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R/mediate.designs.R
In mediation: Causal Mediation Analysis
Defines functions
mediate.sed
mediate.pd
mediate.ped
mediate.ced
mediate.np
boot.pd
mechanism.bounds
summary.mediate.design
print.summary.mediate.design
Documented in
mediate.ced
mediate.pd
mediate.ped
mediate.sed
print.summary.mediate.design
summary.mediate.design
## User interface functions
#single experiment design
#' Estimating Average Causal Mediation Effects under the Single Experiment
#' Design
#'
#' @details 'mediate.sed' estimates average causal mediation effects for the
#' single experiment design. The two options are to use either the sequential
#' ignorability (SI) assumption in which nonparametric estimates of the
#' average causal mediation effect are produced, or, to relax the SI
#' assumption and to calculate the nonparametric bounds on the average causal
#' mediation effect.
#'
#' This function calculates average causal mediation effects (ACME) for the
#' single experiment design, where the treatment is randomized and the
#' mediator/outcome variables are measured. The user specifies whether they
#' want non-parametric point estimates based on the sequential ignorability
#' (SI) assumption, or nonparametric bounds without the SI assumption.
#'
#' @param outcome name of the outcome variable in 'data'. The variable must be
#' binary (factor or numeric 0/1) if 'SI' is FALSE.
#' @param mediator name of the mediator in 'data'. The variable must be binary
#' (factor or numeric 0/1) if 'SI' is FALSE and discrete if TRUE.
#' @param treat name of the treatment variable in 'data'. Must be binary (factor
#' or numeric 0/1).
#' @param data a data frame containing all the above variables.
#' @param SI whether the sequential ignorability assumption is made.
#' @param sims number of bootstrap simulations. Only relevant when 'SI' is TRUE.
#' @param conf.level level of the returned two-sided confidence intervals. Only
#' relevant when 'SI' is TRUE.
#' @param boot a logical value. if 'FALSE' a large sample Delta method
#' approximation is used for confidence intervals; if 'TRUE' nonparametric
#' bootstrap will be used. Default is 'FALSE'. Only relevant if 'SI' is TRUE.
#'
#' @return \code{mediate.sed} returns an object of class
#' "\code{mediate.design}", a list that contains the components listed below.
#'
#' The \code{summary} function can be used to obtain a table of the results.
#'
#' \item{d0, d1}{point estimates or lower/upper bounds for causal mediation
#' effects under the control and treatment conditions, respectively.}
#' \item{d0.ci, d1.ci}{confidence intervals for average causal mediation
#' effects for the nonparametric estimates. The confidence level is set at the
#' value specified in 'conf.level'. The value exists only when 'SI' is TRUE.}
#' \item{boot}{logical, the 'boot' argument used.}
#' \item{conf.level}{the confidence level used. }
#' \item{sims}{number of bootstrap simulations used for confidence interval
#' calculation.}
#' \item{nobs}{number of observations used.}
#' \item{design}{ indicates the design. Equals either "SED.NP.SI" or
#' "SED.NP.NOSI".}
#'
#' @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{summary.mediate.design}}
#'
#' @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., Tingley, D. and Yamamoto, T. (2012) Experimental Designs for
#' Identifying Causal Mechanisms. Journal of the Royal Statistical Society,
#' Series A (Statistics in Society)"
#'
#' 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 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
#' # Example 1: Bounds without SI assumption
#'
#' data(boundsdata)
#'
#' data.SED <- subset(boundsdata, manip == 0)
#' bound1 <- mediate.sed("out", "med", "ttt", data.SED, SI=FALSE)
#' summary(bound1)
#'
#' # Example 2: Nonparametric estimate of ACME under SI assumption
#' # Example with JOBS II Field Experiment
#'
#' data(jobs)
#'
#' foo.1 <- mediate.sed("depress2", "job_disc", "treat", jobs, SI=TRUE)
#' summary(foo.1)
#'
#' foo.2 <- mediate.sed("depress2", "job_disc", "treat", jobs, SI=TRUE, boot=TRUE)
#' summary(foo.2)
mediate.sed <- function(outcome, mediator, treat, data,
SI = FALSE, sims = 1000, conf.level = 0.95, boot = FALSE) {
varnames <- c(outcome, mediator, treat)
data <- data[,varnames]
if(sum(is.na(data))){
warning("NA's in data. Observations with missing data removed.")
data <- na.omit(data)
}
data <- sapply(data, function(x) if(is.factor(x)) as.numeric(x)-1 else as.numeric(as.character(x)))
if(SI) {
out <- mediate.np(data[,outcome], data[,mediator], data[,treat],
sims, conf.level, boot)
out$design <- "SED.NP.SI"
} else {
check <- apply(data, 2, function(x) identical(sort(unique(x)), c(0,1)))
if(sum(check) != ncol(data)) {
stop("Invalid values in variables.")
}
out <- mechanism.bounds(data[,outcome], data[,mediator], data[,treat],
NULL, design = "SED")
out$design <- "SED.NP.NOSI"
}
out
}
#parallel design
#' Estimating Average Causal Mediation Effects under the Parallel Design
#'
#' 'mediate.pd' estimates the average causal mediation effects for the parallel
#' design. If a treatment-mediator interaction is allowed then the nonparametric
#' sharp bounds are calculated. If a treatment-mediator interaction is not
#' allowed then the estimates of the (point-identified) effects are computed
#' along with bootstrapped confidence intervals.
#'
#' @details This function calculates average causal mediation effects (ACME) for
#' the parallel design. The design consists of two randomly separated
#' experimental arms, indicated by 'manipulated'. In one the treatment is
#' randomized and the mediator and outcome variables are measured. In the
#' second arm, the treatment is randomized, the mediator is perfectly
#' manipulated and the outcome variable is measured.
#'
#' Under the parallel design, the ACME is identified when it is assumed that
#' there is no interaction between the treatment and mediator. Without the
#' assumption the nonparametric sharp bounds can be computed. See Imai,
#' Tingley and Yamamoto (2012) for details.
#'
#' @param outcome name of the outcome variable in 'data'.
#' @param mediator name of the mediator in 'data'. The variable must be binary
#' (factor or numeric 0/1).
#' @param treat name of the treatment variable in 'data'. Must be binary (factor
#' or numeric 0/1).
#' @param manipulated name of the binary design indicator in 'data', indicating
#' whether observation received mediator manipulation.
#' @param data a data frame containing all the above variables.
#' @param NINT whether the no interaction assumption is made.
#' @param sims number of bootstrap simulations. Only relevant when 'NINT' is
#' TRUE.
#' @param conf.level level of the returned two-sided confidence intervals. Only
#' relevant when 'NINT' is TRUE.
#'
#' @return \code{mediate.pd} returns an object of class "\code{mediate.design}",
#' a list that contains the components listed below.
#'
#' The function \code{summary} (i.e., \code{summary.mediate.design}) can be
#' used to obtain a table of the results.
#'
#' \item{d0, d1}{ point estimates or bounds for the average causal mediation
#' effects under the control and treatment conditions, respectively.}
#' \item{d0.ci, d1.ci}{ confidence intervals for the effects based on the
#' nonparametric bootstrap. The confidence level is set at the value specified
#' in 'conf.level'. Only exists when 'NINT' is TRUE.} \item{nobs}{ number of
#' observations used.} \item{conf.level}{ confidence level used. Only exists
#' when 'NINT' is TRUE.} \item{sims}{ number of bootstrap simulations used for
#' confidence interval calculation. Only exists when 'NINT' is TRUE.}
#' \item{design}{ indicates the design. "PD.NINT" if no interaction assumed;
#' "PD" if interaction allowed.}
#' @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{summary.mediate.design}}
#'
#' @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., Tingley, D. and Yamamoto, T. (2012) Experimental Designs for
#' Identifying Causal Mechanisms. Journal of the Royal Statistical Society,
#' Series A (Statistics in Society)"
#'
#' 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 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
#' data(boundsdata)
#'
#' bound2 <- mediate.pd("out", "med", "ttt", "manip", boundsdata,
#' NINT = TRUE, sims = 100, conf.level=.95)
#' summary(bound2)
#'
#' bound2.1 <- mediate.pd("out", "med", "ttt", "manip", boundsdata, NINT = FALSE)
#' summary(bound2.1)
mediate.pd <- function(outcome, mediator, treat, manipulated, data,
NINT = TRUE, sims = 1000, conf.level = 0.95) {
varnames <- c(outcome, mediator, treat, manipulated)
data <- data[,varnames]
if(sum(is.na(data))){
warning("NA's in data. Observations with missing data removed.")
data <- na.omit(data)
}
data <- sapply(data, function(x) as.numeric(as.character(x)))
check <- apply(data, 2, function(x) identical(sort(unique(x)), c(0,1)))
if(sum(check) != ncol(data)) {
stop("Invalid values in variables.")
}
if(NINT) {
out <- boot.pd(data[,outcome], data[,mediator], data[,treat],
data[,manipulated], sims, conf.level)
} else {
out <- mechanism.bounds(data[,outcome], data[,mediator], data[,treat],
data[,manipulated], design = "PD")
}
out
}
#parallel encouragement design
#' Computing Bounds on Average Causal Mediation Effects under the Parallel
#' Encouragement Design
#'
#' 'mediate.ped' computes the nonparametric bounds on the average causal
#' mediation effects for the parallel encouragement design.
#'
#' @details This function calculates average causal mediation effects (ACME) for
#' the parallel encouragement design.
#'
#' In the design two experimental arms are
#' used. In one the treatment is randomized and the mediator and outcome
#' variables are measured. In the second arm the treatment is randomized, the
#' mediator is randomly encouraged either up or down, and the outcome variable
#' is measured.
#'
#' Two type of causal quantities are estimated: the population
#' ACME and the complier ACME. The latter refers to the subpopulation of the
#' units for whom the encouragement has its intended effect, and the width of
#' its bounds are tighter than that of the population ACME. See Imai, Tingley
#' and Yamamoto (2012) for details.
#'
#' @param outcome name of the outcome variable in 'data'.
#' @param mediator name of the mediator in 'data'. The variable must be binary
#' (factor or numeric 0/1).
#' @param treat name of the treatment variable in 'data'. Must be binary
#' (factor or numeric 0/1).
#' @param encourage name of the encouragement variable in 'data'. The variable
#' must be a numeric vector taking on either -1, 0, or 1.
#' @param data a data frame containing all the above variables.
#'
#' @return \code{mediate.pd} returns an object of class
#' "\code{mediate.design}", a list that contains the components listed below.
#'
#' The function \code{summary} (i.e., \code{summary.mediate.design}) can be
#' used to obtain a table of the results.
#'
#' \item{d0, d1}{ estimated nonparametric sharp bounds for the population ACME under the control and treatment conditions.}
#' \item{d0.p, d1.p}{ estimated nonparametric sharp bounds for the complier ACME under the control and treatment conditions.}
#' \item{nobs}{ number of observations used.}
#' \item{design}{ indicates the design. Always equals "PED".}
#'
#' @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{medsens}},
#' \code{\link{plot.mediate}}, \code{\link{summary.mediate}},
#' \code{\link{mediations}}
#'
#' @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., Tingley, D. and Yamamoto, T. (2012) Experimental Designs for
#' Identifying Causal Mechanisms. Journal of the Royal Statistical Society,
#' Series A (Statistics in Society)"
#'
#' 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
#' data(boundsdata)
#'
#' bound3 <- mediate.ped("out.enc", "med.enc", "ttt", "enc", boundsdata)
#' summary(bound3)
mediate.ped <- function(outcome, mediator, treat, encourage, data) {
varnames <- c(outcome, mediator, treat, encourage)
data <- data[,varnames]
if(sum(is.na(data))){
warning("NA's in data. Observations with missing data removed.")
data <- na.omit(data)
}
data <- sapply(data, function(x) as.numeric(as.character(x)))
check.1 <- apply(data[,1:3], 2, function(x) identical(sort(unique(x)), c(0,1)))
check.2 <- identical(sort(unique(data[,4])), c(-1,0,1))
if(sum(check.1, check.2) != ncol(data)) {
stop("Invalid values in variables.")
