation Analysis", Journal of
#' Statistical Software, Vol. 59, No. 5, pp. 1-38.
#'
#' Imai, K., Keele, L., Tingley, D. and Yamamoto, T. (2011). Unpacking the
#' Black Box of Causality: Learning about Causal Mechanisms from Experimental
#' and Observational Studies, American Political Science Review, Vol. 105, No.
#' 4 (November), pp. 765-789.
#'
#' Imai, K., Keele, L. and Tingley, D. (2010) A General Approach to Causal
#' Mediation Analysis, Psychological Methods, Vol. 15, No. 4 (December), pp.
#' 309-334.
#'
#' Imai, K., Keele, L. and Yamamoto, T. (2010) Identification, Inference, and
#' Sensitivity Analysis for Causal Mediation Effects, Statistical Science,
#' Vol. 25, No. 1 (February), pp. 51-71.
#'
#' Imai, K., Keele, L., Tingley, D. and Yamamoto, T. (2009) "Causal Mediation
#' Analysis Using R" in Advances in Social Science Research Using R, ed. H. D.
#' Vinod New York: Springer.
#'
#' @examples
#' # Examples with JOBS II Field Experiment
#'
#' # **For illustration purposes a small number of simulations are used**
#' \dontrun{
#' data(jobs)
#' require(lme4)
#'
#' # educ: mediator group
#' # occp: outcome group
#'
#' # Varying intercept for mediator
#' model.m <- glmer(job_dich ~ treat + econ_hard + (1 | educ),
#' family = binomial(link = "probit"), data = jobs)
#'
#' # Varying intercept and slope for outcome
#' model.y <- glmer(work1 ~ treat + job_dich + econ_hard + (1 + treat | occp),
#' family = binomial(link = "probit"), data = jobs)
#'
#' # Output based on mediator group
#' multilevel <- mediate(model.m, model.y, treat = "treat",
#' mediator = "job_dich", sims=50, group.out="educ")
#'
#' # Group-average effects
#' summary(multilevel)
#'
#' # Group-specific effects organized by effect
#' summary(multilevel, output="byeffect")
#'
#' # Group-specific effects organized by group
#' summary(multilevel, output="bygroup")
#' }
#'
#' @export
summary.mediate.mer <- function(object, output=c("default","byeffect","bygroup"),...){
output <- match.arg(output)
switch(output,
default = structure(object, class = c("summary.mediate.mer", class(object))),
byeffect = structure(object, class = c("summary.mediate.mer.2", class(object))),
bygroup = structure(object, class = c("summary.mediate.mer.3", class(object))))
}
#########################################################################
#' @rdname summary.mediate.mer
#' @export
print.summary.mediate.mer <- function(x,...){
clp <- 100 * x$conf.level
cat("\n")
cat("Causal Mediation Analysis \n\n")
if(x$boot){
if(x$boot.ci.type == "perc"){
cat("Nonparametric Bootstrap Confidence Intervals with the Percentile Method\n\n")
} else if(x$boot.ci.type == "bca"){
cat("Nonparametric Bootstrap Confidence Intervals with the BCa Method\n\n")
}
} else {
cat("Quasi-Bayesian Confidence Intervals\n\n")
}
if(!is.null(x$covariates)){
cat("(Inference Conditional on the Covariate Values Specified in `covariates')\n\n")
}
cat("Mediator Groups:", x$group.m,"\n\n")
cat("Outcome Groups:", x$group.y,"\n\n")
cat("Output Based on Overall Averages Across Groups","\n\n")
isLinear.y <- ( (class(x$model.y)[1] %in% c("lm", "rq")) || # lm or quantile
(inherits(x$model.y, "glm") &&
x$model.y$family$family == "gaussian" &&
x$model.y$family$link == "identity") || # glm normal
(inherits(x$model.y, "survreg") &&
x$model.y$dist == "gaussian") || # surv normal
(inherits(x$model.y, "merMod") &&
x$model.y@call[[1]] == "lmer") ) # lmer
printone <- !x$INT && isLinear.y
if(printone){
smat <- c(x$d1, x$d1.ci, x$d1.p)
smat <- rbind(smat, c(x$z0, x$z0.ci, x$z0.p))
smat <- rbind(smat, c(x$tau.coef, x$tau.ci, x$tau.p))
smat <- rbind(smat, c(x$n0, x$n0.ci, x$n0.p))
rownames(smat) <- c("ACME", "ADE",
"Total Effect", "Prop. Mediated")
}else{
smat <- c(x$d0, x$d0.ci, x$d0.p)
smat <- rbind(smat, c(x$d1, x$d1.ci, x$d1.p))
smat <- rbind(smat, c(x$z0, x$z0.ci, x$z0.p))
smat <- rbind(smat, c(x$z1, x$z1.ci, x$z1.p))
smat <- rbind(smat, c(x$tau.coef, x$tau.ci, x$tau.p))
smat <- rbind(smat, c(x$n0, x$n0.ci, x$n0.p))
smat <- rbind(smat, c(x$n1, x$n1.ci, x$n1.p))
smat <- rbind(smat, c(x$d.avg, x$d.avg.ci, x$d.avg.p))
smat <- rbind(smat, c(x$z.avg, x$z.avg.ci, x$z.avg.p))
smat <- rbind(smat, c(x$n.avg, x$n.avg.ci, x$n.avg.p))
rownames(smat) <- c("ACME (control)", "ACME (treated)",
"ADE (control)", "ADE (treated)",
"Total Effect",
"Prop. Mediated (control)",
"Prop. Mediated (treated)",
"ACME (average)",
"ADE (average)",
"Prop. Mediated (average)")
}
colnames(smat) <- c("Estimate", paste(clp, "% CI Lower", sep=""),
paste(clp, "% CI Upper", sep=""), "p-value")
printCoefmat(smat, digits=3)
cat("\n")
cat("Sample Size Used:", x$nobs,"\n\n")
