#' Linear Regression for a Left-Censored Dependent Variable
#' @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 (defaults to 0) The point at which the dependent variable is censored from below.
#' If any values in the dependent variable are observed to be less than the censoring point,
#' it is assumed that that particular observation is censored from below at the observed value.
#'@param above (defaults to 0) The point at which the dependent variable is censored from above
#' If any values in the dependent variable are observed to be more than the censoring point,
#' it is assumed that that particular observation is censored from above at the observed value.
#'@param robust defaults to FALSE. If TRUE, \code{zelig()} computes robust standard errors based on
#' sandwich estimators and the options selected in cluster.
#'@param cluster if robust = TRUE, you may select a variable to define groups of correlated
#' observations. Let x3 be a variable that consists of either discrete numeric values, character
#' strings, or factors that define strata. Then z.out <- zelig(y ~ x1 + x2, robust = TRUE,
#' cluster = "x3", model = "tobit", data = mydata)means that the observations can be correlated
#' within the strata defined by the variable x3, and that robust standard errors should be
#' calculated according to those clusters. If robust = TRUE but cluster is not specified,
#' zelig() assumes that each observation falls into its own cluster.
#'
#' @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{bootstrap}: logical or numeric. If \code{FALSE} don't use bootstraps to
#' robustly estimate uncertainty around model parameters due to sampling error.
#' If an integer is supplied, the number of boostraps to run.
#' For more information see:
#' \url{http://docs.zeligproject.org/articles/bootstraps.html}.
#' }
#'
#' @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}}.
#'
#' @examples
#' library(Zelig)
#' data(tobin)
#' z.out <- zelig(durable ~ age + quant, model = "tobit", data = tobin)
#' summary(z.out)
#'
#' @seealso Vignette: \url{http://docs.zeligproject.org/articles/zelig_tobit.html}
#' @import methods
#' @export Zelig-tobit
#' @exportClass Zelig-tobit
#'
#' @include model-zelig.R
ztobit <- setRefClass("Zelig-tobit",
contains = "Zelig",
fields = list(above = "numeric",
below = "numeric"))
ztobit$methods(
initialize = function() {
callSuper()
.self$name <- "tobit"
.self$authors <- "Kosuke Imai, Gary King, Olivia Lau"
.self$packageauthors <- "Christian Kleiber and Achim Zeileis"
.self$year <- 2011
.self$description = "Linear regression for Left-Censored Dependent Variable"
.self$fn <- quote(AER::tobit)
# JSON
.self$outcome <- "continous"
.self$wrapper <- "tobit"
.self$acceptweights <- TRUE
}
)
ztobit$methods(
zelig = function(formula, ..., below = 0, above = Inf,
robust = FALSE, data, weights = NULL, by = NULL, bootstrap = FALSE) {
.self$zelig.call <- match.call(expand.dots = TRUE)
.self$model.call <- .self$zelig.call
.self$below <- below
.self$above <- above
.self$model.call$below <- NULL
.self$model.call$above <- NULL
.self$model.call$left <- below
.self$model.call$right <- above
callSuper(formula = formula, data = data, ..., weights = weights, by = by, bootstrap = bootstrap)
if(!robust){
fn2 <- function(fc, data) {
fc$data <- data
return(fc)
}
robust.model.call <- .self$model.call
robust.model.call$robust <- TRUE
robust.zelig.out <- .self$data %>%
group_by_(.self$by) %>%
do(z.out = eval(fn2(robust.model.call, quote(as.data.frame(.))))$var )
.self$test.statistics<- list(robust.se = robust.zelig.out$z.out)
}
}
)
ztobit$methods(
param = function(z.out, method="mvn") {
if(identical(method,"mvn")){
mu <- c(coef(z.out), log(z.out$scale))
simfull <- mvrnorm(n = .self$num, mu = mu, Sigma = vcov(z.out))
simparam.local <- as.matrix(simfull[, -ncol(simfull)])
simalpha <- exp(as.matrix(simfull[, ncol(simfull)]))
simparam.local <- list(simparam = simparam.local, simalpha = simalpha)
return(simparam.local)
} else if(identical(method,"point")){
return(list(simparam = t(as.matrix(coef(z.out))), simalpha = log(z.out$scale) ))
}
}
)
ztobit$methods(
qi = function(simparam, mm) {
Coeff <- simparam$simparam %*% t(mm)
SD <- simparam$simalpha
alpha <- simparam$simalpha
lambda <- dnorm(Coeff / SD) / (pnorm(Coeff / SD))
ev <- pnorm(Coeff / SD) * (Coeff + SD * lambda)
pv <- ev
pv <- matrix(nrow = nrow(ev), ncol = ncol(ev))
for (j in 1:ncol(ev)) {
pv[, j] <- rnorm(nrow(ev), mean = ev[, j], sd = SD)
pv[, j] <- pmin(pmax(pv[, j], .self$below), .self$above)
}
return(list(ev = ev, pv = pv))
}
)
ztobit$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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