}
out <- mechanism.bounds(data[,outcome], data[,mediator], data[,treat],
data[,encourage], design = "PED")
out
}
#crossover encouragement design
#' Estimating Average Causal Mediation Effects under the Crossover Encouragement
#' Design
#'
#' 'mediate.ced' estimates the average causal mediation effects for the
#' crossover encouragement design.
#'
#' @details This function estimates the average indirect effects for the pliable
#' units under the crossover encouragement design. The design has two stages.
#' In the first stage the treatment is randomized and the mediator and outcome
#' variables are measured. In the second the treatment is set to the value
#' opposite of first period and a randomly selected group of units receives
#' encouragement to take on the mediator opposite to the values observed in
#' the first stage. See Imai, Tingley and Yamamoto (2012) for a full
#' description. The confidence intervals are calculated via the nonparametric
#' bootstrap.
#'
#' Note that \code{outcome} should be the observed responses in the
#' \emph{second} stage whereas \code{treat} should be the values in the
#' \emph{first} stage.
#'
#' @param outcome variable name in 'data' containing the outcome values observed
#' in the second experiment. The variable must be binary (factor or numeric
#' 0/1).
#' @param med.1 variable name in 'data' containing the mediator values observed
#' in the first experiment. The variable must be binary (factor or numeric
#' 0/1).
#' @param med.2 variable name in 'data' containing the mediator values observed
#' in the second experiment.
#' @param treat variable name in 'data' containing the treatment values in the
#' first experiment. Must be binary (factor or numeric 0/1).
#' @param encourage name of the encouragement indicator in 'data'. Must be
#' binary (factor or numeric 0/1).
#' @param data a data frame containing all the above variables.
#' @param sims number of bootstrap simulations.
#' @param conf.level level of the returned two-sided confidence intervals.
#'
#' @return \code{mediate.ced} returns an object of class
#' "\code{mediate.design}", a list that contains the components listed below.
#'
#' The \code{summary} function can be used to obtain a table of the results.
#'
#' \item{d0, d1}{point estimates of the average indirect effects under the control and treatment conditions.}
#' \item{d0.ci, d1.ci}{confidence intervals for the effects. The confidence level is set at the value specified in 'conf.level'.}
#' \item{conf.level}{ confidence level used.}
#' \item{sims}{ number of bootstrap simulations.}
#' \item{nobs}{ number of observations used.}
#' \item{design}{ indicates the design. Always equals "CED".}
#'
#' @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{summary.mediate.design}}
#'
#' @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., Tingley, D. and Yamamoto, T. (2012) Experimental Designs for
#' Identifying Causal Mechanisms. Journal of the Royal Statistical Society,
#' Series A (Statistics in Society)"
#'
#' 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 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
#' data(CEDdata)
#'
#' res <- mediate.ced("Y2", "M1", "M2", "T1", "Z", CEDdata, sims = 100)
#' summary(res)
mediate.ced <- function(outcome, med.1, med.2, treat, encourage, data,
sims = 1000, conf.level = .95){
varnames <- c(outcome, treat, med.1, med.2, encourage)
data <- data[,varnames]
if(sum(is.na(data))){
warning("NA's in data. Observations with missing data removed.")
data <- na.omit(data)
}
data <- sapply(data, function(x) as.numeric(as.character(x)))
data <- as.data.frame(data)
check <- apply(data, 2, function(x) identical(sort(unique(x)), c(0,1)))
if(sum(check) != ncol(data)) {
stop("Invalid values in variables.")
}
names(data) <- c("Y2","T","M1","M2","V")
n <- nrow(data)
# Storage
d.p.c <- d.p.t <- matrix(NA, sims, 1)
# Bootstrap function.
for(b in 1:(sims+1)){
index <- sample(1:n, n, replace = TRUE)
if(b == sims + 1){
index <- 1:n
}
d <- data[index,]
#Atmv
A111 <- sum(d$M2==1 & d$T==1 & d$M1==1 & d$V==1)/sum(d$T==1 & d$M1==1 & d$V==1)
A011 <- sum(d$M2==1 & d$T==0 & d$M1==1 & d$V==1)/sum(d$T==0 & d$M1==1 & d$V==1)
A101 <- sum(d$M2==1 & d$T==1 & d$M1==0 & d$V==1)/sum(d$T==1 & d$M1==0 & d$V==1)
A001 <- sum(d$M2==1 & d$T==0 & d$M1==0 & d$V==1)/sum(d$T==0 & d$M1==0 & d$V==1)
A110 <- sum(d$M2==1 & d$T==1 & d$M1==1 & d$V==0)/sum(d$T==1 & d$M1==1 & d$V==0)
A010 <- sum(d$M2==1 & d$T==0 & d$M1==1 & d$V==0)/sum(d$T==0 & d$M1==1 & d$V==0)
A100 <- sum(d$M2==1 & d$T==1 & d$M1==0 & d$V==0)/sum(d$T==1 & d$M1==0 & d$V==0)
A000 <- sum(d$M2==1 & d$T==0 & d$M1==0 & d$V==0)/sum(d$T==0 & d$M1==0 & d$V==0)
#Gtm1m2
G1111 <- mean(d$Y2[d$T==1 & d$M1==1 & d$M2==1 & d$V==1])
G0111 <- mean(d$Y2[d$T==0 & d$M1==1 & d$M2==1 & d$V==1])
G1011 <- mean(d$Y2[d$T==1 & d$M1==0 & d$M2==1 & d$V==1])
G0011 <- mean(d$Y2[d$T==0 & d$M1==0 & d$M2==1 & d$V==1])
G1101 <- mean(d$Y2[d$T==1 & d$M1==1 & d$M2==0 & d$V==1])
G0101 <- mean(d$Y2[d$T==0 & d$M1==1 & d$M2==0 & d$V==1])
G1001 <- mean(d$Y2[d$T==1 & d$M1==0 & d$M2==0 & d$V==1])
G0001 <- mean(d$Y2[d$T==0 & d$M1==0 & d$M2==0 & d$V==1])
G1110 <- mean(d$Y2[d$T==1 & d$M1==1 & d$M2==1 & d$V==0])
G0110 <- mean(d$Y2[d$T==0 & d$M1==1 & d$M2==1 & d$V==0])
G1010 <- mean(d$Y2[d$T==1 & d$M1==0 & d$M2==1 & d$V==0])
G0010 <- mean(d$Y2[d$T==0 & d$M1==0 & d$M2==1 & d$V==0])
G1100 <- mean(d$Y2[d$T==1 & d$M1==1 & d$M2==0 & d$V==0])
G0100 <- mean(d$Y2[d$T==0 & d$M1==1 & d$M2==0 & d$V==0])
G1000 <- mean(d$Y2[d$T==1 & d$M1==0 & d$M2==0 & d$V==0])
G0000 <- mean(d$Y2[d$T==0 & d$M1==0 & d$M2==0 & d$V==0])
Q11 <- sum(d$T==1 & d$M1==1)/sum(d$T==1)
Q10 <- sum(d$T==1 & d$M1==0)/sum(d$T==1)
Q01 <- sum(d$T==0 & d$M1==1)/sum(d$T==0)
Q00 <- sum(d$T==0 & d$M1==0)/sum(d$T==0)
B11 <- Q11/((A100 - A101)*Q10 + (A111 - A110)*Q11)
B10 <- Q10/((A100 - A101)*Q10 + (A111 - A110)*Q11)
B01 <- Q01/((A000 - A001)*Q00 + (A011 - A010)*Q01)
B00 <- Q00/((A000 - A001)*Q00 + (A011 - A010)*Q01)
if(b == sims + 1){
d.p.c.mu <- (-A110*G1110 - (1-A110)*G1100 + A111*G1111 + (1-A111)*G1101) * B11 +
(-A100*G1010 - (1-A100)*G1000 + A101*G1011 + (1-A101)*G1001) * B10
d.p.t.mu <- (A000*G0010 + (1-A000)*G0000 - A001*G0011 - (1-A001)*G0001) * B00 +
(A010*G0110 + (1-A010)*G0100 - A011*G0111 - (1-A011)*G0101) * B01
} else {
d.p.c[b] <- (-A110*G1110 - (1-A110)*G1100 + A111*G1111 + (1-A111)*G1101) * B11 +
(-A100*G1010 - (1-A100)*G1000 + A101*G1011 + (1-A101)*G1001) * B10
d.p.t[b] <- (A000*G0010 + (1-A000)*G0000 - A001*G0011 - (1-A001)*G0001) * B00 +
(A010*G0110 + (1-A010)*G0100 - A011*G0111 - (1-A011)*G0101) * B01
}
}#bootstraploop
if(is.nan(d.p.c.mu) | is.nan(d.p.t.mu)){
warning("NaN produced; distribution of observed variables may be too sparse")
}
d.p.c[d.p.c==-Inf] <- NA
d.p.t[d.p.t==-Inf] <- NA
d.p.c[d.p.c==Inf] <- NA
d.p.t[d.p.t==Inf] <- NA
low <- (1 - conf.level)/2
high <- 1 - low
d.p.c.ci <- quantile(d.p.c, c(low,high), na.rm=TRUE)
d.p.t.ci <- quantile(d.p.t, c(low,high), na.rm=TRUE)
out <- list(d0 = d.p.c.mu, d1 = d.p.t.mu, d0.ci = d.p.c.ci, d1.ci = d.p.t.ci,
nobs = n, sims = sims, conf.level = conf.level, design = "CED")
class(out) <- "mediate.design"
out
}
## Internal functions
#nonparametric under SI assumption
mediate.np <- function(Y, M, T, sims, conf.level, boot){
# samp <- data.frame(na.omit(cbind(M,Y,T)))
samp <- data.frame(Y=Y, M=M, T=T)
m.cat <- sort(unique(samp$M))
n <- length(samp$Y)
n1 <- sum(samp$T)
n0 <- sum(1-samp$T)
t <- (1 - conf.level)/2
if(boot){
idx <- seq(1,n,1)
d0.bs <- matrix(NA,sims,1)
d1.bs <- matrix(NA,sims,1)
for(b in 1:(sims+1)){
resample <- sample(idx,n,replace=TRUE)
if(b == sims + 1){
resample <- 1:n
}
samp.star <- samp[resample,]
delta_0m <- delta_1m <- matrix(NA, length(m.cat), 1)
for(i in 1:length(m.cat)){
delta_0m[i] <- (sum(samp.star$T[samp.star$M==m.cat[i]]) *
sum(samp.star$Y[samp.star$M==m.cat[i] & samp.star$T==0])) /
(n1*(sum((1 - samp.star$T[samp.star$M==m.cat[i]]))))
delta_1m[i] <- (sum((1 - samp.star$T[samp.star$M==m.cat[i]])) *