cat("\n")
cat("Simulations:", x$sims,"\n\n")
invisible(x)
}
#########################################################################
#' @rdname summary.mediate.mer
#' @export
print.summary.mediate.mer.2 <- function(x,...){
clp <- 100 * x$conf.level
cat("\n")
cat("Causal Mediation Analysis \n\n")
if(x$boot){
if(x$boot.ci.type == "perc"){
cat("Nonparametric Bootstrap Confidence Intervals with the Percentile Method\n\n")
} else if(x$boot.ci.type == "bca"){
cat("Nonparametric Bootstrap Confidence Intervals with the BCa Method\n\n")
}
} else {
cat("Quasi-Bayesian Confidence Intervals\n\n")
}
if(!is.null(x$covariates)){
cat("(Inference Conditional on the Covariate Values Specified in `covariates')\n\n")
}
cat("Mediator Groups:", x$group.m,"\n\n")
cat("Outcome Groups:", x$group.y,"\n\n")
cat("Output Based on", x$group.name,"\n\n")
if(is.factor(x$group.id)){
gname <- levels(x$group.id)
} else {
gname <- sort(unique(x$group.id))
}
isLinear.y <- ( (class(x$model.y)[1] %in% c("lm", "rq")) || # lm or quantile
(inherits(x$model.y, "glm") &&
x$model.y$family$family == "gaussian" &&
x$model.y$family$link == "identity") || # glm normal
(inherits(x$model.y, "survreg") &&
x$model.y$dist == "gaussian") || # surv normal
(inherits(x$model.y, "merMod") &&
x$model.y@call[[1]] == "lmer") ) # lmer
printone <- !x$INT && isLinear.y
if(printone){
cat("ACME","\n\n")
smat<-cbind(x$d0.group,x$d0.ci.group,x$d0.p.group)
rownames(smat) <- gname
colnames(smat) <- c("Estimate", paste(clp, "% CI Lower", sep=""),
paste(clp, "% CI Upper", sep=""), "p-value")
printCoefmat(smat, digits=3)
cat("\n")
cat("ADE","\n\n")
smat<-cbind(x$z0.group, x$z0.ci.group, x$z0.p.group)
rownames(smat) <- gname
colnames(smat) <- c("Estimate", paste(clp, "% CI Lower", sep=""),
paste(clp, "% CI Upper", sep=""), "p-value")
printCoefmat(smat, digits=3)
cat("\n")
cat("Total Effect","\n\n")
smat<-cbind(x$tau.coef.group, x$tau.ci.group, x$tau.p.group)
rownames(smat) <- gname
colnames(smat) <- c("Estimate", paste(clp, "% CI Lower", sep=""),
paste(clp, "% CI Upper", sep=""), "p-value")
printCoefmat(smat, digits=3)
cat("\n")
cat("Prop. Mediated","\n\n")
smat<-cbind(x$n0.group, x$n0.ci.group, x$n0.p.group)
rownames(smat) <- gname
colnames(smat) <- c("Estimate", paste(clp, "% CI Lower", sep=""),
paste(clp, "% CI Upper", sep=""), "p-value")
printCoefmat(smat, digits=3)
cat("\n")
cat("\n")
cat("Sample Size Used:", x$nobs,"\n\n")
cat("\n")
cat("Simulations:", x$sims,"\n\n")
invisible(x)
}else{
cat("ACME (control)","\n\n")
smat<-cbind(x$d0.group,x$d0.ci.group,x$d0.p.group)
rownames(smat) <- gname
colnames(smat) <- c("Estimate", paste(clp, "% CI Lower", sep=""),
paste(clp, "% CI Upper", sep=""), "p-value")
printCoefmat(smat, digits=3)
cat("\n")
cat("ACME (treated)","\n\n")
smat<-cbind(x$d1.group, x$d1.ci.group, x$d1.p.group)
rownames(smat) <- gname
colnames(smat) <- c("Estimate", paste(clp, "% CI Lower", sep=""),
paste(clp, "% CI Upper", sep=""), "p-value")
printCoefmat(smat, digits=3)
cat("\n")
cat("ADE (control)","\n\n")
smat<-cbind(x$z0.group, x$z0.ci.group, x$z0.p.group)
rownames(smat) <- gname
colnames(smat) <- c("Estimate", paste(clp, "% CI Lower", sep=""),
paste(clp, "% CI Upper", sep=""), "p-value")
printCoefmat(smat, digits=3)
cat("\n")
cat("ADE (treated)","\n\n")
smat<-cbind(x$z1.group, x$z1.ci.group, x$z1.p.group)
rownames(smat) <- gname
colnames(smat) <- c("Estimate", paste(clp, "% CI Lower", sep=""),
paste(clp, "% CI Upper", sep=""), "p-value")
printCoefmat(smat, digits=3)
cat("\n")
cat("Total Effect","\n\n")
smat<-cbind(x$tau.coef.group, x$tau.ci.group, x$tau.p.group)
rownames(smat) <- gname
colnames(smat) <- c("Estimate", paste(clp, "% CI Lower", sep=""),
paste(clp, "% CI Upper", sep=""), "p-value")
printCoefmat(smat, digits=3)
cat("\n")
cat("Prop. Mediated (control)","\n\n")
smat<-cbind(x$n0.group, x$n0.ci.group, x$n0.p.group)
rownames(smat) <- gname
colnames(smat) <- c("Estimate", paste(clp, "% CI Lower", sep=""),
paste(clp, "% CI Upper", sep=""), "p-value")
printCoefmat(smat, digits=3)
cat("\n")
cat("Prop. Mediated (treated)","\n\n")
smat<-cbind(x$n1.group, x$n1.ci.group, x$n1.p.group)
rownames(smat) <- gname
colnames(smat) <- c("Estimate", paste(clp, "% CI Lower", sep=""),
paste(clp, "% CI Upper", sep=""), "p-value")
printCoefmat(smat, digits=3)
cat("\n")
cat("ACME (average)","\n\n")
smat<-cbind(x$d.avg.group, x$d.avg.ci.group, x$d.avg.p.group)
rownames(smat) <- gname
colnames(smat) <- c("Estimate", paste(clp, "% CI Lower", sep=""),
paste(clp, "% CI Upper", sep=""), "p-value")
printCoefmat(smat, digits=3)
cat("\n")
cat("ADE (average)","\n\n")
