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#' Bayesian Ordered Probit Regression
#' @param formula a symbolic representation of the model to be
#' estimated, in the form \code{y ~ x1 + x2}, where \code{y} is the
#' dependent variable and \code{x1} and \code{x2} are the explanatory
#' variables, and \code{y}, \code{x1}, and \code{x2} are contained in the
#' same dataset. (You may include more than two explanatory variables,
#' of course.) The \code{+} symbol means ``inclusion'' not
#' ``addition.'' You may also include interaction terms and main
#' effects in the form \code{x1*x2} without computing them in prior
#' steps; \code{I(x1*x2)} to include only the interaction term and
#' exclude the main effects; and quadratic terms in the form
#' \code{I(x1^2)}.
#'@param model the name of a statistical model to estimate.
#' For a list of other supported models and their documentation see:
#' \url{http://docs.zeligproject.org/articles/}.
#'@param data the name of a data frame containing the variables
#' referenced in the formula or a list of multiply imputed data frames
#' each having the same variable names and row numbers (created by
#' \code{Amelia} or \code{\link{to_zelig_mi}}).
#'@param ... additional arguments passed to \code{zelig},
#' relevant for the model to be estimated.
#'@param by a factor variable contained in \code{data}. If supplied,
#' \code{zelig} will subset
#' the data frame based on the levels in the \code{by} variable, and
#' estimate a model for each subset. This can save a considerable amount of
#' effort. You may also use \code{by} to run models using MatchIt
#' subclasses.
#'@param cite If is set to 'TRUE' (default), the model citation will be printed
#' to the console.
#'
#'@details
#' Additional parameters avaialable to many models include:
#' \itemize{
#' \item \code{weights}: vector of weight values or a name of a variable in the dataset
#' by which to weight the model. For more information see:
#' \url{http://docs.zeligproject.org/articles/weights.html}.
#' \item \code{burnin}: number of the initial MCMC iterations to be discarded (defaults to 1,000).
#' \item \code{mcmc}: number of the MCMC iterations after burnin (defaults to 10,000).
#' \item \code{thin}: thinning interval for the Markov chain. Only every thin-th draw from
#' the Markov chain is kept. The value of mcmc must be divisible by this value. The default
#' value is 1.
#' \item \code{verbose}: defaults to FALSE. If TRUE, the progress of the sampler (every 10\%)
#' is printed to the screen.
#' \item \code{seed}: seed for the random number generator. The default is \code{NA} which
#' corresponds to a random seed of 12345.
#' \item \code{beta.start}: starting values for the Markov chain, either a scalar or vector
#' with length equal to the number of estimated coefficients. The default is \code{NA}, such
#' that the maximum likelihood estimates are used as the starting values.
#' }
#' Use the following parameters to specify the model's priors:
#' \itemize{
#' \item \code{b0}: prior mean for the coefficients, either a numeric vector or a
#' scalar. If a scalar value, that value will be the prior mean for all the
#' coefficients. The default is 0.
#' \item \code{B0}: prior precision parameter for the coefficients, either a
#' square matrix (with the dimensions equal to the number of the coefficients) or
#' a scalar. If a scalar value, that value times an identity matrix will be the
#' prior precision parameter. The default is 0, which leads to an improper prior.
#' }
#' @return Depending on the class of model selected, \code{zelig} will return
#' an object with elements including \code{coefficients}, \code{residuals},
#' and \code{formula} which may be summarized using
#' \code{summary(z.out)} or individually extracted using, for example,
#' \code{coef(z.out)}. See
#' \url{http://docs.zeligproject.org/articles/getters.html} for a list of
#' functions to extract model components. You can also extract whole fitted
#' model objects using \code{\link{from_zelig_model}}.
#'
#' Vignette: \url{http://docs.zeligproject.org/articles/zelig_oprobitbayes.html}
#' @import methods
#' @export Zelig-oprobit-bayes
#' @exportClass Zelig-oprobit-bayes
#'
#' @include model-zelig.R
#' @include model-bayes.R
zoprobitbayes <- setRefClass("Zelig-oprobit-bayes",
contains = c("Zelig-bayes"))
zoprobitbayes$methods(
initialize = function() {
callSuper()
.self$name <- "oprobit-bayes"
.self$year <- 2013
.self$category <- "discrete"
.self$authors <- "Ben Goodrich, Ying Lu"
.self$description = "Bayesian Probit Regression for Dichotomous Dependent Variables"
.self$fn <- quote(MCMCpack::MCMCoprobit)
# JSON from parent
.self$wrapper <- "oprobit.bayes"
}
)
zoprobitbayes$methods(
param = function(z.out) {
mysimparam <- callSuper(z.out)
# Produce the model matrix in order to get all terms (explicit and implicit)
# from the regression model.
mat <- model.matrix(.self$formula, data = .self$data)
# Response Terms
p <- ncol(mat)
# All coefficients
coefficients <- mysimparam
# Coefficients for predictor variables
beta <- coefficients[, 1:p]
# Middle values of "gamma" matrix
mid.gamma <- coefficients[, -(1:p)]
# ...
level <- ncol(coefficients) - p + 2
# Initialize the "gamma" parameters
gamma <- matrix(NA, nrow(coefficients), level + 1)
# The first, second and last values are fixed
gamma[, 1] <- -Inf
gamma[, 2] <- 0
gamma[, ncol(gamma)] <- Inf
# All others are determined by the coef-matrix (now stored in mid.gamma)
if (ncol(gamma) > 3)
gamma[, 3:(ncol(gamma) - 1)] <- mid.gamma
# return
mysimparam <- list(simparam = beta, simalpha = gamma)
return(mysimparam)
}
)
zoprobitbayes$methods(
qi = function(simparam, mm) {
beta <- simparam$simparam
gamma <- simparam$simalpha
labels <- levels(model.response(model.frame(.self$formula, data = .self$data)))
# x is implicitly cast into a matrix
eta <- beta %*% t(mm)
# **TODO: Sort out sizes of matrices for these things.
ev <- array(NA, c(nrow(eta), ncol(gamma) - 1, ncol(eta)))
pv <- matrix(NA, nrow(eta), ncol(eta))
# Compute Expected Values
# ***********************
# Note that the inverse link function is:
# pnorm(gamma[, j+1]-eta) - pnorm(gamma[, j]-eta)
for (j in 1:(ncol(gamma) - 1)) {
ev[, j, ] <- pnorm(gamma[, j + 1] - eta) - pnorm(gamma[, j] - eta)
}
colnames(ev) <- labels
# Compute Predicted Values
# ************************
for (j in 1:nrow(pv)) {
mu <- eta[j, ]
pv[j, ] <- as.character(cut(mu, gamma[j, ], labels = labels))
}
pv <- as.factor(pv)
# **TODO: Update summarize to work with at most 3-dimensional arrays
ev <- ev[, , 1]
return(list(ev = ev, pv = pv))
}
)
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