sum(samp.star$Y[samp.star$M==m.cat[i] & samp.star$T==1])) /
(n0*(sum(samp.star$T[samp.star$M==m.cat[i]])))
}
if(b == sims + 1){
d0 <- sum(delta_0m) - mean(samp.star$Y[samp.star$T==0])
d1 <- mean(samp.star$Y[samp.star$T==1]) - sum(delta_1m)
} else {
d0.bs[b,] <- sum(delta_0m) - mean(samp.star$Y[samp.star$T==0])
d1.bs[b,] <- mean(samp.star$Y[samp.star$T==1]) - sum(delta_1m)
}
}
low <- (1 - conf.level)/2
high <- 1 - low
d0.ci <- quantile(d0.bs,c(low,high), na.rm=TRUE)
d1.ci <- quantile(d1.bs,c(low,high), na.rm=TRUE)
} else {
delta_0m <- delta_1m <- matrix(NA, length(m.cat), 1)
for(i in 1:length(m.cat)){
delta_0m[i] <- (sum(samp$T[samp$M==m.cat[i]]) *
sum(samp$Y[samp$M==m.cat[i] & samp$T==0])) /
(n1*(sum((1 - samp$T[samp$M==m.cat[i]]))))
delta_1m[i] <- (sum((1 - samp$T[samp$M==m.cat[i]])) *
sum(samp$Y[samp$M==m.cat[i] & samp$T==1])) /
(n0*(sum(samp$T[samp$M==m.cat[i]])))
}
d0 <- sum(delta_0m) - mean(samp$Y[samp$T==0])
d1 <- mean(samp$Y[samp$T==1]) - sum(delta_1m)
pr.t.1 <- sum(samp$T)/n
pr.t.0 <- sum(1-samp$T)/n
lambda.1m <- lambda.0m <- matrix(NA, length(m.cat), 1)
for(i in 1:length(m.cat)){
lambda.1m[i] <- (sum(length(samp$M[samp$M==m.cat[i] & samp$T==1])))/n /pr.t.1
lambda.0m[i] <- (sum(length(samp$M[samp$M==m.cat[i] & samp$T==0])))/n /pr.t.0
}
mu.1m <- mu.0m <- matrix(NA, length(m.cat), 1)
for(i in 1:length(m.cat)){
mu.1m[i] <- mean(samp$Y[samp$M==m.cat[i] & samp$T==1])
mu.0m[i] <- mean(samp$Y[samp$M==m.cat[i] & samp$T==0])
}
# Variance of Delta_0
var.delta.0m <- matrix(NA, length(m.cat), 1)
for(i in 1:length(m.cat)){
var.delta.0m[i] <- lambda.1m[i]*(((lambda.1m[i]/lambda.0m[i]) - 2) *
var(samp$Y[samp$M==m.cat[i] & samp$T==0]) +
((n0*(1-lambda.1m[i])*mu.0m[i]^2)/n1))
}
m.leng <- length(m.cat)
mterm.d0 <- c()
for(i in 1:m.leng-1){
mterm.d0 <- c(mterm.d0, lambda.1m[i] * lambda.1m[(i+1):m.leng] *
mu.0m[i] * mu.0m[(i+1):m.leng])
}
var.delta_0 <- (1/n0) * sum(var.delta.0m) - (2/n1) * sum(mterm.d0) +
var(samp$Y[samp$T == 0])/n0
# Variance of Delta_1
var.delta.1m <- matrix(NA, length(m.cat), 1)
for(i in 1:length(m.cat)){
var.delta.1m[i] <- lambda.0m[i]*(((lambda.0m[i]/lambda.1m[i]) - 2) *
var(samp$Y[samp$M==m.cat[i] & samp$T==1]) +
((n1*(1-lambda.0m[i])*mu.1m[i]^2)/n0))
}
mterm.d1 <- c()
for(i in 1:m.leng-1){
mterm.d1 <- c(mterm.d1, lambda.0m[i] * lambda.0m[(i+1):m.leng] *
mu.1m[i] * mu.1m[(i+1):m.leng])
}
var.delta_1 <- (1/n1) * sum(var.delta.1m) - (2/n0)* sum(mterm.d1) +
var(samp$Y[samp$T == 1])/n1
d0.ci <- c(d0 - (-qnorm(t)*sqrt(var.delta_0)), d0 + (-qnorm(t)*sqrt(var.delta_0)))
d1.ci <- c(d1 - (-qnorm(t)*sqrt(var.delta_1)), d1 + (-qnorm(t)*sqrt(var.delta_1)))
}
out <- list(d0=d0, d1=d1, d0.ci=d0.ci, d1.ci=d1.ci,
conf.level=conf.level, nobs=n, boot=boot)
class(out) <- "mediate.design"
out
}
#parallel design under no interaction assumption
boot.pd <- function(outcome, mediator, treatment, manipulated,
sims, conf.level) {
n <- length(outcome)
data <- matrix(, nrow = n, ncol = 4)
data[,1] <- outcome
data[,2] <- treatment
data[,3] <- mediator
data[,4] <- manipulated
data <- as.data.frame(data)
names(data) <- c("Y","T","M","D")
acme <- matrix(NA, sims, 1)
for(b in 1:(sims+1)){ # bootstrap
index <- sample(1:n, n, replace = TRUE)
if(b == sims + 1){
index <- 1:n
}
d <- data[index,]
tau <- mean(d$Y[d$T==1 & d$D==0]) - mean(d$Y[d$T==0 & d$D==0])
weight.m1 <- sum(d$M==1 & d$D==1 )/sum(d$D==1)
weight.m0 <- sum(d$M==0 & d$D==1 )/sum(d$D==1)
m1 <- mean(d$Y[d$T==1 & d$M==1 & d$D==1]) - mean(d$Y[d$T==0 &
d$M==1 & d$D==1])
m0 <- mean(d$Y[d$T==1 & d$M==0 & d$D==1]) - mean(d$Y[d$T==0 &
d$M==0 & d$D==1])
z <- weight.m1*m1 + weight.m0*m0
if(b == sims + 1){
acme.mu <- tau - z
} else {
acme[b] <- tau - z
}
}
acme[acme==-Inf] <- NA
acme[acme==Inf] <- NA
low <- (1 - conf.level)/2
high <- 1 - low
acme.ci <- quantile(acme, c(low,high), na.rm=TRUE)
out <- list(d0 = acme.mu, d1 = acme.mu, d0.ci = acme.ci, d1.ci =
acme.ci,
nobs = n, conf.level = conf.level, sims = sims, design
= "PD.NINT")
class(out) <- "mediate.design"
out
}
#Bounds Function for parallel, parallel encouragement, and single experiment designs
mechanism.bounds <- function(outcome, mediator, treatment, DorZ, design) {
d <- matrix(, nrow=length(outcome), ncol=3)
d[,1] <- outcome
d[,2] <- treatment
d[,3] <- mediator
d <- as.data.frame(d)
names(d) <- c("Y","T","M")
nobs <- nrow(d)
## "DorZ" indicates the variable that assigns manipulation direction.
## Z in the JRSSA paper. This is left to null for the single experiment design.
# Single Experiment
if(design=="SED") {
d$Z <- 0
P111 <- sum(d$Y==1 & d$M==1 & d$Z==0 & d$T==1)/sum(d$T==1 & d$Z==0)
P101 <- sum(d$Y==1 & d$M==0 & d$Z==0 & d$T==1)/sum(d$T==1 & d$Z==0)
P001 <- sum(d$Y==0 & d$M==0 & d$Z==0 & d$T==1)/sum(d$T==1 & d$Z==0)
P011 <- sum(d$Y==0 & d$M==1 & d$Z==0 & d$T==1)/sum(d$T==1 & d$Z==0)
P110 <- sum(d$Y==1 & d$M==1 & d$Z==0 & d$T==0)/sum(d$T==0 & d$Z==0)
P100 <- sum(d$Y==1 & d$M==0 & d$Z==0 & d$T==0)/sum(d$T==0 & d$Z==0)
P000 <- sum(d$Y==0 & d$M==0 & d$Z==0 & d$T==0)/sum(d$T==0 & d$Z==0)
P010 <- sum(d$Y==0 & d$M==1 & d$Z==0 & d$T==0)/sum(d$T==0 & d$Z==0)
l.delta.t <- max(-P001-P011, -P000-P001-P100, -P011-P010-P110)
u.delta.t <- min(P101+P111, P000+P100+P101, P010+P110+P111)
l.delta.c <- max(-P100-P110, -P001-P101-P100, -P011-P111-P110)
u.delta.c <- min(P000+P010, P011+P111+P010, P000+P001+P101)
S.t <- cbind(l.delta.t,u.delta.t)
S.c <- cbind(l.delta.c,u.delta.c)
# Parallel
} else if(design=="PD") {
## D indicates if there was manipulation
d$D <- DorZ
Z111 <- sum(d$Y==1 & d$T==1 & d$M==1 & d$D==1)/sum(d$T==1 & d$M==1 & d$D==1)
Z011 <- sum(d$Y==0 & d$T==1 & d$M==1 & d$D==1)/sum(d$T==1 & d$M==1 & d$D==1)
Z001 <- sum(d$Y==0 & d$T==1 & d$M==0 & d$D==1)/sum(d$T==1 & d$M==0 & d$D==1)
Z110 <- sum(d$Y==1 & d$T==0 & d$M==1 & d$D==1)/sum(d$T==0 & d$M==1 & d$D==1)
Z010 <- sum(d$Y==0 & d$T==0 & d$M==1 & d$D==1)/sum(d$T==0 & d$M==1 & d$D==1)
Z000 <- sum(d$Y==0 & d$T==0 & d$M==0 & d$D==1)/sum(d$T==0 & d$M==0 & d$D==1)
Z101 <- sum(d$Y==1 & d$T==1 & d$M==0 & d$D==1)/sum(d$T==1 & d$M==0 & d$D==1)
Z100 <- sum(d$Y==1 & d$T==0 & d$M==0 & d$D==1)/sum(d$T==0 & d$M==0 & d$D==1)
P111 <- sum(d$Y==1 & d$M==1 & d$T==1 & d$D==0)/sum(d$T==1 & d$D==0)
P101 <- sum(d$Y==1 & d$M==0 & d$T==1 & d$D==0)/sum(d$T==1 & d$D==0)
P001 <- sum(d$Y==0 & d$M==0 & d$T==1 & d$D==0)/sum(d$T==1 & d$D==0)
P011 <- sum(d$Y==0 & d$M==1 & d$T==1 & d$D==0)/sum(d$T==1 & d$D==0)
P110 <- sum(d$Y==1 & d$M==1 & d$T==0 & d$D==0)/sum(d$T==0 & d$D==0)
P100 <- sum(d$Y==1 & d$M==0 & d$T==0 & d$D==0)/sum(d$T==0 & d$D==0)
P000 <- sum(d$Y==0 & d$M==0 & d$T==0 & d$D==0)/sum(d$T==0 & d$D==0)
P010 <- sum(d$Y==0 & d$M==1 & d$T==0 & d$D==0)/sum(d$T==0 & d$D==0)
P.l.delta.t <- max(-P001-P011, -P011-P010-P110-P001+Z001, -P000-P001-P100-P011+Z011, -P001-P011+Z001-Z111, -P001+P101-Z101, -P011+P111-Z111)
P.u.delta.t <- min(P101+P111, P010+P110+P101+P111-Z101, P000+P100+P101+P111-Z111, P101+P111+Z001-Z111, P111-P011+Z011, P101-P001+Z001)
P.l.delta.c <- max(-P100-P110, -P011-P111-P110-P100+Z000, -P001-P101-P100-P110+Z110,-P100-P110+Z100-Z010, -P110+P010-Z010, -P100+P000-Z100)
P.u.delta.c <- min(P000+P010, P011+P111+P010+P000-Z100, P000+P001+P101+P010-Z010, P000+P010+Z100-Z010, P010-P110+Z110, P000-P100+Z100)
P.t <- cbind(P.l.delta.t,P.u.delta.t)
P.c <- cbind(P.l.delta.c,P.u.delta.c)
#Parallel Encouragement
} else if(design=="PED") {
d$Z <- DorZ
dP000 <- sum(d$Y==0 & d$M==0 & d$T==0 & d$Z==-1)/sum(d$T==0 & d$Z==-1)
dP001 <- sum(d$Y==0 & d$M==0 & d$T==1 & d$Z==-1)/sum(d$T==1 & d$Z==-1)
dP010 <- sum(d$Y==0 & d$M==1 & d$T==0 & d$Z==-1)/sum(d$T==0 & d$Z==-1)
dP011 <- sum(d$Y==0 & d$M==1 & d$T==1 & d$Z==-1)/sum(d$T==1 & d$Z==-1)
dP100 <- sum(d$Y==1 & d$M==0 & d$T==0 & d$Z==-1)/sum(d$T==0 & d$Z==-1)
dP101 <- sum(d$Y==1 & d$M==0 & d$T==1 & d$Z==-1)/sum(d$T==1 & d$Z==-1)
dP110 <- sum(d$Y==1 & d$M==1 & d$T==0 & d$Z==-1)/sum(d$T==0 & d$Z==-1)
dP111 <- sum(d$Y==1 & d$M==1 & d$T==1 & d$Z==-1)/sum(d$T==1 & d$Z==-1)
tP000 <- sum(d$Y==0 & d$M==0 & d$T==0 & d$Z==0)/sum(d$T==0 & d$Z==0)