smat<-cbind(x$z.avg.group, x$z.avg.ci.group, x$z.avg.p.group)
rownames(smat) <- gname
colnames(smat) <- c("Estimate", paste(clp, "% CI Lower", sep=""),
paste(clp, "% CI Upper", sep=""), "p-value")
printCoefmat(smat, digits=3)
cat("\n")
cat("Prop. Mediated (average)","\n\n")
smat<-cbind(x$n.avg.group, x$n.avg.ci.group, x$n.avg.p.group)
rownames(smat) <- gname
colnames(smat) <- c("Estimate", paste(clp, "% CI Lower", sep=""),
paste(clp, "% CI Upper", sep=""), "p-value")
printCoefmat(smat, digits=3)
cat("\n")
cat("\n")
cat("Sample Size Used:", x$nobs,"\n\n")
cat("\n")
cat("Simulations:", x$sims,"\n\n")
invisible(x)
}
}
#########################################################################
#' @rdname summary.mediate.mer
#' @export
print.summary.mediate.mer.3 <- function(x,...){
clp <- 100 * x$conf.level
cat("\n")
cat("Causal Mediation Analysis \n\n")
if(x$boot){
if(x$boot.ci.type == "perc"){
cat("Nonparametric Bootstrap Confidence Intervals with the Percentile Method\n\n")
} else if(x$boot.ci.type == "bca"){
cat("Nonparametric Bootstrap Confidence Intervals with the BCa Method\n\n")
}
} else {
cat("Quasi-Bayesian Confidence Intervals\n\n")
}
if(!is.null(x$covariates)){
cat("(Inference Conditional on the Covariate Values Specified in `covariates')\n\n")
}
cat("Mediator Groups:", x$group.m,"\n\n")
cat("Outcome Groups:", x$group.y,"\n\n")
cat("Output Based on", x$group.name,"\n\n")
if(is.factor(x$group.id)){
gname <- levels(x$group.id)
} else {
gname <- sort(unique(x$group.id))
}
G<-length(gname)
isLinear.y <- ( (class(x$model.y)[1] %in% c("lm", "rq")) || # lm or quantile
(inherits(x$model.y, "glm") &&
x$model.y$family$family == "gaussian" &&
x$model.y$family$link == "identity") || # glm normal
(inherits(x$model.y, "survreg") &&
x$model.y$dist == "gaussian") || # surv normal
(inherits(x$model.y, "merMod") &&
x$model.y@call[[1]] == "lmer") ) # lmer
printone <- !x$INT && isLinear.y
if(printone){
for (g in 1:G){
cat("\n")
cat("Group:",gname[g],"\n")
smat <- c(x$d0.group[g], x$d0.ci.group[g,], x$d0.p.group[g])
smat <- rbind(smat, c(x$z0.group[g], x$z0.ci.group[g,], x$z0.p.group[g]))
smat <- rbind(smat, c(x$tau.coef.group[g], x$tau.ci.group[g,], x$tau.p.group[g]))
smat <- rbind(smat, c(x$n0.group[g], x$n0.ci.group[g,], x$n0.p.group[g]))
rownames(smat) <- c("ACME",
"ADE",
"Total Effect",
"Prop. Mediated")
colnames(smat) <- c("Estimate", paste(clp, "% CI Lower", sep=""),
paste(clp, "% CI Upper", sep=""), "p-value")
printCoefmat(smat, digits=3)
}
cat("\n")
cat("Sample Size Used:", x$nobs,"\n\n")
cat("\n")
cat("Simulations:", x$sims,"\n\n")
invisible(x)
}else{
for (g in 1:G){
cat("\n")
cat("Group:",gname[g],"\n")
smat <- c(x$d0.group[g], x$d0.ci.group[g,], x$d0.p.group[g])
smat <- rbind(smat, c(x$d1.group[g], x$d1.ci.group[g,], x$d1.p.group[g]))
smat <- rbind(smat, c(x$z0.group[g], x$z0.ci.group[g,], x$z0.p.group[g]))
smat <- rbind(smat, c(x$z1.group[g], x$z1.ci.group[g,], x$z1.p.group[g]))
smat <- rbind(smat, c(x$tau.coef.group[g], x$tau.ci.group[g,], x$tau.p.group[g]))
smat <- rbind(smat, c(x$n0.group[g], x$n0.ci.group[g,], x$n0.p.group[g]))
smat <- rbind(smat, c(x$n1.group[g], x$n1.ci.group[g,], x$n1.p.group[g]))
smat <- rbind(smat, c(x$d.avg.group[g], x$d.avg.ci.group[g,], x$d.avg.p.group[g]))
smat <- rbind(smat, c(x$z.avg.group[g], x$z.avg.ci.group[g,], x$z.avg.p.group[g]))
smat <- rbind(smat, c(x$n.avg.group[g], x$n.avg.ci.group[g,], x$n.avg.p.group[g]))
rownames(smat) <- c("ACME (control)", "ACME (treated)",
"ADE (control)", "ADE (treated)",
"Total Effect",
"Prop. Mediated (control)",
"Prop. Mediated (treated)",
"ACME (average)",
"ADE (average)",
"Prop. Mediated (average)")
colnames(smat) <- c("Estimate", paste(clp, "% CI Lower", sep=""),
paste(clp, "% CI Upper", sep=""), "p-value")
printCoefmat(smat, digits=3)
}
cat("\n")
cat("Sample Size Used:", x$nobs,"\n\n")
cat("\n")
cat("Simulations:", x$sims,"\n\n")
invisible(x)
}
}
#########################################################################
#' @export
summary.mediate.order <- function(object, ...){
structure(object, class = c("summary.mediate.order", class(object)))
}
#' @export
print.summary.mediate.order <- function(x, ...){
tab.d0 <- rbind(x$d0, x$d0.ci, x$d0.p)
tab.d1 <- rbind(x$d1, x$d1.ci, x$d1.p)
tab.z0 <- rbind(x$z0, x$z0.ci, x$z0.p)
tab.z1 <- rbind(x$z1, x$z1.ci, x$z1.p)
tab.tau <- rbind(x$tau.coef, x$tau.ci, x$tau.p)
# Outcome Table Labels
y.lab <- sort(unique(levels(model.frame(x$model.y)[,1])))
out.names <- c()
for(i in 1:length(y.lab)){
out.names.tmp <- paste("Pr(Y=",y.lab[i],")",sep="")
out.names <- c(out.names, out.names.tmp)
}
# Label Tables
rownames(tab.d0)[1] <- "ACME (control) "
