# Part of the rstanarm package for estimating model parameters
# Copyright (C) 2013, 2014, 2015, 2016, 2017 Trustees of Columbia University
#
# This program is free software; you can redistribute it and/or
# modify it under the terms of the GNU General Public License
# as published by the Free Software Foundation; either version 3
# of the License, or (at your option) any later version.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with this program; if not, write to the Free Software
# Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
#' Bayesian generalized linear models via Stan
#'
#' \if{html}{\figure{stanlogo.png}{options: width="25" alt="https://mc-stan.org/about/logo/"}}
#' Generalized linear modeling with optional prior distributions for the
#' coefficients, intercept, and auxiliary parameters.
#'
#' @export
#' @templateVar armRef (Ch. 3-6)
#' @templateVar pkg stats
#' @templateVar pkgfun glm
#' @templateVar sameargs model,offset,weights
#' @templateVar rareargs na.action,contrasts
#' @templateVar fun stan_glm, stan_glm.nb
#' @templateVar fitfun stan_glm.fit
#' @template return-stanreg-object
#' @template return-stanfit-object
#' @template see-also
#' @template args-formula-data-subset
#' @template args-same-as
#' @template args-same-as-rarely
#' @template args-dots
#' @template args-prior_intercept
#' @template args-priors
#' @template args-prior_aux
#' @template args-prior_PD
#' @template args-algorithm
#' @template args-adapt_delta
#' @template args-QR
#' @template args-sparse
#' @template reference-gelman-hill
#' @template reference-muth
#'
#' @param family Same as \code{\link[stats]{glm}}, except negative binomial GLMs
#' are also possible using the \code{\link{neg_binomial_2}} family object.
#' @param y In \code{stan_glm}, logical scalar indicating whether to
#' return the response vector. In \code{stan_glm.fit}, a response vector.
#' @param x In \code{stan_glm}, logical scalar indicating whether to
#' return the design matrix. In \code{stan_glm.fit}, usually a design matrix
#' but can also be a list of design matrices with the same number of rows, in
#' which case the first element of the list is interpreted as the primary design
#' matrix and the remaining list elements collectively constitute a basis for a
#' smooth nonlinear function of the predictors indicated by the \code{formula}
#' argument to \code{\link{stan_gamm4}}.
#' @param mean_PPD A logical value indicating whether the sample mean of the
#' posterior predictive distribution of the outcome should be calculated in
#' the \code{generated quantities} block. If \code{TRUE} then \code{mean_PPD}
#' is computed and displayed as a diagnostic in the
#' \link[=print.stanreg]{printed output}. The default is \code{TRUE} except if
#' \code{algorithm=="optimizing"}. A useful heuristic is to check if
#' \code{mean_PPD} is plausible when compared to \code{mean(y)}. If it is
#' plausible then this does \emph{not} mean that the model is good in general
#' (only that it can reproduce the sample mean), but if \code{mean_PPD} is
#' implausible then there may be something wrong, e.g., severe model
#' misspecification, problems with the data and/or priors, computational
#' issues, etc.
#'
#' @details The \code{stan_glm} function is similar in syntax to
#' \code{\link[stats]{glm}} but rather than performing maximum likelihood
#' estimation of generalized linear models, full Bayesian estimation is
#' performed (if \code{algorithm} is \code{"sampling"}) via MCMC. The Bayesian
#' model adds priors (independent by default) on the coefficients of the GLM.
#' The \code{stan_glm} function calls the workhorse \code{stan_glm.fit}
#' function, but it is also possible to call the latter directly.
#'
#' The \code{stan_glm.nb} function, which takes the extra argument
#' \code{link}, is a wrapper for \code{stan_glm} with \code{family =
#' \link{neg_binomial_2}(link)}.
#'
#' @seealso The various vignettes for \code{stan_glm} at
#' \url{https://mc-stan.org/rstanarm/articles/}.