tP001 <- sum(d$Y==0 & d$M==0 & d$T==1 & d$Z==0)/sum(d$T==1 & d$Z==0)
tP010 <- sum(d$Y==0 & d$M==1 & d$T==0 & d$Z==0)/sum(d$T==0 & d$Z==0)
tP011 <- sum(d$Y==0 & d$M==1 & d$T==1 & d$Z==0)/sum(d$T==1 & d$Z==0)
tP100 <- sum(d$Y==1 & d$M==0 & d$T==0 & d$Z==0)/sum(d$T==0 & d$Z==0)
tP101 <- sum(d$Y==1 & d$M==0 & d$T==1 & d$Z==0)/sum(d$T==1 & d$Z==0)
tP110 <- sum(d$Y==1 & d$M==1 & d$T==0 & d$Z==0)/sum(d$T==0 & d$Z==0)
tP111 <- sum(d$Y==1 & d$M==1 & d$T==1 & d$Z==0)/sum(d$T==1 & d$Z==0)
sP000 <- sum(d$Y==0 & d$M==0 & d$T==0 & d$Z==1)/sum(d$T==0 & d$Z==1)
sP001 <- sum(d$Y==0 & d$M==0 & d$T==1 & d$Z==1)/sum(d$T==1 & d$Z==1)
sP010 <- sum(d$Y==0 & d$M==1 & d$T==0 & d$Z==1)/sum(d$T==0 & d$Z==1)
sP011 <- sum(d$Y==0 & d$M==1 & d$T==1 & d$Z==1)/sum(d$T==1 & d$Z==1)
sP100 <- sum(d$Y==1 & d$M==0 & d$T==0 & d$Z==1)/sum(d$T==0 & d$Z==1)
sP101 <- sum(d$Y==1 & d$M==0 & d$T==1 & d$Z==1)/sum(d$T==1 & d$Z==1)
sP110 <- sum(d$Y==1 & d$M==1 & d$T==0 & d$Z==1)/sum(d$T==0 & d$Z==1)
sP111 <- sum(d$Y==1 & d$M==1 & d$T==1 & d$Z==1)/sum(d$T==1 & d$Z==1)
P0 <- c(dP000,dP010,dP100,dP110,tP000,tP010,tP100,tP110,sP000,sP010,sP100,sP110)
P1 <- c(dP001,dP011,dP101,dP111,tP001,tP011,tP101,tP111,sP001,sP011,sP101,sP111)
Q0 <- c(dP010+dP110,tP010+tP110,sP010+sP110)
Q1 <- c(dP011+dP111,tP011+tP111,sP011+sP111)
#Linear programming functions
bounds.bidir.cmpl <- function(P,Q,dir){
f.obj <- c(rep(0,16), 0,0,1,0, 0,0,1,0, 0,-1,0,0, 0,-1,0,0,
0,0,-1,0, 0,0,-1,0, 0,1,0,0, 0,1,0,0, rep(0,16))
f.con <- matrix(c(
rep(c(1,1,1,0),8), rep(0,32), #dP00t
rep(c(rep(c(0,0,0,1),4), rep(0,16)),2), #dP01t
rep(0,32), rep(c(1,1,1,0),8), #dP10t
rep(c(rep(0,16), rep(c(0,0,0,1),4)),2), #dP11t
rep(c(1,1,0,0),8), rep(0,32), #tP00t
rep(c(rep(c(0,0,1,1),4), rep(0,16)),2), #tP01t
rep(0,32), rep(c(1,1,0,0),8), #tP10t
rep(c(rep(0,16), rep(c(0,0,1,1),4)),2), #tP11t
rep(c(1,0,0,0),8), rep(0,32), #sP00t
rep(c(rep(c(0,1,1,1),4), rep(0,16)),2), #sP01t
rep(0,32), rep(c(1,0,0,0),8), #sP10t
rep(c(rep(0,16), rep(c(0,1,1,1),4)),2), #sP11t
rep(c(rep(0,12), rep(1,4)),4), #dQ
rep(c(rep(0,8), rep(1,8)),4), #tQ
rep(c(rep(0,4), rep(1,12)),4), #sQ
rep(1,64) #sum=1
), nrow=16, byrow=T)
f.dir <- rep("=", 16)
f.rhs <- c(P,Q,1)
r <- lp(dir, f.obj, f.con, f.dir, f.rhs)
r$objval
}
bounds.bidir.popl <- function(P,Q,dir){
f.obj <- c(rep(0,16), 0,0,1,1, 0,0,1,1, -1,-1,0,0, -1,-1,0,0,
0,0,-1,-1, 0,0,-1,-1, 1,1,0,0, 1,1,0,0, rep(0,16))
f.con <- matrix(c(
rep(c(1,1,1,0),8), rep(0,32), #dP00t
rep(c(rep(c(0,0,0,1),4), rep(0,16)),2), #dP01t
rep(0,32), rep(c(1,1,1,0),8), #dP10t
rep(c(rep(0,16), rep(c(0,0,0,1),4)),2), #dP11t
rep(c(1,1,0,0),8), rep(0,32), #tP00t
rep(c(rep(c(0,0,1,1),4), rep(0,16)),2), #tP01t
rep(0,32), rep(c(1,1,0,0),8), #tP10t
rep(c(rep(0,16), rep(c(0,0,1,1),4)),2), #tP11t
rep(c(1,0,0,0),8), rep(0,32), #sP00t
rep(c(rep(c(0,1,1,1),4), rep(0,16)),2), #sP01t
rep(0,32), rep(c(1,0,0,0),8), #sP10t
rep(c(rep(0,16), rep(c(0,1,1,1),4)),2), #sP11t
rep(c(rep(0,12), rep(1,4)),4), #dQ
rep(c(rep(0,8), rep(1,8)),4), #tQ
rep(c(rep(0,4), rep(1,12)),4), #sQ
rep(1,64) #sum=1
), nrow=16, byrow=T)
f.dir <- rep("=", 16)
f.rhs <- c(P,Q,1)
r <- lp(dir, f.obj, f.con, f.dir, f.rhs)
r$objval
}
BE.t <- c(bounds.bidir.popl(P1, Q0, "min"), bounds.bidir.popl(P1, Q0, "max"))
BE.c <- c(-bounds.bidir.popl(P0 ,Q1, "max"), -bounds.bidir.popl(P0, Q1, "min"))
num.BET.t.lo <- bounds.bidir.cmpl(P1, Q0, "min")
num.BET.t.up <- bounds.bidir.cmpl(P1, Q0, "max")
num.BET.c.lo <- -bounds.bidir.cmpl(P0, Q1, "max")
num.BET.c.up <- -bounds.bidir.cmpl(P0, Q1, "min")
denom.BET.t <- P1[1] + P1[3] - P1[9] - P1[11]
denom.BET.c <- P0[1] + P0[3] - P0[9] - P0[11]
BET.t <- c(num.BET.t.lo/denom.BET.t, num.BET.t.up/denom.BET.t)
BET.c <- c(num.BET.c.lo/denom.BET.c, num.BET.c.up/denom.BET.c)
}#end computation section
# Output
if(design=="SED"){
out <- list(d1 = S.t, d0 = S.c, design=design, nobs=nobs)
} else if(design=="PD"){
out <- list(d1 = P.t, d0 = P.c, design=design, nobs=nobs)
} else if(design=="PED") {
out <- list(d1=BE.t, d0=BE.c, d1.p=BET.t, d0.p=BET.c, design=design, nobs=nobs)
}
rm(d)
class(out) <- "mediate.design"
out
}
## Summary methods
#' Summarizing Output from Design Based Mediation Analysis
#'
#' Function to report results from design based mediation analysis. Reported
#' categories differ depending on the design and assumptions used.
#'
#'
#' @aliases summary.mediate.design print.summary.mediate.design
#'
#' @param object object of class \code{mediate.design}, typically output from a
#' function for design-based mediation analysis (such as
#' \code{\link{mediate.sed}}).
#' @param x output from the summary 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}.
#'
#' @seealso \code{\link{mediate}}, \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., Tingley, D. and Yamamoto, T. (2012) Experimental Designs for
#' Identifying Causal Mechanisms. Journal of the Royal Statistical Society,
#' Series A (Statistics in Society)
#'
#' 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 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.design <- function(object, ...){
structure(object, class = c("summary.mediate.design", class(object)))
}
#' @rdname summary.mediate.design
#' @export
print.summary.mediate.design <- function(x, ...){
cat("\n")
cat("Design-Based Causal Mediation Analysis\n\n")
# Print values
if(x$design=="SED.NP.NOSI" | x$design=="PD"){
if(x$design=="SED.NP.NOSI"){
cat("Single Experiment Design (without Sequential Ignorability) \n\n")
}
if(x$design=="PD"){
cat("Parallel Design (Interaction Allowed) \n\n")
}
smat <- rbind(x$d0, x$d1)
colnames(smat) <- c("Lower Bound", "Upper Bound")
rownames(smat) <- c("ACME (control)", "ACME (treated)")
} else if(x$design=="PD.NINT"){
clp <- 100 * x$conf.level
cat("Parallel Design (with No Interaction Assumption) \n\n")
smat <- t(as.matrix(c(x$d0, x$d0.ci)))
colnames(smat) <- c("Estimate", paste(clp, "% CI Lower", sep=""),
paste(clp, "% CI Upper", sep=""))
rownames(smat) <- "ACME"
} else if(x$design=="PED"){
cat("Parallel Encouragement Design\n\n")
smat <- rbind(x$d0, x$d0.p, x$d1, x$d1.p)
colnames(smat) <- c("Lower Bound", "Upper Bound")
rownames(smat) <- c("Population ACME (control)", "Complier ACME (control)",
"Population ACME (treated)", "Complier ACME (treated)")
} else if(x$design=="CED"){
clp <- 100 * x$conf.level
cat("Crossover Encouragement Design \n\n")
smat <- rbind(c(x$d0, x$d0.ci), c(x$d1, x$d1.ci))
colnames(smat) <- c("Estimate", paste(clp, "% CI Lower", sep=""),
paste(clp, "% CI Upper", sep=""))
rownames(smat) <- c("Pliable ACME (control)", "Pliable ACME (treated)")
} else if(x$design=="SED.NP.SI"){
clp <- 100 * x$conf.level
cat("Single Experiment Design with Sequential Ignorability \n\n")
if(x$boot==TRUE){
cat("Confidence Intervals Based on Nonparametric Bootstrap\n\n")
} else {
cat("Confidence Intervals Based on Asymptotic Variance\n\n")
}
smat <- rbind(c(x$d0, x$d0.ci), c(x$d1, x$d1.ci))
colnames(smat) <- c("Estimate", paste(clp, "% CI Lower", sep=""),
paste(clp, "% CI Upper", sep=""))
rownames(smat) <- c("ACME (control)", "ACME (treated)")
}
printCoefmat(smat, digits=4)
cat("\n")
cat("Sample Size Used: ", x$nobs,"\n\n")
invisible(x)
}
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Defines functions mediate.sed mediate.pd mediate.ped mediate.ced mediate.np boot.pd mechanism.bounds summary.mediate.design print.summary.mediate.design
Documented in mediate.ced mediate.pd mediate.ped mediate.sed print.summary.mediate.design summary.mediate.design
## User interface functions
#single experiment design
#' Estimating Average Causal Mediation Effects under the Single Experiment
#' Design
#'
#' @details 'mediate.sed' estimates average causal mediation effects for the
#' single experiment design. The two options are to use either the sequential
#' ignorability (SI) assumption in which nonparametric estimates of the
#' average causal mediation effect are produced, or, to relax the SI
#' assumption and to calculate the nonparametric bounds on the average causal
#' mediation effect.
