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#' Bayesian Poisson 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.
#' @examples
#' data(sanction)
#' z.out <- zelig(num ~ target + coop, model = "poisson.bayes",data = sanction, verbose = FALSE)
#'
#' @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{tune}: Metropolis tuning parameter, either a positive scalar or a vector of length
#' kk, where kk is the number of coefficients. The tuning parameter should be set such that the
#' acceptance rate of the Metropolis algorithm is satisfactory (typically between 0.20 and 0.5).
#' The default value is 1.1.
#' \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}}.
#'
#'
#' @seealso Vignette: \url{http://docs.zeligproject.org/articles/zelig_poissonbayes.html}
#' @import methods
#' @export Zelig-poisson-bayes
#' @exportClass Zelig-poisson-bayes
#'
#' @include model-zelig.R
#' @include model-bayes.R
#' @include model-poisson.R
zpoissonbayes <- setRefClass("Zelig-poisson-bayes",
contains = c("Zelig-bayes",
"Zelig-poisson"))
zpoissonbayes$methods(
initialize = function() {
callSuper()
.self$name <- "poisson-bayes"
.self$family <- "poisson"
.self$link <- "log"
.self$linkinv <- eval(call(.self$family, .self$link))$linkinv
.self$year <- 2013
.self$category <- "continuous"
.self$authors <- "Ben Goodrich, Ying Lu"
.self$description = "Bayesian Poisson Regression"
.self$fn <- quote(MCMCpack::MCMCpoisson)
# JSON from parent
.self$wrapper <- "poisson.bayes"
}
)
zpoissonbayes$methods(
mcfun = function(x, b0=0, b1=1, ..., sim=TRUE){
lambda <- exp(b0 + b1 * x)
if(sim){
y <- rpois(n=length(x), lambda=lambda)
return(y)
}else{
return(lambda)
}
}
)
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