rownames(tab.d0)[4] <- "p-value "
colnames(tab.d0) <- out.names
rownames(tab.d1)[1] <- "ACME (treated) "
rownames(tab.d1)[4] <- "p-value "
colnames(tab.d1) <- out.names
rownames(tab.z0)[1] <- "ADE (control) "
rownames(tab.z0)[4] <- "p-value "
colnames(tab.z0) <- out.names
rownames(tab.z1)[1] <- "ADE (treated) "
rownames(tab.z1)[4] <- "p-value "
colnames(tab.z1) <- out.names
rownames(tab.tau)[1] <- "Total Effect "
rownames(tab.tau)[4] <- "p-value "
colnames(tab.tau) <- out.names
cat("\n")
cat("Causal Mediation Analysis \n\n")
if(x$boot.ci.type == "perc"){
cat("Nonparametric Bootstrap Confidence Intervals with the Percentile Method\n\n")
} else if(x$boot.ci.type == "bca"){
cat("Nonparametric Bootstrap Confidence Intervals with the BCa Method\n\n")
}
if(!is.null(x$covariates)){
cat("(Inference Conditional on the Covariate Values Specified in `covariates')\n\n")
}
print(tab.d0, digits=3)
cat("\n")
print(tab.d1, digits=3)
cat("\n")
print(tab.z0, digits=3)
cat("\n")
print(tab.z1, digits=3)
cat("\n")
print(tab.tau, digits=3)
cat("\n\n")
cat("Sample Size Used:", x$nobs,"\n\n")
cat("\n\n")
cat("Simulations:", x$sims,"\n\n")
invisible(x)
}
#########################################################################
plot.process <- function(model) {
coef.vec.1 <- c(model$d1, model$z1)
lower.vec.1 <- c(model$d1.ci[1], model$z1.ci[1])
upper.vec.1 <- c(model$d1.ci[2], model$z1.ci[2])
tau.vec <- c(model$tau.coef,model$tau.ci[1],model$tau.ci[2])
range.1 <- range(model$d1.ci[1], model$z1.ci[1],model$tau.ci[1],
model$d1.ci[2], model$z1.ci[2],model$tau.ci[2])
coef.vec.0 <- c(model$d0, model$z0)
lower.vec.0 <- c(model$d0.ci[1], model$z0.ci[1])
upper.vec.0 <- c(model$d0.ci[2], model$z0.ci[2])
range.0 <- range(model$d0.ci[1], model$z0.ci[1],model$tau.ci[1],
model$d0.ci[2], model$z0.ci[2],model$tau.ci[2])
return(list(coef.vec.1=coef.vec.1, lower.vec.1=lower.vec.1,
upper.vec.1=upper.vec.1, coef.vec.0=coef.vec.0,
lower.vec.0=lower.vec.0, upper.vec.0=upper.vec.0, tau.vec=tau.vec,
range.1=range.1, range.0=range.0))
}
#########################################################################
#' Plotting Indirect, Direct, and Total Effects from Mediation Analysis
#'
#' Function to plot results from \code{mediate}. The vertical axis lists
#' indirect, direct, and total effects and the horizontal axis indicates the
#' respective magnitudes. Most standard options for plot function available.
#'
#' @aliases plot.mediate plot.mediate.order
#'
#' @param x object of class \code{mediate} or \code{mediate.order} as produced
#' by \code{mediate}.
#' @param treatment a character string indicating the baseline treatment value
#' of the estimated causal mediation effect and direct effect to plot. Can be
#' either "control", "treated" or "both". If 'NULL' (default), both sets of
#' estimates are plotted if and only if they differ.
#' @param labels a vector of character strings indicating the labels for the
#' estimated effects. The default labels will be used if NULL.
#' @param effect.type a vector indicating which quantities of interest to plot.
#' Default is to plot all three quantities (indirect, direct and total
#' effects).
#' @param xlim range of the horizontal axis.
#' @param ylim range of the vertical axis.
#' @param xlab label of the horizontal axis.
#' @param ylab label of the vertical axis.
#' @param main main title.
#' @param lwd width of the horizontal bars for confidence intervals.
#' @param cex size of the dots for point estimates.
#' @param col color of the dots and horizontal bars for the estimates.
#' @param ... additional parameters passed to 'plot'.
#'
#' @return \code{mediate} returns an object of class "\code{mediate}". The
#' function \code{summary} is used to obtain a table of the results. The
#' \code{plot} function plots these quantities.
#'
#' @author Dustin Tingley, Harvard University,
#' \email{dtingley@@gov.harvard.edu}; Teppei Yamamoto, Massachusetts Institute
#' of Technology, \email{teppei@@mit.edu}.
#'
#' @seealso \code{\link{mediate}}, \code{\link{plot}}
#'
#' @references Tingley, D., Yamamoto, T., Hirose, K., Imai, K. and Keele, L.
#' (2014). "mediation: R package for Causal Mediation Analysis", Journal of
#' Statistical Software, Vol. 59, No. 5, pp. 1-38.
#'
#' Imai, K., Keele, L. and Tingley, D. (2010) A General Approach to Causal
#' Mediation Analysis, Psychological Methods, Vol. 15, No. 4 (December), pp.
#' 309-334.
#'
#' Imai, K., Keele, L. and Yamamoto, T. (2010) Identification, Inference, and
#' Sensitivity Analysis for Causal Mediation Effects, Statistical Science,
#' Vol. 25, No. 1 (February), pp. 51-71.