#'
#' This function calculates average causal mediation effects (ACME) for the
#' single experiment design, where the treatment is randomized and the
#' mediator/outcome variables are measured. The user specifies whether they
#' want non-parametric point estimates based on the sequential ignorability
#' (SI) assumption, or nonparametric bounds without the SI assumption.
#'
#' @param outcome name of the outcome variable in 'data'. The variable must be
#' binary (factor or numeric 0/1) if 'SI' is FALSE.
#' @param mediator name of the mediator in 'data'. The variable must be binary
#' (factor or numeric 0/1) if 'SI' is FALSE and discrete if TRUE.
#' @param treat name of the treatment variable in 'data'. Must be binary (factor
#' or numeric 0/1).
#' @param data a data frame containing all the above variables.
#' @param SI whether the sequential ignorability assumption is made.
#' @param sims number of bootstrap simulations. Only relevant when 'SI' is TRUE.
#' @param conf.level level of the returned two-sided confidence intervals. Only
#' relevant when 'SI' is TRUE.
#' @param boot a logical value. if 'FALSE' a large sample Delta method
#' approximation is used for confidence intervals; if 'TRUE' nonparametric
#' bootstrap will be used. Default is 'FALSE'. Only relevant if 'SI' is TRUE.
#'
#' @return \code{mediate.sed} returns an object of class
#' "\code{mediate.design}", a list that contains the components listed below.
#'
#' The \code{summary} function can be used to obtain a table of the results.
#'
#' \item{d0, d1}{point estimates or lower/upper bounds for causal mediation
#' effects under the control and treatment conditions, respectively.}
#' \item{d0.ci, d1.ci}{confidence intervals for average causal mediation
#' effects for the nonparametric estimates. The confidence level is set at the
#' value specified in 'conf.level'. The value exists only when 'SI' is TRUE.}
#' \item{boot}{logical, the 'boot' argument used.}
#' \item{conf.level}{the confidence level used. }
#' \item{sims}{number of bootstrap simulations used for confidence interval
#' calculation.}
#' \item{nobs}{number of observations used.}
#' \item{design}{ indicates the design. Equals either "SED.NP.SI" or
#' "SED.NP.NOSI".}
#'
#' @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{summary.mediate.design}}
#'
#' @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., Tingley, D. and Yamamoto, T. (2012) Experimental Designs for
#' Identifying Causal Mechanisms. Journal of the Royal Statistical Society,
#' Series A (Statistics in Society)"
#'
#' 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 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
#' # Example 1: Bounds without SI assumption
#'
#' data(boundsdata)
#'
#' data.SED <- subset(boundsdata, manip == 0)
#' bound1 <- mediate.sed("out", "med", "ttt", data.SED, SI=FALSE)
#' summary(bound1)
#'
#' # Example 2: Nonparametric estimate of ACME under SI assumption
#' # Example with JOBS II Field Experiment
#'
#' data(jobs)
#'
#' foo.1 <- mediate.sed("depress2", "job_disc", "treat", jobs, SI=TRUE)
#' summary(foo.1)
#'
#' foo.2 <- mediate.sed("depress2", "job_disc", "treat", jobs, SI=TRUE, boot=TRUE)
#' summary(foo.2)
mediate.sed <- function(outcome, mediator, treat, data,
SI = FALSE, sims = 1000, conf.level = 0.95, boot = FALSE) {
varnames <- c(outcome, mediator, treat)
data <- data[,varnames]
if(sum(is.na(data))){
warning("NA's in data. Observations with missing data removed.")
data <- na.omit(data)
}
data <- sapply(data, function(x) if(is.factor(x)) as.numeric(x)-1 else as.numeric(as.character(x)))
if(SI) {
out <- mediate.np(data[,outcome], data[,mediator], data[,treat],
sims, conf.level, boot)
out$design <- "SED.NP.SI"
} else {
check <- apply(data, 2, function(x) identical(sort(unique(x)), c(0,1)))
if(sum(check) != ncol(data)) {
stop("Invalid values in variables.")
}
out <- mechanism.bounds(data[,outcome], data[,mediator], data[,treat],
NULL, design = "SED")
out$design <- "SED.NP.NOSI"
}
out
}
#parallel design
#' Estimating Average Causal Mediation Effects under the Parallel Design
#'
#' 'mediate.pd' estimates the average causal mediation effects for the parallel
#' design. If a treatment-mediator interaction is allowed then the nonparametric
#' sharp bounds are calculated. If a treatment-mediator interaction is not
#' allowed then the estimates of the (point-identified) effects are computed
#' along with bootstrapped confidence intervals.
#'
#' @details This function calculates average causal mediation effects (ACME) for
#' the parallel design. The design consists of two randomly separated
#' experimental arms, indicated by 'manipulated'. In one the treatment is
#' randomized and the mediator and outcome variables are measured. In the
#' second arm, the treatment is randomized, the mediator is perfectly
#' manipulated and the outcome variable is measured.
#'
#' Under the parallel design, the ACME is identified when it is assumed that
#' there is no interaction between the treatment and mediator. Without the
#' assumption the nonparametric sharp bounds can be computed. See Imai,
#' Tingley and Yamamoto (2012) for details.
#'
#' @param outcome name of the outcome variable in 'data'.
#' @param mediator name of the mediator in 'data'. The variable must be binary
#' (factor or numeric 0/1).
#' @param treat name of the treatment variable in 'data'. Must be binary (factor
#' or numeric 0/1).
#' @param manipulated name of the binary design indicator in 'data', indicating
#' whether observation received mediator manipulation.
#' @param data a data frame containing all the above variables.
#' @param NINT whether the no interaction assumption is made.
#' @param sims number of bootstrap simulations. Only relevant when 'NINT' is
#' TRUE.
#' @param conf.level level of the returned two-sided confidence intervals. Only
#' relevant when 'NINT' is TRUE.
#'
#' @return \code{mediate.pd} returns an object of class "\code{mediate.design}",
#' a list that contains the components listed below.
#'
#' The function \code{summary} (i.e., \code{summary.mediate.design}) can be
#' used to obtain a table of the results.
#'
#' \item{d0, d1}{ point estimates or bounds for the average causal mediation
#' effects under the control and treatment conditions, respectively.}
#' \item{d0.ci, d1.ci}{ confidence intervals for the effects based on the
#' nonparametric bootstrap. The confidence level is set at the value specified
#' in 'conf.level'. Only exists when 'NINT' is TRUE.} \item{nobs}{ number of
#' observations used.} \item{conf.level}{ confidence level used. Only exists
#' when 'NINT' is TRUE.} \item{sims}{ number of bootstrap simulations used for
#' confidence interval calculation. Only exists when 'NINT' is TRUE.}
#' \item{design}{ indicates the design. "PD.NINT" if no interaction assumed;
#' "PD" if interaction allowed.}
#' @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{summary.mediate.design}}
#'
#' @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., Tingley, D. and Yamamoto, T. (2012) Experimental Designs for
#' Identifying Causal Mechanisms. Journal of the Royal Statistical Society,
#' Series A (Statistics in Society)"
#'
#' 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 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
#' data(boundsdata)
#'
#' bound2 <- mediate.pd("out", "med", "ttt", "manip", boundsdata,
#' NINT = TRUE, sims = 100, conf.level=.95)
#' summary(bound2)
#'
#' bound2.1 <- mediate.pd("out", "med", "ttt", "manip", boundsdata, NINT = FALSE)
#' summary(bound2.1)
mediate.pd <- function(outcome, mediator, treat, manipulated, data,
NINT = TRUE, sims = 1000, conf.level = 0.95) {
varnames <- c(outcome, mediator, treat, manipulated)
data <- data[,varnames]
if(sum(is.na(data))){
warning("NA's in data. Observations with missing data removed.")
data <- na.omit(data)
}
data <- sapply(data, function(x) as.numeric(as.character(x)))
check <- apply(data, 2, function(x) identical(sort(unique(x)), c(0,1)))
if(sum(check) != ncol(data)) {
stop("Invalid values in variables.")
}
if(NINT) {
out <- boot.pd(data[,outcome], data[,mediator], data[,treat],
data[,manipulated], sims, conf.level)
} else {
out <- mechanism.bounds(data[,outcome], data[,mediator], data[,treat],
data[,manipulated], design = "PD")
}
out
}
#parallel encouragement design
#' Computing Bounds on Average Causal Mediation Effects under the Parallel
#' Encouragement Design
#'
#' 'mediate.ped' computes the nonparametric bounds on the average causal
#' mediation effects for the parallel encouragement design.
#'
#' @details This function calculates average causal mediation effects (ACME) for
#' the parallel encouragement design.
#'
#' In the design two experimental arms are
#' used. In one the treatment is randomized and the mediator and outcome
#' variables are measured. In the second arm the treatment is randomized, the
#' mediator is randomly encouraged either up or down, and the outcome variable
#' is measured.
#'
#' Two type of causal quantities are estimated: the population
#' ACME and the complier ACME. The latter refers to the subpopulation of the
#' units for whom the encouragement has its intended effect, and the width of
#' its bounds are tighter than that of the population ACME. See Imai, Tingley
#' and Yamamoto (2012) for details.
#'
#' @param outcome name of the outcome variable in 'data'.
#' @param mediator name of the mediator in 'data'. The variable must be binary
#' (factor or numeric 0/1).
#' @param treat name of the treatment variable in 'data'. Must be binary
#' (factor or numeric 0/1).
#' @param encourage name of the encouragement variable in 'data'. The variable
#' must be a numeric vector taking on either -1, 0, or 1.
#' @param data a data frame containing all the above variables.
#'
#' @return \code{mediate.pd} returns an object of class
#' "\code{mediate.design}", a list that contains the components listed below.
#'
#' The function \code{summary} (i.e., \code{summary.mediate.design}) can be
#' used to obtain a table of the results.
#'
#' \item{d0, d1}{ estimated nonparametric sharp bounds for the population ACME under the control and treatment conditions.}
#' \item{d0.p, d1.p}{ estimated nonparametric sharp bounds for the complier ACME under the control and treatment conditions.}
#' \item{nobs}{ number of observations used.}
#' \item{design}{ indicates the design. Always equals "PED".}
#'
#' @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{medsens}},
#' \code{\link{plot.mediate}}, \code{\link{summary.mediate}},
#' \code{\link{mediations}}
#'
#' @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., Tingley, D. and Yamamoto, T. (2012) Experimental Designs for
#' Identifying Causal Mechanisms. Journal of the Royal Statistical Society,
#' Series A (Statistics in Society)"
#'
#' 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
#' data(boundsdata)
#'
#' bound3 <- mediate.ped("out.enc", "med.enc", "ttt", "enc", boundsdata)
#' summary(bound3)
mediate.ped <- function(outcome, mediator, treat, encourage, data) {
varnames <- c(outcome, mediator, treat, encourage)
data <- data[,varnames]
if(sum(is.na(data))){
warning("NA's in data. Observations with missing data removed.")
data <- na.omit(data)
}
data <- sapply(data, function(x) as.numeric(as.character(x)))
check.1 <- apply(data[,1:3], 2, function(x) identical(sort(unique(x)), c(0,1)))
check.2 <- identical(sort(unique(data[,4])), c(-1,0,1))
if(sum(check.1, check.2) != ncol(data)) {
stop("Invalid values in variables.")