#'
#' @examples
#' if (.Platform$OS.type != "windows" || .Platform$r_arch != "i386") {
#' ### Linear regression
#' mtcars$mpg10 <- mtcars$mpg / 10
#' fit <- stan_glm(
#' mpg10 ~ wt + cyl + am,
#' data = mtcars,
#' QR = TRUE,
#' # for speed of example only (default is "sampling")
#' algorithm = "fullrank",
#' refresh = 0
#' )
#'
#' plot(fit, prob = 0.5)
#' plot(fit, prob = 0.5, pars = "beta")
#' plot(fit, "hist", pars = "sigma")
#' \donttest{
#' ### Logistic regression
#' head(wells)
#' wells$dist100 <- wells$dist / 100
#' fit2 <- stan_glm(
#' switch ~ dist100 + arsenic,
#' data = wells,
#' family = binomial(link = "logit"),
#' prior_intercept = normal(0, 10),
#' QR = TRUE,
#' refresh = 0,
#' # for speed of example only
#' chains = 2, iter = 200
#' )
#' print(fit2)
#' prior_summary(fit2)
#'
#' # ?bayesplot::mcmc_areas
#' plot(fit2, plotfun = "areas", prob = 0.9,
#' pars = c("(Intercept)", "arsenic"))
#'
#' # ?bayesplot::ppc_error_binned
#' pp_check(fit2, plotfun = "error_binned")
#'
#'
#' ### Poisson regression (example from help("glm"))
#' count_data <- data.frame(
#' counts = c(18,17,15,20,10,20,25,13,12),
#' outcome = gl(3,1,9),
#' treatment = gl(3,3)
#' )
#' fit3 <- stan_glm(
#' counts ~ outcome + treatment,
#' data = count_data,
#' family = poisson(link="log"),
#' prior = normal(0, 2),
#' refresh = 0,
#' # for speed of example only
#' chains = 2, iter = 250
#' )
#' print(fit3)
#'
#' bayesplot::color_scheme_set("viridis")
#' plot(fit3)
#' plot(fit3, regex_pars = c("outcome", "treatment"))
#' plot(fit3, plotfun = "combo", regex_pars = "treatment") # ?bayesplot::mcmc_combo
#' posterior_vs_prior(fit3, regex_pars = c("outcome", "treatment"))
#'
#' ### Gamma regression (example from help("glm"))
#' clotting <- data.frame(log_u = log(c(5,10,15,20,30,40,60,80,100)),
#' lot1 = c(118,58,42,35,27,25,21,19,18),
#' lot2 = c(69,35,26,21,18,16,13,12,12))
#' fit4 <- stan_glm(
#' lot1 ~ log_u,
#' data = clotting,
#' family = Gamma(link="log"),
#' iter = 500, # for speed of example only
#' refresh = 0
#' )
#' print(fit4, digits = 2)
#'
#' fit5 <- update(fit4, formula = lot2 ~ log_u)
#'
#' # ?bayesplot::ppc_dens_overlay
#' bayesplot::bayesplot_grid(
#' pp_check(fit4, seed = 123),
#' pp_check(fit5, seed = 123),
#' titles = c("lot1", "lot2")
#' )
#'
#'
#' ### Negative binomial regression
#' fit6 <- stan_glm.nb(
#' Days ~ Sex/(Age + Eth*Lrn),
#' data = MASS::quine,
#' link = "log",
#' prior_aux = exponential(1.5, autoscale=TRUE),
#' chains = 2, iter = 200, # for speed of example only
#' refresh = 0
#' )
#'
#' prior_summary(fit6)
#' bayesplot::color_scheme_set("brightblue")
#' plot(fit6)
#' pp_check(fit6, plotfun = "hist", nreps = 5) # ?bayesplot::ppc_hist
#'
#' # 80% interval of estimated reciprocal_dispersion parameter
#' posterior_interval(fit6, pars = "reciprocal_dispersion", prob = 0.8)
#' plot(fit6, "areas", pars = "reciprocal_dispersion", prob = 0.8)
#' }
#' }
stan_glm <-
function(formula,
family = gaussian(),
data,
weights,
subset,
na.action = NULL,
offset = NULL,
model = TRUE,
x = FALSE,
y = TRUE,
contrasts = NULL,
...,
prior = default_prior_coef(family),
prior_intercept = default_prior_intercept(family),
prior_aux = exponential(autoscale=TRUE),
prior_PD = FALSE,
algorithm = c("sampling", "optimizing", "meanfield", "fullrank"),
