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#' Bayesian Tobit 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.
#' @param below: point at which the dependent variable is censored from below.
#' If the dependent variable is only censored from above, set \code{below = -Inf}.
#' The default value is 0.
#' @param above: point at which the dependent variable is censored from above.
#' If the dependent variable is only censored from below, set \code{above = Inf}.
#' The default value is \code{Inf}.
#' @details
#' Additional parameters avaialable to this model 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.
#' \item \code{c0}: \code{c0}/2 is the shape parameter for the Inverse Gamma prior on the variance of the
#' disturbance terms.
#' \item \code{d0}: \code{d0}/2 is the scale parameter for the Inverse Gamma prior on the variance of the
#' disturbance terms.
#' }
#' @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}}.
#' @param below: point at which the dependent variable is censored from below. If the dependent variable is only censored from above, set below = -Inf. The default value is 0.
#' @param above: point at which the dependent variable is censored from above. If the dependent variable is only censored from below, set above = Inf. The default value is Inf.
#'
#' @examples
#' data(turnout)
#' z.out <- zelig(vote ~ race + educate, model = "tobit.bayes",data = turnout, verbose = FALSE)
#'
#' @seealso Vignette: \url{http://docs.zeligproject.org/articles/zelig_tobitbayes.html}
#' @import methods
#' @export Zelig-tobit-bayes
#' @exportClass Zelig-tobit-bayes
#'
#' @include model-zelig.R
#' @include model-bayes.R
#' @include model-tobit.R
ztobitbayes <- setRefClass("Zelig-tobit-bayes",
contains = c("Zelig-bayes",
"Zelig-tobit"))
ztobitbayes$methods(
initialize = function() {
callSuper()
.self$name <- "tobit-bayes"
.self$year <- 2013
.self$category <- "dichotomous"
.self$authors <- "Ben Goodrich, Ying Lu"
.self$description = "Bayesian Tobit Regression for a Censored Dependent Variable"
.self$fn <- quote(MCMCpack::MCMCtobit)
# JSON from parent
.self$wrapper <- "tobit.bayes"
}
)
ztobitbayes$methods(
param = function(z.out) {
if (length(.self$below) == 0)
.self$below <- 0
if (length(.self$above) == 0)
.self$above <- Inf
simparam.local <- list()
simparam.local$simparam <- z.out[, 1:(ncol(z.out) - 1)]
simparam.local$simalpha <- sqrt(z.out[, ncol(z.out)])
return(simparam.local)
}
)
ztobitbayes$methods(
mcfun = function(x, b0=0, b1=1, alpha=1, sim=TRUE){
mu <- b0 + b1 * x
ystar <- rnorm(n=length(x), mean=mu, sd=alpha)
if(sim){
y <- (ystar>0) * ystar # censoring from below at zero
return(y)
}else{
y.uncensored.hat.tobit<- mu + dnorm(mu, mean=0, sd=alpha)/pnorm(mu, mean=0, sd=alpha)
y.hat.tobit<- y.uncensored.hat.tobit * (1- pnorm(0, mean=mu, sd=alpha) ) # expected value of censored outcome
return(y.hat.tobit)
}
}
)
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