}
out <- mechanism.bounds(data[,outcome], data[,mediator], data[,treat],
data[,encourage], design = "PED")
out
}
#crossover encouragement design
#' Estimating Average Causal Mediation Effects under the Crossover Encouragement
#' Design
#'
#' 'mediate.ced' estimates the average causal mediation effects for the
#' crossover encouragement design.
#'
#' @details This function estimates the average indirect effects for the pliable
#' units under the crossover encouragement design. The design has two stages.
#' In the first stage the treatment is randomized and the mediator and outcome
#' variables are measured. In the second the treatment is set to the value
#' opposite of first period and a randomly selected group of units receives
#' encouragement to take on the mediator opposite to the values observed in
#' the first stage. See Imai, Tingley and Yamamoto (2012) for a full
#' description. The confidence intervals are calculated via the nonparametric
#' bootstrap.
#'
#' Note that \code{outcome} should be the observed responses in the
#' \emph{second} stage whereas \code{treat} should be the values in the
#' \emph{first} stage.
#'
#' @param outcome variable name in 'data' containing the outcome values observed
#' in the second experiment. The variable must be binary (factor or numeric
#' 0/1).
#' @param med.1 variable name in 'data' containing the mediator values observed
#' in the first experiment. The variable must be binary (factor or numeric
#' 0/1).
#' @param med.2 variable name in 'data' containing the mediator values observed
#' in the second experiment.
#' @param treat variable name in 'data' containing the treatment values in the
#' first experiment. Must be binary (factor or numeric 0/1).
#' @param encourage name of the encouragement indicator in 'data'. Must be
#' binary (factor or numeric 0/1).
#' @param data a data frame containing all the above variables.
#' @param sims number of bootstrap simulations.
#' @param conf.level level of the returned two-sided confidence intervals.
#'
#' @return \code{mediate.ced} returns an object of class
#' "\code{mediate.design}", a list that contains the components listed below.
#'
#' The \code{summary} function can be used to obtain a table of the results.
#'
#' \item{d0, d1}{point estimates of the average indirect effects under the control and treatment conditions.}
#' \item{d0.ci, d1.ci}{confidence intervals for the effects. The confidence level is set at the value specified in 'conf.level'.}
#' \item{conf.level}{ confidence level used.}
#' \item{sims}{ number of bootstrap simulations.}
#' \item{nobs}{ number of observations used.}
#' \item{design}{ indicates the design. Always equals "CED".}
#'
#' @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{summary.mediate.design}}
#'
#' @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., Tingley, D. and Yamamoto, T. (2012) Experimental Designs for
#' Identifying Causal Mechanisms. Journal of the Royal Statistical Society,
#' Series A (Statistics in Society)"
#'
#' 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 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
#' data(CEDdata)
#'
#' res <- mediate.ced("Y2", "M1", "M2", "T1", "Z", CEDdata, sims = 100)
#' summary(res)
mediate.ced <- function(outcome, med.1, med.2, treat, encourage, data,
sims = 1000, conf.level = .95){
varnames <- c(outcome, treat, med.1, med.2, encourage)
data <- data[,varnames]
if(sum(is.na(data))){
warning("NA's in data. Observations with missing data removed.")
data <- na.omit(data)
}
data <- sapply(data, function(x) as.numeric(as.character(x)))
data <- as.data.frame(data)
check <- apply(data, 2, function(x) identical(sort(unique(x)), c(0,1)))
if(sum(check) != ncol(data)) {
stop("Invalid values in variables.")
}
names(data) <- c("Y2","T","M1","M2","V")
n <- nrow(data)
# Storage
d.p.c <- d.p.t <- matrix(NA, sims, 1)
# Bootstrap function.
for(b in 1:(sims+1)){
index <- sample(1:n, n, replace = TRUE)
if(b == sims + 1){
index <- 1:n
}
d <- data[index,]
#Atmv
A111 <- sum(d$M2==1 & d$T==1 & d$M1==1 & d$V==1)/sum(d$T==1 & d$M1==1 & d$V==1)
A011 <- sum(d$M2==1 & d$T==0 & d$M1==1 & d$V==1)/sum(d$T==0 & d$M1==1 & d$V==1)
A101 <- sum(d$M2==1 & d$T==1 & d$M1==0 & d$V==1)/sum(d$T==1 & d$M1==0 & d$V==1)
A001 <- sum(d$M2==1 & d$T==0 & d$M1==0 & d$V==1)/sum(d$T==0 & d$M1==0 & d$V==1)
A110 <- sum(d$M2==1 & d$T==1 & d$M1==1 & d$V==0)/sum(d$T==1 & d$M1==1 & d$V==0)
A010 <- sum(d$M2==1 & d$T==0 & d$M1==1 & d$V==0)/sum(d$T==0 & d$M1==1 & d$V==0)
A100 <- sum(d$M2==1 & d$T==1 & d$M1==0 & d$V==0)/sum(d$T==1 & d$M1==0 & d$V==0)
A000 <- sum(d$M2==1 & d$T==0 & d$M1==0 & d$V==0)/sum(d$T==0 & d$M1==0 & d$V==0)
#Gtm1m2
G1111 <- mean(d$Y2[d$T==1 & d$M1==1 & d$M2==1 & d$V==1])
G0111 <- mean(d$Y2[d$T==0 & d$M1==1 & d$M2==1 & d$V==1])
G1011 <- mean(d$Y2[d$T==1 & d$M1==0 & d$M2==1 & d$V==1])
G0011 <- mean(d$Y2[d$T==0 & d$M1==0 & d$M2==1 & d$V==1])
G1101 <- mean(d$Y2[d$T==1 & d$M1==1 & d$M2==0 & d$V==1])
G0101 <- mean(d$Y2[d$T==0 & d$M1==1 & d$M2==0 & d$V==1])
G1001 <- mean(d$Y2[d$T==1 & d$M1==0 & d$M2==0 & d$V==1])
G0001 <- mean(d$Y2[d$T==0 & d$M1==0 & d$M2==0 & d$V==1])
G1110 <- mean(d$Y2[d$T==1 & d$M1==1 & d$M2==1 & d$V==0])
G0110 <- mean(d$Y2[d$T==0 & d$M1==1 & d$M2==1 & d$V==0])
G1010 <- mean(d$Y2[d$T==1 & d$M1==0 & d$M2==1 & d$V==0])
G0010 <- mean(d$Y2[d$T==0 & d$M1==0 & d$M2==1 & d$V==0])
G1100 <- mean(d$Y2[d$T==1 & d$M1==1 & d$M2==0 & d$V==0])
G0100 <- mean(d$Y2[d$T==0 & d$M1==1 & d$M2==0 & d$V==0])
G1000 <- mean(d$Y2[d$T==1 & d$M1==0 & d$M2==0 & d$V==0])
G0000 <- mean(d$Y2[d$T==0 & d$M1==0 & d$M2==0 & d$V==0])
Q11 <- sum(d$T==1 & d$M1==1)/sum(d$T==1)
Q10 <- sum(d$T==1 & d$M1==0)/sum(d$T==1)
Q01 <- sum(d$T==0 & d$M1==1)/sum(d$T==0)
Q00 <- sum(d$T==0 & d$M1==0)/sum(d$T==0)
B11 <- Q11/((A100 - A101)*Q10 + (A111 - A110)*Q11)
B10 <- Q10/((A100 - A101)*Q10 + (A111 - A110)*Q11)
B01 <- Q01/((A000 - A001)*Q00 + (A011 - A010)*Q01)
B00 <- Q00/((A000 - A001)*Q00 + (A011 - A010)*Q01)
if(b == sims + 1){
d.p.c.mu <- (-A110*G1110 - (1-A110)*G1100 + A111*G1111 + (1-A111)*G1101) * B11 +
(-A100*G1010 - (1-A100)*G1000 + A101*G1011 + (1-A101)*G1001) * B10
d.p.t.mu <- (A000*G0010 + (1-A000)*G0000 - A001*G0011 - (1-A001)*G0001) * B00 +
(A010*G0110 + (1-A010)*G0100 - A011*G0111 - (1-A011)*G0101) * B01
} else {
d.p.c[b] <- (-A110*G1110 - (1-A110)*G1100 + A111*G1111 + (1-A111)*G1101) * B11 +
(-A100*G1010 - (1-A100)*G1000 + A101*G1011 + (1-A101)*G1001) * B10
d.p.t[b] <- (A000*G0010 + (1-A000)*G0000 - A001*G0011 - (1-A001)*G0001) * B00 +
(A010*G0110 + (1-A010)*G0100 - A011*G0111 - (1-A011)*G0101) * B01
}
}#bootstraploop
if(is.nan(d.p.c.mu) | is.nan(d.p.t.mu)){
warning("NaN produced; distribution of observed variables may be too sparse")
}
d.p.c[d.p.c==-Inf] <- NA
d.p.t[d.p.t==-Inf] <- NA
d.p.c[d.p.c==Inf] <- NA
d.p.t[d.p.t==Inf] <- NA
low <- (1 - conf.level)/2
high <- 1 - low
d.p.c.ci <- quantile(d.p.c, c(low,high), na.rm=TRUE)
d.p.t.ci <- quantile(d.p.t, c(low,high), na.rm=TRUE)
out <- list(d0 = d.p.c.mu, d1 = d.p.t.mu, d0.ci = d.p.c.ci, d1.ci = d.p.t.ci,
nobs = n, sims = sims, conf.level = conf.level, design = "CED")
class(out) <- "mediate.design"
out
}
## Internal functions
#nonparametric under SI assumption
mediate.np <- function(Y, M, T, sims, conf.level, boot){
# samp <- data.frame(na.omit(cbind(M,Y,T)))
samp <- data.frame(Y=Y, M=M, T=T)
m.cat <- sort(unique(samp$M))
n <- length(samp$Y)
n1 <- sum(samp$T)
n0 <- sum(1-samp$T)
t <- (1 - conf.level)/2
if(boot){
idx <- seq(1,n,1)
d0.bs <- matrix(NA,sims,1)
d1.bs <- matrix(NA,sims,1)
for(b in 1:(sims+1)){
resample <- sample(idx,n,replace=TRUE)
if(b == sims + 1){
resample <- 1:n
}
samp.star <- samp[resample,]
delta_0m <- delta_1m <- matrix(NA, length(m.cat), 1)