mean_PPD = algorithm != "optimizing" && !prior_PD,
adapt_delta = NULL,
QR = FALSE,
sparse = FALSE) {
algorithm <- match.arg(algorithm)
family <- validate_family(family)
validate_glm_formula(formula)
data <- validate_data(data, if_missing = environment(formula))
call <- match.call(expand.dots = TRUE)
mf <- match.call(expand.dots = FALSE)
m <- match(c("formula", "subset", "weights", "na.action", "offset"),
table = names(mf), nomatch = 0L)
mf <- mf[c(1L, m)]
mf$data <- data
mf$drop.unused.levels <- TRUE
mf[[1L]] <- as.name("model.frame")
mf <- eval(mf, parent.frame())
mf <- check_constant_vars(mf)
mt <- attr(mf, "terms")
Y <- array1D_check(model.response(mf, type = "any"))
if (is.empty.model(mt))
stop("No intercept or predictors specified.", call. = FALSE)
X <- model.matrix(mt, mf, contrasts)
contrasts <- attr(X, "contrasts")
weights <- validate_weights(as.vector(model.weights(mf)))
offset <- validate_offset(as.vector(model.offset(mf)), y = Y)
if (binom_y_prop(Y, family, weights)) {
y1 <- as.integer(as.vector(Y) * weights)
Y <- cbind(y1, y0 = weights - y1)
weights <- double(0)
}
if (prior_PD) {
# can result in errors (e.g. from poisson) if draws from prior are weird
mean_PPD <- FALSE
}
stanfit <- stan_glm.fit(
x = X,
y = Y,
weights = weights,
offset = offset,
family = family,
prior = prior,
prior_intercept = prior_intercept,
prior_aux = prior_aux,
prior_PD = prior_PD,
algorithm = algorithm,
mean_PPD = mean_PPD,
adapt_delta = adapt_delta,
QR = QR,
sparse = sparse,
...
)
if (algorithm != "optimizing" && !is(stanfit, "stanfit")) return(stanfit)
if (family$family == "Beta regression") {
family$family <- "beta"
}
sel <- apply(X, 2L, function(x) !all(x == 1) && length(unique(x)) < 2)
X <- X[ , !sel, drop = FALSE]
fit <- nlist(stanfit, algorithm, family, formula, data, offset, weights,
x = X, y = Y, model = mf, terms = mt, call,
na.action = attr(mf, "na.action"),
contrasts = contrasts,
stan_function = "stan_glm")
out <- stanreg(fit)
if (algorithm == "optimizing") {
out$log_p <- stanfit$log_p
out$log_g <- stanfit$log_g
out$psis <- stanfit$psis
out$ir_idx <- stanfit$ir_idx
out$diagnostics <- stanfit$diagnostics
}
out$compute_mean_PPD <- mean_PPD
out$xlevels <- .getXlevels(mt, mf)
if (!x)
out$x <- NULL
if (!y)
out$y <- NULL
if (!model)
out$model <- NULL
return(out)
}
#' @rdname stan_glm
#' @export
#' @param link For \code{stan_glm.nb} only, the link function to use. See
#' \code{\link{neg_binomial_2}}.
#'
stan_glm.nb <-
function(formula,
data,
weights,
subset,
na.action = NULL,
offset = NULL,
model = TRUE,
x = FALSE,
y = TRUE,
contrasts = NULL,
link = "log",
...,
prior = default_prior_coef(family),
prior_intercept = default_prior_intercept(family),
prior_aux = exponential(autoscale=TRUE),
prior_PD = FALSE,
algorithm = c("sampling", "optimizing", "meanfield", "fullrank"),
mean_PPD = algorithm != "optimizing",
adapt_delta = NULL,
QR = FALSE) {
if ("family" %in% names(list(...)))
stop("'family' should not be specified.")
mc <- call <- match.call()
if (!"formula" %in% names(call))
names(call)[2L] <- "formula"
mc[[1L]] <- quote(stan_glm)
mc$link <- NULL
mc$family <- neg_binomial_2(link = link)
out <- eval(mc, parent.frame())
out$call <- call
out$stan_function <- "stan_glm.nb"
return(out)
}
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