#'
#' Imai, K., Keele, L., Tingley, D. and Yamamoto, T. (2009) "Causal Mediation
#' Analysis Using R" in Advances in Social Science Research Using R, ed. H. D.
#' Vinod New York: Springer.
#' @export
plot.mediate <- function(x, treatment = NULL, labels = NULL,
effect.type = c("indirect","direct","total"),
xlim = NULL, ylim = NULL, xlab = "", ylab = "",
main = NULL, lwd = 1.5, cex = .85,
col = "black", ...){
# Determine which graph to plot
isLinear.y <- ( (class(x$model.y)[1] %in% c("lm", "rq")) ||
(inherits(x$model.y, "glm") &&
x$model.y$family$family == "gaussian" &&
x$model.y$family$link == "identity") ||
(inherits(x$model.y, "survreg") &&
x$model.y$dist == "gaussian") )
printone <- !x$INT && isLinear.y
effect.type <- match.arg(effect.type, several.ok=TRUE)
IND <- "indirect" %in% effect.type
DIR <- "direct" %in% effect.type
TOT <- "total" %in% effect.type
if(is.null(treatment)){
if(printone){
treatment <- 1
} else {
treatment <- c(0,1)
}
} else {
treatment <- switch(treatment,
control = 0,
treated = 1,
both = c(0,1))
}
param <- plot.process(x)
y.axis <- (IND + DIR + TOT):1
# Set xlim
if(is.null(xlim)){
if(length(treatment) > 1) {
xlim <- range(param$range.1, param$range.0) * 1.2
} else if (treatment == 1){
xlim <- param$range.1 * 1.2
} else {
xlim <- param$range.0 * 1.2
}
}
# Set ylim
if(is.null(ylim)){
ylim <- c(min(y.axis) - 0.5, max(y.axis) + 0.5)
}
# Create blank plot first
plot(rep(0,IND+DIR+TOT), y.axis, type = "n", xlab = xlab, ylab = ylab,
yaxt = "n", xlim = xlim, ylim = ylim, main = main, ...)
# Set offset values depending on number of bars to plot
if(length(treatment) == 1){
adj <- 0
} else {
adj <- 0.05
}
if(1 %in% treatment){
if(IND && DIR) {
points(param$coef.vec.1, y.axis[1:2] + adj, type = "p", pch = 19, cex = cex, col = col)
segments(param$lower.vec.1, y.axis[1:2] + adj, param$upper.vec.1, y.axis[1:2] + adj,
lwd = lwd, col = col)
}
if(IND && !DIR) {
points(param$coef.vec.1[1], y.axis[1] + adj, type = "p", pch = 19, cex = cex, col = col)
segments(param$lower.vec.1[1], y.axis[1] + adj, param$upper.vec.1[1], y.axis[1] + adj,
lwd = lwd, col = col)
}
if(!IND && DIR) {
points(param$coef.vec.1[2], y.axis[1] + adj, type = "p", pch = 19, cex = cex, col = col)
segments(param$lower.vec.1[2], y.axis[1] + adj, param$upper.vec.1[2], y.axis[1] + adj,
lwd = lwd, col = col)
}
}
if(0 %in% treatment) {
if(IND && DIR) {
points(param$coef.vec.0, y.axis[1:2] - adj, type = "p", pch = 1, cex = cex, col = col)
segments(param$lower.vec.0, y.axis[1:2] - adj, param$upper.vec.0, y.axis[1:2] - adj,
lwd = lwd, lty = 3, col = col)
}
if(IND && !DIR) {
points(param$coef.vec.0[1], y.axis[1] - adj, type = "p", pch = 1, cex = cex, col = col)
segments(param$lower.vec.0[1], y.axis[1] - adj, param$upper.vec.0[1], y.axis[1] - adj,
lwd = lwd, lty = 3, col = col)
}
if(!IND && DIR) {
points(param$coef.vec.0[2], y.axis[1] - adj, type = "p", pch = 1, cex = cex, col = col)
segments(param$lower.vec.0[2], y.axis[1] - adj, param$upper.vec.0[2], y.axis[1] - adj,
lwd = lwd, lty = 3, col = col)
}
}
if (TOT) {
points(param$tau.vec[1], 1 , type = "p", pch = 19, cex = cex, col = col)
segments(param$tau.vec[2], 1 , param$tau.vec[3], 1 ,
lwd = lwd, col = col)
}
if(is.null(labels)){
labels <- c("ACME","ADE","Total\nEffect")[c(IND,DIR,TOT)]
}
axis(2, at = y.axis, labels = labels, las = 1, tick = TRUE, ...)
abline(v = 0, lty = 2)
}
#########################################################################
plot.process.mer <- function(model) {
coef.vec.1 <- c(model$d1, model$z1)
lower.vec.1 <- c(model$d1.ci[1], model$z1.ci[1])
upper.vec.1 <- c(model$d1.ci[2], model$z1.ci[2])
tau.vec <- c(model$tau.coef,model$tau.ci[1],model$tau.ci[2])
range.1 <- range(model$d1.ci[1], model$z1.ci[1],model$tau.ci[1],
model$d1.ci[2], model$z1.ci[2],model$tau.ci[2])
coef.vec.0 <- c(model$d0, model$z0)
lower.vec.0 <- c(model$d0.ci[1], model$z0.ci[1])
upper.vec.0 <- c(model$d0.ci[2], model$z0.ci[2])
range.0 <- range(model$d0.ci[1], model$z0.ci[1],model$tau.ci[1],
model$d0.ci[2], model$z0.ci[2],model$tau.ci[2])
coef.vec.0.group <- cbind(model$d0.group, model$z0.group)
lower.vec.0.group <- cbind(model$d0.ci.group[,1], model$z0.ci.group[,1])
upper.vec.0.group <- cbind(model$d0.ci.group[,2], model$z0.ci.group[,2])
coef.vec.1.group <- cbind(model$d1.group, model$z1.group)
lower.vec.1.group <- cbind(model$d1.ci.group[,1], model$z1.ci.group[,1])
upper.vec.1.group <- cbind(model$d1.ci.group[,2], model$z1.ci.group[,2])
tau.vec.group <- cbind(model$tau.coef.group, model$tau.ci.group[,1], model$tau.ci.group[,2])
return(list(coef.vec.1=coef.vec.1, lower.vec.1=lower.vec.1,
upper.vec.1=upper.vec.1, coef.vec.0=coef.vec.0,
lower.vec.0=lower.vec.0, upper.vec.0=upper.vec.0, tau.vec=tau.vec,
range.1=range.1, range.0=range.0,coef.vec.1.group=coef.vec.1.group, lower.vec.1.group=lower.vec.1.group,
upper.vec.1.group=upper.vec.1.group, coef.vec.0.group=coef.vec.0.group,
lower.vec.0.group=lower.vec.0.group, upper.vec.0.group=upper.vec.0.group, tau.vec.group=tau.vec.group))
}
#########################################################################
#' Plotting Indirect, Direct, and Total Effects from Mediation Analysis of
#' Multilevel Models
#'
#' Function to plot group-specific effects derived from causal mediation
#' analysis of multilevel models.