for(i in 1:length(m.cat)){
delta_0m[i] <- (sum(samp.star$T[samp.star$M==m.cat[i]]) *
sum(samp.star$Y[samp.star$M==m.cat[i] & samp.star$T==0])) /
(n1*(sum((1 - samp.star$T[samp.star$M==m.cat[i]]))))
delta_1m[i] <- (sum((1 - samp.star$T[samp.star$M==m.cat[i]])) *
sum(samp.star$Y[samp.star$M==m.cat[i] & samp.star$T==1])) /
(n0*(sum(samp.star$T[samp.star$M==m.cat[i]])))
}
if(b == sims + 1){
d0 <- sum(delta_0m) - mean(samp.star$Y[samp.star$T==0])
d1 <- mean(samp.star$Y[samp.star$T==1]) - sum(delta_1m)
} else {
d0.bs[b,] <- sum(delta_0m) - mean(samp.star$Y[samp.star$T==0])
d1.bs[b,] <- mean(samp.star$Y[samp.star$T==1]) - sum(delta_1m)
}
}
low <- (1 - conf.level)/2
high <- 1 - low
d0.ci <- quantile(d0.bs,c(low,high), na.rm=TRUE)
d1.ci <- quantile(d1.bs,c(low,high), na.rm=TRUE)
} else {
delta_0m <- delta_1m <- matrix(NA, length(m.cat), 1)
for(i in 1:length(m.cat)){
delta_0m[i] <- (sum(samp$T[samp$M==m.cat[i]]) *
sum(samp$Y[samp$M==m.cat[i] & samp$T==0])) /
(n1*(sum((1 - samp$T[samp$M==m.cat[i]]))))
delta_1m[i] <- (sum((1 - samp$T[samp$M==m.cat[i]])) *
sum(samp$Y[samp$M==m.cat[i] & samp$T==1])) /
(n0*(sum(samp$T[samp$M==m.cat[i]])))
}
d0 <- sum(delta_0m) - mean(samp$Y[samp$T==0])
d1 <- mean(samp$Y[samp$T==1]) - sum(delta_1m)
pr.t.1 <- sum(samp$T)/n
pr.t.0 <- sum(1-samp$T)/n
lambda.1m <- lambda.0m <- matrix(NA, length(m.cat), 1)
for(i in 1:length(m.cat)){
lambda.1m[i] <- (sum(length(samp$M[samp$M==m.cat[i] & samp$T==1])))/n /pr.t.1
lambda.0m[i] <- (sum(length(samp$M[samp$M==m.cat[i] & samp$T==0])))/n /pr.t.0
}
mu.1m <- mu.0m <- matrix(NA, length(m.cat), 1)
for(i in 1:length(m.cat)){
mu.1m[i] <- mean(samp$Y[samp$M==m.cat[i] & samp$T==1])
mu.0m[i] <- mean(samp$Y[samp$M==m.cat[i] & samp$T==0])
}
# Variance of Delta_0
var.delta.0m <- matrix(NA, length(m.cat), 1)
for(i in 1:length(m.cat)){
var.delta.0m[i] <- lambda.1m[i]*(((lambda.1m[i]/lambda.0m[i]) - 2) *
var(samp$Y[samp$M==m.cat[i] & samp$T==0]) +
((n0*(1-lambda.1m[i])*mu.0m[i]^2)/n1))
}
m.leng <- length(m.cat)
mterm.d0 <- c()
for(i in 1:m.leng-1){
mterm.d0 <- c(mterm.d0, lambda.1m[i] * lambda.1m[(i+1):m.leng] *
mu.0m[i] * mu.0m[(i+1):m.leng])
}
var.delta_0 <- (1/n0) * sum(var.delta.0m) - (2/n1) * sum(mterm.d0) +
var(samp$Y[samp$T == 0])/n0
# Variance of Delta_1
var.delta.1m <- matrix(NA, length(m.cat), 1)
for(i in 1:length(m.cat)){
var.delta.1m[i] <- lambda.0m[i]*(((lambda.0m[i]/lambda.1m[i]) - 2) *
var(samp$Y[samp$M==m.cat[i] & samp$T==1]) +
((n1*(1-lambda.0m[i])*mu.1m[i]^2)/n0))
}
mterm.d1 <- c()
for(i in 1:m.leng-1){
mterm.d1 <- c(mterm.d1, lambda.0m[i] * lambda.0m[(i+1):m.leng] *
mu.1m[i] * mu.1m[(i+1):m.leng])
}
var.delta_1 <- (1/n1) * sum(var.delta.1m) - (2/n0)* sum(mterm.d1) +
var(samp$Y[samp$T == 1])/n1
d0.ci <- c(d0 - (-qnorm(t)*sqrt(var.delta_0)), d0 + (-qnorm(t)*sqrt(var.delta_0)))
d1.ci <- c(d1 - (-qnorm(t)*sqrt(var.delta_1)), d1 + (-qnorm(t)*sqrt(var.delta_1)))
}
out <- list(d0=d0, d1=d1, d0.ci=d0.ci, d1.ci=d1.ci,
conf.level=conf.level, nobs=n, boot=boot)
class(out) <- "mediate.design"
out
}
#parallel design under no interaction assumption
boot.pd <- function(outcome, mediator, treatment, manipulated,
sims, conf.level) {
n <- length(outcome)
data <- matrix(, nrow = n, ncol = 4)
data[,1] <- outcome
data[,2] <- treatment
data[,3] <- mediator
data[,4] <- manipulated
data <- as.data.frame(data)
names(data) <- c("Y","T","M","D")
acme <- matrix(NA, sims, 1)
for(b in 1:(sims+1)){ # bootstrap
index <- sample(1:n, n, replace = TRUE)
if(b == sims + 1){
index <- 1:n
}
d <- data[index,]
tau <- mean(d$Y[d$T==1 & d$D==0]) - mean(d$Y[d$T==0 & d$D==0])
weight.m1 <- sum(d$M==1 & d$D==1 )/sum(d$D==1)
weight.m0 <- sum(d$M==0 & d$D==1 )/sum(d$D==1)
m1 <- mean(d$Y[d$T==1 & d$M==1 & d$D==1]) - mean(d$Y[d$T==0 &
d$M==1 & d$D==1])
m0 <- mean(d$Y[d$T==1 & d$M==0 & d$D==1]) - mean(d$Y[d$T==0 &
d$M==0 & d$D==1])
z <- weight.m1*m1 + weight.m0*m0
if(b == sims + 1){
acme.mu <- tau - z
} else {
acme[b] <- tau - z
}
}
acme[acme==-Inf] <- NA
acme[acme==Inf] <- NA
low <- (1 - conf.level)/2
high <- 1 - low
acme.ci <- quantile(acme, c(low,high), na.rm=TRUE)
out <- list(d0 = acme.mu, d1 = acme.mu, d0.ci = acme.ci, d1.ci =
acme.ci,
nobs = n, conf.level = conf.level, sims = sims, design
= "PD.NINT")
class(out) <- "mediate.design"
out
}
#Bounds Function for parallel, parallel encouragement, and single experiment designs
mechanism.bounds <- function(outcome, mediator, treatment, DorZ, design) {
d <- matrix(, nrow=length(outcome), ncol=3)
d[,1] <- outcome
d[,2] <- treatment
d[,3] <- mediator
d <- as.data.frame(d)
names(d) <- c("Y","T","M")
nobs <- nrow(d)
## "DorZ" indicates the variable that assigns manipulation direction.
## Z in the JRSSA paper. This is left to null for the single experiment design.
# Single Experiment
if(design=="SED") {
d$Z <- 0
P111 <- sum(d$Y==1 & d$M==1 & d$Z==0 & d$T==1)/sum(d$T==1 & d$Z==0)
P101 <- sum(d$Y==1 & d$M==0 & d$Z==0 & d$T==1)/sum(d$T==1 & d$Z==0)
P001 <- sum(d$Y==0 & d$M==0 & d$Z==0 & d$T==1)/sum(d$T==1 & d$Z==0)
P011 <- sum(d$Y==0 & d$M==1 & d$Z==0 & d$T==1)/sum(d$T==1 & d$Z==0)
P110 <- sum(d$Y==1 & d$M==1 & d$Z==0 & d$T==0)/sum(d$T==0 & d$Z==0)
P100 <- sum(d$Y==1 & d$M==0 & d$Z==0 & d$T==0)/sum(d$T==0 & d$Z==0)
P000 <- sum(d$Y==0 & d$M==0 & d$Z==0 & d$T==0)/sum(d$T==0 & d$Z==0)
P010 <- sum(d$Y==0 & d$M==1 & d$Z==0 & d$T==0)/sum(d$T==0 & d$Z==0)
l.delta.t <- max(-P001-P011, -P000-P001-P100, -P011-P010-P110)
u.delta.t <- min(P101+P111, P000+P100+P101, P010+P110+P111)
l.delta.c <- max(-P100-P110, -P001-P101-P100, -P011-P111-P110)
u.delta.c <- min(P000+P010, P011+P111+P010, P000+P001+P101)
S.t <- cbind(l.delta.t,u.delta.t)
S.c <- cbind(l.delta.c,u.delta.c)
# Parallel
} else if(design=="PD") {
## D indicates if there was manipulation
d$D <- DorZ
Z111 <- sum(d$Y==1 & d$T==1 & d$M==1 & d$D==1)/sum(d$T==1 & d$M==1 & d$D==1)
Z011 <- sum(d$Y==0 & d$T==1 & d$M==1 & d$D==1)/sum(d$T==1 & d$M==1 & d$D==1)
Z001 <- sum(d$Y==0 & d$T==1 & d$M==0 & d$D==1)/sum(d$T==1 & d$M==0 & d$D==1)
Z110 <- sum(d$Y==1 & d$T==0 & d$M==1 & d$D==1)/sum(d$T==0 & d$M==1 & d$D==1)
Z010 <- sum(d$Y==0 & d$T==0 & d$M==1 & d$D==1)/sum(d$T==0 & d$M==1 & d$D==1)
Z000 <- sum(d$Y==0 & d$T==0 & d$M==0 & d$D==1)/sum(d$T==0 & d$M==0 & d$D==1)
Z101 <- sum(d$Y==1 & d$T==1 & d$M==0 & d$D==1)/sum(d$T==1 & d$M==0 & d$D==1)
Z100 <- sum(d$Y==1 & d$T==0 & d$M==0 & d$D==1)/sum(d$T==0 & d$M==0 & d$D==1)
P111 <- sum(d$Y==1 & d$M==1 & d$T==1 & d$D==0)/sum(d$T==1 & d$D==0)
P101 <- sum(d$Y==1 & d$M==0 & d$T==1 & d$D==0)/sum(d$T==1 & d$D==0)
P001 <- sum(d$Y==0 & d$M==0 & d$T==1 & d$D==0)/sum(d$T==1 & d$D==0)
P011 <- sum(d$Y==0 & d$M==1 & d$T==1 & d$D==0)/sum(d$T==1 & d$D==0)
P110 <- sum(d$Y==1 & d$M==1 & d$T==0 & d$D==0)/sum(d$T==0 & d$D==0)
P100 <- sum(d$Y==1 & d$M==0 & d$T==0 & d$D==0)/sum(d$T==0 & d$D==0)
P000 <- sum(d$Y==0 & d$M==0 & d$T==0 & d$D==0)/sum(d$T==0 & d$D==0)
P010 <- sum(d$Y==0 & d$M==1 & d$T==0 & d$D==0)/sum(d$T==0 & d$D==0)
P.l.delta.t <- max(-P001-P011, -P011-P010-P110-P001+Z001, -P000-P001-P100-P011+Z011, -P001-P011+Z001-Z111, -P001+P101-Z101, -P011+P111-Z111)
P.u.delta.t <- min(P101+P111, P010+P110+P101+P111-Z101, P000+P100+P101+P111-Z111, P101+P111+Z001-Z111, P111-P011+Z011, P101-P001+Z001)
P.l.delta.c <- max(-P100-P110, -P011-P111-P110-P100+Z000, -P001-P101-P100-P110+Z110,-P100-P110+Z100-Z010, -P110+P010-Z010, -P100+P000-Z100)
P.u.delta.c <- min(P000+P010, P011+P111+P010+P000-Z100, P000+P001+P101+P010-Z010, P000+P010+Z100-Z010, P010-P110+Z110, P000-P100+Z100)
P.t <- cbind(P.l.delta.t,P.u.delta.t)
P.c <- cbind(P.l.delta.c,P.u.delta.c)
#Parallel Encouragement
} else if(design=="PED") {
d$Z <- DorZ
dP000 <- sum(d$Y==0 & d$M==0 & d$T==0 & d$Z==-1)/sum(d$T==0 & d$Z==-1)
dP001 <- sum(d$Y==0 & d$M==0 & d$T==1 & d$Z==-1)/sum(d$T==1 & d$Z==-1)