#'
#' @param x object of class 'mediate.mer' produced by 'mediate'.
#' @param treatment a character string indicating the baseline treatment value
#' of the estimated causal mediation effect and direct effect to plot. Can be
#' either "control", "treated", or "both". If 'NULL' (default), both sets of
#' estimates are plotted if and only if they differ.
#' @param group.plots a logical value indicating whether group-specific effects
#' should be plotted in addition to the population-averaged effects.
#' @param ask a logical value. If 'TRUE', the user is asked for input before a
#' new figure is plotted. Default is to ask only if the number of plots on
#' current screen is fewer than necessary.
#' @param xlim range of the horizontal axis.
#' @param ylim range of the vertical axis.
#' @param xlab label of the horizontal axis.
#' @param ylab label of the vertical axis.
#' @param main main title.
#' @param lwd width of the horizontal bars for confidence intervals .
#' @param cex size of the dots for point estimates.
#' @param col color of the dots and horizontal bars for the estimates..
#' @param ... additional parameters passed to 'plot'.
#'
#' @author Kentaro Hirose, Princeton University, \email{hirose@@princeton.edu}.
#'
#' @seealso \code{\link{mediate}}, \code{\link{summary.mediate.mer}}.
#'
#' @references Tingley, D., Yamamoto, T., Hirose, K., Imai, K. and Keele, L.
#' (2014). "mediation: R package for Causal Mediation Analysis", Journal of
#' Statistical Software, Vol. 59, No. 5, pp. 1-38.
#'
#' @examples
#' # Examples with JOBS II Field Experiment
#'
#' # **For illustration purposes a small number of simulations are used**
#' \dontrun{
#' data(jobs)
#' require(lme4)
#'
#' # educ: mediator group
#' # occp: outcome group
#'
#' # Varying intercept for mediator
#' model.m <- glmer(job_dich ~ treat + econ_hard + (1 | educ),
#' family = binomial(link = "probit"), data = jobs)
#'
#' # Varying intercept and slope for outcome
#' model.y <- glmer(work1 ~ treat + job_dich + econ_hard + (1 + treat | occp),
#' family = binomial(link = "probit"), data = jobs)
#'
#' # Output based on mediator group
#' multilevel <- mediate(model.m, model.y, treat = "treat",
#' mediator = "job_dich", sims=50, group.out="educ")
#'
#' #plot(multilevel, group.plots=TRUE)
#' }
#'
#' @export
plot.mediate.mer <- function(x, treatment = NULL, group.plots = FALSE,
ask = prod(par("mfcol")) < nplots,
xlim = NULL, ylim = NULL, xlab = "", ylab = "",
main = NULL, lwd = 1.5, cex = .85,
col = "black", ...){
param <- plot.process.mer(x)
isLinear.y <- ( (class(x$model.y)[1] %in% c("lm", "rq")) || # lm or quantile
(inherits(x$model.y, "glm") &&
x$model.y$family$family == "gaussian" &&
x$model.y$family$link == "identity") || # glm normal
(inherits(x$model.y, "survreg") &&
x$model.y$dist == "gaussian") || # surv normal
(inherits(x$model.y, "merMod") &&
x$model.y@call[[1]] == "lmer") ) # lmer
printone <- !x$INT && isLinear.y
if(is.null(treatment)){
if(printone){
treatment <- 1
} else {
treatment <- c(0,1)
}
} else {
treatment <- switch(treatment,
control = 0,
treated = 1,
both = c(0,1))
}
nplots <- 1 + group.plots * (2 * length(treatment) + 1) # n of plots necessary
if(ask){
oask <- devAskNewPage(TRUE)
on.exit(devAskNewPage(oask))
}
# 1. Summary plot for population effects
labels = c("ACME","ADE","Total\nEffect")
y.axis <- c(length(param$coef.vec.1):.5)
y.axis <- y.axis + 1
if(is.null(xlim)){
if(length(treatment) > 1) {
xlim <- range(param$range.1, param$range.0) * 1.2
} else if (treatment == 1){
xlim <- param$range.1 * 1.2
} else {
xlim <- param$range.0 * 1.2
}
}
if(is.null(ylim)){
ylim <- c(min(y.axis) -1- 0.5, max(y.axis) + 0.5)
}
plot(param$coef.vec.1, y.axis, type = "n", xlab = xlab, ylab = ylab,
yaxt = "n", xlim = xlim, ylim = ylim, main = main, ...)
if(length(treatment) == 1){
adj <- 0
} else {
adj <- 0.05
}
if(1 %in% treatment){
points(param$coef.vec.1, y.axis + adj, type = "p", pch = 19, cex = cex, col = col)
segments(param$lower.vec.1, y.axis + adj, param$upper.vec.1, y.axis + adj,
lwd = lwd, col = col)
points(param$tau.vec[1], 1, type = "p", pch = 19, cex = cex, col = col)
segments(param$tau.vec[2], 1 , param$tau.vec[3], 1 ,
lwd = lwd, col = col)
}
if(0 %in% treatment) {
points(param$coef.vec.0, y.axis - adj, type = "p", pch = 1, cex = cex, col = col)
segments(param$lower.vec.0, y.axis - adj, param$upper.vec.0, y.axis - adj,
lwd = lwd, lty = 3, col = col)
}
y.axis.new <- c(3,2,1)
axis(2, at = y.axis.new, labels = labels, las = 1, tick = TRUE, ...)