dP010 <- sum(d$Y==0 & d$M==1 & d$T==0 & d$Z==-1)/sum(d$T==0 & d$Z==-1)
dP011 <- sum(d$Y==0 & d$M==1 & d$T==1 & d$Z==-1)/sum(d$T==1 & d$Z==-1)
dP100 <- sum(d$Y==1 & d$M==0 & d$T==0 & d$Z==-1)/sum(d$T==0 & d$Z==-1)
dP101 <- sum(d$Y==1 & d$M==0 & d$T==1 & d$Z==-1)/sum(d$T==1 & d$Z==-1)
dP110 <- sum(d$Y==1 & d$M==1 & d$T==0 & d$Z==-1)/sum(d$T==0 & d$Z==-1)
dP111 <- sum(d$Y==1 & d$M==1 & d$T==1 & d$Z==-1)/sum(d$T==1 & d$Z==-1)
tP000 <- sum(d$Y==0 & d$M==0 & d$T==0 & d$Z==0)/sum(d$T==0 & d$Z==0)
tP001 <- sum(d$Y==0 & d$M==0 & d$T==1 & d$Z==0)/sum(d$T==1 & d$Z==0)
tP010 <- sum(d$Y==0 & d$M==1 & d$T==0 & d$Z==0)/sum(d$T==0 & d$Z==0)
tP011 <- sum(d$Y==0 & d$M==1 & d$T==1 & d$Z==0)/sum(d$T==1 & d$Z==0)
tP100 <- sum(d$Y==1 & d$M==0 & d$T==0 & d$Z==0)/sum(d$T==0 & d$Z==0)
tP101 <- sum(d$Y==1 & d$M==0 & d$T==1 & d$Z==0)/sum(d$T==1 & d$Z==0)
tP110 <- sum(d$Y==1 & d$M==1 & d$T==0 & d$Z==0)/sum(d$T==0 & d$Z==0)
tP111 <- sum(d$Y==1 & d$M==1 & d$T==1 & d$Z==0)/sum(d$T==1 & d$Z==0)
sP000 <- sum(d$Y==0 & d$M==0 & d$T==0 & d$Z==1)/sum(d$T==0 & d$Z==1)
sP001 <- sum(d$Y==0 & d$M==0 & d$T==1 & d$Z==1)/sum(d$T==1 & d$Z==1)
sP010 <- sum(d$Y==0 & d$M==1 & d$T==0 & d$Z==1)/sum(d$T==0 & d$Z==1)
sP011 <- sum(d$Y==0 & d$M==1 & d$T==1 & d$Z==1)/sum(d$T==1 & d$Z==1)
sP100 <- sum(d$Y==1 & d$M==0 & d$T==0 & d$Z==1)/sum(d$T==0 & d$Z==1)
sP101 <- sum(d$Y==1 & d$M==0 & d$T==1 & d$Z==1)/sum(d$T==1 & d$Z==1)
sP110 <- sum(d$Y==1 & d$M==1 & d$T==0 & d$Z==1)/sum(d$T==0 & d$Z==1)
sP111 <- sum(d$Y==1 & d$M==1 & d$T==1 & d$Z==1)/sum(d$T==1 & d$Z==1)
P0 <- c(dP000,dP010,dP100,dP110,tP000,tP010,tP100,tP110,sP000,sP010,sP100,sP110)
P1 <- c(dP001,dP011,dP101,dP111,tP001,tP011,tP101,tP111,sP001,sP011,sP101,sP111)
Q0 <- c(dP010+dP110,tP010+tP110,sP010+sP110)
Q1 <- c(dP011+dP111,tP011+tP111,sP011+sP111)
#Linear programming functions
bounds.bidir.cmpl <- function(P,Q,dir){
f.obj <- c(rep(0,16), 0,0,1,0, 0,0,1,0, 0,-1,0,0, 0,-1,0,0,
0,0,-1,0, 0,0,-1,0, 0,1,0,0, 0,1,0,0, rep(0,16))
f.con <- matrix(c(
rep(c(1,1,1,0),8), rep(0,32), #dP00t
rep(c(rep(c(0,0,0,1),4), rep(0,16)),2), #dP01t
rep(0,32), rep(c(1,1,1,0),8), #dP10t
rep(c(rep(0,16), rep(c(0,0,0,1),4)),2), #dP11t
rep(c(1,1,0,0),8), rep(0,32), #tP00t
rep(c(rep(c(0,0,1,1),4), rep(0,16)),2), #tP01t
rep(0,32), rep(c(1,1,0,0),8), #tP10t
rep(c(rep(0,16), rep(c(0,0,1,1),4)),2), #tP11t
rep(c(1,0,0,0),8), rep(0,32), #sP00t
rep(c(rep(c(0,1,1,1),4), rep(0,16)),2), #sP01t
rep(0,32), rep(c(1,0,0,0),8), #sP10t
rep(c(rep(0,16), rep(c(0,1,1,1),4)),2), #sP11t
rep(c(rep(0,12), rep(1,4)),4), #dQ
rep(c(rep(0,8), rep(1,8)),4), #tQ
rep(c(rep(0,4), rep(1,12)),4), #sQ
rep(1,64) #sum=1
), nrow=16, byrow=T)
f.dir <- rep("=", 16)
f.rhs <- c(P,Q,1)
r <- lp(dir, f.obj, f.con, f.dir, f.rhs)
r$objval
}
bounds.bidir.popl <- function(P,Q,dir){
f.obj <- c(rep(0,16), 0,0,1,1, 0,0,1,1, -1,-1,0,0, -1,-1,0,0,
0,0,-1,-1, 0,0,-1,-1, 1,1,0,0, 1,1,0,0, rep(0,16))
f.con <- matrix(c(
rep(c(1,1,1,0),8), rep(0,32), #dP00t
rep(c(rep(c(0,0,0,1),4), rep(0,16)),2), #dP01t
rep(0,32), rep(c(1,1,1,0),8), #dP10t
rep(c(rep(0,16), rep(c(0,0,0,1),4)),2), #dP11t
rep(c(1,1,0,0),8), rep(0,32), #tP00t
rep(c(rep(c(0,0,1,1),4), rep(0,16)),2), #tP01t
rep(0,32), rep(c(1,1,0,0),8), #tP10t
rep(c(rep(0,16), rep(c(0,0,1,1),4)),2), #tP11t
rep(c(1,0,0,0),8), rep(0,32), #sP00t
rep(c(rep(c(0,1,1,1),4), rep(0,16)),2), #sP01t
rep(0,32), rep(c(1,0,0,0),8), #sP10t
rep(c(rep(0,16), rep(c(0,1,1,1),4)),2), #sP11t
rep(c(rep(0,12), rep(1,4)),4), #dQ
rep(c(rep(0,8), rep(1,8)),4), #tQ
rep(c(rep(0,4), rep(1,12)),4), #sQ
rep(1,64) #sum=1
), nrow=16, byrow=T)
f.dir <- rep("=", 16)
f.rhs <- c(P,Q,1)
r <- lp(dir, f.obj, f.con, f.dir, f.rhs)
r$objval
}
BE.t <- c(bounds.bidir.popl(P1, Q0, "min"), bounds.bidir.popl(P1, Q0, "max"))
BE.c <- c(-bounds.bidir.popl(P0 ,Q1, "max"), -bounds.bidir.popl(P0, Q1, "min"))
num.BET.t.lo <- bounds.bidir.cmpl(P1, Q0, "min")
num.BET.t.up <- bounds.bidir.cmpl(P1, Q0, "max")
num.BET.c.lo <- -bounds.bidir.cmpl(P0, Q1, "max")
num.BET.c.up <- -bounds.bidir.cmpl(P0, Q1, "min")
denom.BET.t <- P1[1] + P1[3] - P1[9] - P1[11]
denom.BET.c <- P0[1] + P0[3] - P0[9] - P0[11]
BET.t <- c(num.BET.t.lo/denom.BET.t, num.BET.t.up/denom.BET.t)
BET.c <- c(num.BET.c.lo/denom.BET.c, num.BET.c.up/denom.BET.c)
}#end computation section
# Output
if(design=="SED"){
out <- list(d1 = S.t, d0 = S.c, design=design, nobs=nobs)
} else if(design=="PD"){
out <- list(d1 = P.t, d0 = P.c, design=design, nobs=nobs)
} else if(design=="PED") {
out <- list(d1=BE.t, d0=BE.c, d1.p=BET.t, d0.p=BET.c, design=design, nobs=nobs)
}
rm(d)
class(out) <- "mediate.design"
out
}
## Summary methods
#' Summarizing Output from Design Based Mediation Analysis
#'
#' Function to report results from design based mediation analysis. Reported
#' categories differ depending on the design and assumptions used.
#'
#'
#' @aliases summary.mediate.design print.summary.mediate.design
#'
#' @param object object of class \code{mediate.design}, typically output from a
#' function for design-based mediation analysis (such as
#' \code{\link{mediate.sed}}).
#' @param x output from the summary 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}.
#'
#' @seealso \code{\link{mediate}}, \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., Tingley, D. and Yamamoto, T. (2012) Experimental Designs for
#' Identifying Causal Mechanisms. Journal of the Royal Statistical Society,
#' Series A (Statistics in Society)
#'
#' 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 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.design <- function(object, ...){
structure(object, class = c("summary.mediate.design", class(object)))
}
#' @rdname summary.mediate.design
#' @export
print.summary.mediate.design <- function(x, ...){
cat("\n")
cat("Design-Based Causal Mediation Analysis\n\n")
# Print values
if(x$design=="SED.NP.NOSI" | x$design=="PD"){
if(x$design=="SED.NP.NOSI"){
cat("Single Experiment Design (without Sequential Ignorability) \n\n")
}
if(x$design=="PD"){
cat("Parallel Design (Interaction Allowed) \n\n")
}
smat <- rbind(x$d0, x$d1)
colnames(smat) <- c("Lower Bound", "Upper Bound")
rownames(smat) <- c("ACME (control)", "ACME (treated)")
} else if(x$design=="PD.NINT"){
clp <- 100 * x$conf.level
cat("Parallel Design (with No Interaction Assumption) \n\n")
smat <- t(as.matrix(c(x$d0, x$d0.ci)))
colnames(smat) <- c("Estimate", paste(clp, "% CI Lower", sep=""),
paste(clp, "% CI Upper", sep=""))
rownames(smat) <- "ACME"
} else if(x$design=="PED"){
cat("Parallel Encouragement Design\n\n")
smat <- rbind(x$d0, x$d0.p, x$d1, x$d1.p)
colnames(smat) <- c("Lower Bound", "Upper Bound")
rownames(smat) <- c("Population ACME (control)", "Complier ACME (control)",
"Population ACME (treated)", "Complier ACME (treated)")
} else if(x$design=="CED"){
clp <- 100 * x$conf.level
cat("Crossover Encouragement Design \n\n")
smat <- rbind(c(x$d0, x$d0.ci), c(x$d1, x$d1.ci))
colnames(smat) <- c("Estimate", paste(clp, "% CI Lower", sep=""),
paste(clp, "% CI Upper", sep=""))
rownames(smat) <- c("Pliable ACME (control)", "Pliable ACME (treated)")
} else if(x$design=="SED.NP.SI"){
clp <- 100 * x$conf.level
cat("Single Experiment Design with Sequential Ignorability \n\n")
if(x$boot==TRUE){
cat("Confidence Intervals Based on Nonparametric Bootstrap\n\n")
} else {
cat("Confidence Intervals Based on Asymptotic Variance\n\n")
}
smat <- rbind(c(x$d0, x$d0.ci), c(x$d1, x$d1.ci))
colnames(smat) <- c("Estimate", paste(clp, "% CI Lower", sep=""),
paste(clp, "% CI Upper", sep=""))
rownames(smat) <- c("ACME (control)", "ACME (treated)")
}
printCoefmat(smat, digits=4)
cat("\n")
cat("Sample Size Used: ", x$nobs,"\n\n")
invisible(x)
}
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