abline(v = 0, lty = 2)
# 2. Group effects
if(group.plots){
#########################################################################
if(is.factor(x$group.id)){
labels <- levels(x$group.id)
} else {
labels = sort(unique(x$group.id))
}
#########################################################################
if(0 %in% treatment){
y.axis <- c(length(param$coef.vec.0.group[,1]):.5)
y.axis <- y.axis + 1
xlim <- c(param$lower.vec.0.group[,1], param$coef.vec.0.group[,1], param$upper.vec.0.group[,1])
MIN <- ifelse(min(xlim)>0, min(xlim)*0.9, min(xlim)*1.1)
MAX <- ifelse(max(xlim)>0, max(xlim)*1.1, max(xlim)*0.9)
xlim <- c(MIN, MAX)
ylim <- c(min(y.axis), max(y.axis))
plot(param$coef.vec.0.group[,1], y.axis, type = "n", xlab = xlab, ylab = ylab,
yaxt = "n", xlim = xlim, ylim = ylim, main = "ACME (control)", ...)
points(param$coef.vec.0.group[,1], y.axis, type = "p", pch = 1, cex = cex, col = col)
segments(param$lower.vec.0.group[,1], y.axis, param$upper.vec.0.group[,1], y.axis,
lwd = lwd, col = col)
axis(2, at = y.axis, labels = labels, las = 1, tick = TRUE, ...)
abline(v = 0, lty = 2)
}
#########################################################################
if(1 %in% treatment){
y.axis <- c(length(param$coef.vec.1.group[,1]):.5)
y.axis <- y.axis + 1
xlim <- c(param$lower.vec.1.group[,1], param$coef.vec.1.group[,1], param$upper.vec.1.group[,1])
MIN <- ifelse(min(xlim)>0, min(xlim)*0.9, min(xlim)*1.1)
MAX <- ifelse(max(xlim)>0, max(xlim)*1.1, max(xlim)*0.9)
xlim <- c(MIN, MAX)
ylim <- c(min(y.axis), max(y.axis))
plot(param$coef.vec.1.group[,1], y.axis, type = "n", xlab = xlab, ylab = ylab,
yaxt = "n", xlim = xlim, ylim = ylim, main = ifelse(printone, "ACME", "ACME (treated)"), ...)
points(param$coef.vec.1.group[,1], y.axis, type = "p", pch = 19, cex = cex, col = col)
segments(param$lower.vec.1.group[,1], y.axis, param$upper.vec.1.group[,1], y.axis,
lwd = lwd, col = col)
axis(2, at = y.axis, labels = labels, las = 1, tick = TRUE, ...)
abline(v = 0, lty = 2)
}
#########################################################################
if(0 %in% treatment){
y.axis <- c(length(param$coef.vec.0.group[,2]):.5)
y.axis <- y.axis + 1
xlim <- c(param$lower.vec.0.group[,2], param$coef.vec.0.group[,2], param$upper.vec.0.group[,2])
MIN <- ifelse(min(xlim)>0, min(xlim)*0.9, min(xlim)*1.1)
MAX <- ifelse(max(xlim)>0, max(xlim)*1.1, max(xlim)*0.9)
xlim <- c(MIN, MAX)
ylim <- c(min(y.axis), max(y.axis))
plot(param$coef.vec.0.group[,2], y.axis, type = "n", xlab = xlab, ylab = ylab,
yaxt = "n", xlim = xlim, ylim = ylim, main = "ADE (control)", ...)
points(param$coef.vec.0.group[,2], y.axis, type = "p", pch = 1, cex = cex, col = col)
segments(param$lower.vec.0.group[,2], y.axis, param$upper.vec.0.group[,2], y.axis,
lwd = lwd, lty = 3, col = col)
axis(2, at = y.axis, labels = labels, las = 1, tick = TRUE, ...)
abline(v = 0, lty = 2)
}
#########################################################################
if(1 %in% treatment){
y.axis <- c(length(param$coef.vec.1.group[,2]):.5)
y.axis <- y.axis + 1
xlim <- c(param$lower.vec.1.group[,2], param$coef.vec.1.group[,2], param$upper.vec.1.group[,2])
MIN <- ifelse(min(xlim)>0, min(xlim)*0.9, min(xlim)*1.1)
MAX <- ifelse(max(xlim)>0, max(xlim)*1.1, max(xlim)*0.9)
xlim <- c(MIN, MAX)
ylim <- c(min(y.axis), max(y.axis))
plot(param$coef.vec.1.group[,2], y.axis, type = "n", xlab = xlab, ylab = ylab,
yaxt = "n", xlim = xlim, ylim = ylim, main = ifelse(printone, "ADE", "ADE (treated)"), ...)
points(param$coef.vec.1.group[,2], y.axis, type = "p", pch = 19, cex = cex, col = col)
segments(param$lower.vec.1.group[,2], y.axis, param$upper.vec.1.group[,2], y.axis,
lwd = lwd, lty = 3, col = col)
axis(2, at = y.axis, labels = labels, las = 1, tick = TRUE, ...)
abline(v = 0, lty = 2)
}
#########################################################################
y.axis <- c(length(param$tau.vec.group[,1]):.5)
y.axis <- y.axis + 1
xlim <- c(param$tau.vec.group[,1], param$tau.vec.group[,2], param$tau.vec.group[,3])
MIN <- ifelse(min(xlim)>0, min(xlim)*0.9, min(xlim)*1.1)
MAX <- ifelse(max(xlim)>0, max(xlim)*1.1, max(xlim)*0.9)
xlim <- c(MIN, MAX)
ylim <- c(min(y.axis), max(y.axis))
plot(param$tau.vec.group[,1], y.axis, type = "n", xlab = xlab, ylab = ylab,
yaxt = "n", xlim = xlim, ylim = ylim, main = "Total\nEffect", ...)
points(param$tau.vec.group[,1], y.axis , type = "p", pch = 19, cex = cex, col = col)
segments(param$tau.vec.group[,2], y.axis , param$tau.vec.group[,3], y.axis ,
lwd = lwd, col = col)
axis(2, at = y.axis, labels = labels, las = 1, tick = TRUE, ...)
abline(v = 0, lty = 2)
}
}
#########################################################################
plot.process.order <- function(model){
length <- length(model$d1)
coef.vec.1 <- lower.vec.1 <- upper.vec.1 <-
coef.vec.0 <- lower.vec.0 <- upper.vec.0 <- matrix(NA,ncol=2,nrow=length)
tau.vec<-matrix(NA,ncol=3,nrow=length)
for(j in 1:length){
coef.vec.1[j,] <- c(model$d1[j], model$z1[j])
lower.vec.1[j,] <- c(model$d1.ci[1,j], model$z1.ci[1,j])
upper.vec.1[j,] <- c(model$d1.ci[2,j], model$z1.ci[2,j])
coef.vec.0[j,] <- c(model$d0[j], model$z0[j])
lower.vec.0[j,] <- c(model$d0.ci[1,j], model$z0.ci[1,j])
upper.vec.0[j,] <- c(model$d0.ci[2,j], model$z0.ci[2,j])
tau.vec[j,] <- c(model$tau.coef[j], model$tau.ci[1,j], model$tau.ci[2,j])
}
range.1 <- range(model$d1.ci[1,], model$z1.ci[1,],model$tau.ci[1,],
model$d1.ci[2,], model$z1.ci[2,],model$tau.ci[2,])
range.0 <- range(model$d0.ci[1,], model$z0.ci[1,],model$tau.ci[1,],
model$d0.ci[2,], model$z0.ci[2,],model$tau.ci[2,])
return(list(coef.vec.1=coef.vec.1, lower.vec.1=lower.vec.1,
upper.vec.1=upper.vec.1, coef.vec.0=coef.vec.0,
lower.vec.0=lower.vec.0, upper.vec.0=upper.vec.0,
tau.vec=tau.vec,
range.1=range.1, range.0=range.0, length=length))
}
#########################################################################
#' @export
plot.mediate.order <- function(x, treatment = NULL,
labels = c("ACME","ADE","Total\nEffect"),
xlim = NULL, ylim = NULL, xlab = "", ylab = "",
main = NULL, lwd = 1.5, cex = .85,
col = "black", ...){
# Determine which graph to plot
if(is.null(treatment)){
if(x$INT){
treatment <- c(0,1)
} else {
treatment <- 1
}
} else {
treatment <- switch(treatment,
control = 0,
treated = 1,
both = c(0,1))
}
param <- plot.process.order(x)
y.axis <- c(ncol(param$coef.vec.1):.5)
y.axis <- y.axis + 1
# create indicator for y.axis, descending so labels go from top to bottom
# Set xlim
if(is.null(xlim)){
if(length(treatment) > 1) {
xlim <- range(param$range.1, param$range.0) * 1.2
} else if (treatment == 1){
xlim <- param$range.1 * 1.2
} else {
xlim <- param$range.0 * 1.2
}
}
# Set ylim
if(is.null(ylim)){
ylim <- c(min(y.axis) - 1 - 0.5, max(y.axis) + 0.5)
}
# Plot
plot(param$coef.vec.1[1,], y.axis, type = "n", xlab = xlab, ylab = ylab,
yaxt = "n", xlim = xlim, ylim = ylim, main = main, ...)
# Set offset values depending on number of bars to plot
if(length(treatment) == 1){
adj <- 0
} else {
adj <- 0.05
}
if(1 %in% treatment){
adj.1 <- adj * nrow(param$coef.vec.1)
for(z in 1:nrow(param$coef.vec.1)){
points(param$coef.vec.1[z,], y.axis + adj.1,
type = "p", pch = 19, cex = cex, col = col)
segments(param$lower.vec.1[z,], y.axis + adj.1,
param$upper.vec.1[z,], y.axis + adj.1,
lwd = lwd, col = col)
points(param$tau.vec[z,1], 1 + adj.1 ,
type = "p", pch = 19, cex = cex, col = col)
segments(param$tau.vec[z,2], 1 + adj.1 ,
param$tau.vec[z,3], 1 + adj.1 ,
lwd = lwd, col = col)
adj.1 <- adj.1 - 0.05
}
}
if(0 %in% treatment) {
adj.0 <- adj
for(z in 1:nrow(param$coef.vec.0)){
points(param$coef.vec.0[z,], y.axis - adj.0,
type = "p", pch = 1, cex = cex, col = col)
segments(param$lower.vec.0[z,], y.axis - adj.0,
param$upper.vec.0[z,], y.axis - adj.0,
lwd = lwd, lty = 3, col = col)
adj.0 <- adj.0 + 0.05
}
}
if (treatment[1]==0 & length(treatment)==1){
print("test")
adj.1 <- adj * nrow(param$coef.vec.1)
for(z in 1:nrow(param$tau.vec)){
points(param$tau.vec[z,1], 1 + adj.1 ,
type = "p", pch = 19, cex = cex, col = col)
segments(param$tau.vec[z,2], 1 + adj.1 ,
param$tau.vec[z,3], 1 +adj.1 ,
lwd = lwd, col = col)
adj.1 <- adj.1 - 0.05
}
}
y.axis.new <- c(3,2,1)
axis(2, at = y.axis.new, labels = labels, las = 1, tick = TRUE, ...)
abline(v = 0, lty = 2)
}
pval <- function(x, xhat){
## Compute p-values
if (xhat == 0) out <- 1
else {
out <- 2 * min(sum(x > 0), sum(x < 0)) / length(x)
}
return(min(out, 1))
}
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