Nothing
R/MCMCirt1d.R
In MCMCpack: Markov Chain Monte Carlo (MCMC) Package
##########################################################################
## sample from the posterior distribution of a one-dimensional item
## response theory model in R using linked C++ code in Scythe.
##
## This software is distributed under the terms of the GNU GENERAL
## PUBLIC LICENSE Version 2, June 1991. See the package LICENSE
## file for more information.
##
## ADM and KQ 1/23/2003
## updated extensively ADM & KQ 7/28/2004
## store.ability arg added KQ 1/27/2006
##
## Copyright (C) 2003-2007 Andrew D. Martin and Kevin M. Quinn
## Copyright (C) 2007-present Andrew D. Martin, Kevin M. Quinn,
## and Jong Hee Park
##########################################################################
#' Markov Chain Monte Carlo for One Dimensional Item Response Theory Model
#'
#' This function generates a sample from the posterior distribution of a one
#' dimensional item response theory (IRT) model, with Normal priors on the
#' subject abilities (ideal points), and multivariate Normal priors on the item
#' parameters. The user supplies data and priors, and a sample from the
#' posterior distribution is returned as an mcmc object, which can be
#' subsequently analyzed with functions provided in the coda package.
#'
#' If you are interested in fitting K-dimensional item response theory models,
#' or would rather identify the model by placing constraints on the item
#' parameters, please see \code{\link[MCMCpack]{MCMCirtKd}}.
#'
#' \code{MCMCirt1d} simulates from the posterior distribution using standard
#' Gibbs sampling using data augmentation (a Normal draw for the subject
#' abilities, a multivariate Normal draw for the item parameters, and a
#' truncated Normal draw for the latent utilities). The simulation proper is
#' done in compiled C++ code to maximize efficiency. Please consult the coda
#' documentation for a comprehensive list of functions that can be used to
#' analyze the posterior sample.
#'
#' The model takes the following form. We assume that each subject has an
#' subject ability (ideal point) denoted \eqn{\theta_j} and that each
#' item has a difficulty parameter \eqn{\alpha_i} and discrimination
#' parameter \eqn{\beta_i}. The observed choice by subject \eqn{j}
#' on item \eqn{i} is the observed data matrix which is \eqn{(I \times
#' J)}. We assume that the choice is dictated by an unobserved
#' utility:
#'
#' \deqn{z_{i,j} = -\alpha_i + \beta_i \theta_j + \varepsilon_{i,j}}
#'
#'
#' Where the errors are assumed to be distributed standard Normal.
#' The parameters of interest are the subject abilities (ideal points)
#' and the item parameters.
#'
#' We assume the following priors. For the subject abilities (ideal points):
#'
#' \deqn{\theta_j \sim \mathcal{N}(t_{0},T_{0}^{-1})}
#'
#' For the item parameters, the prior is:
#'
#' \deqn{\left[\alpha_i, \beta_i \right]' \sim \mathcal{N}_2 (ab_{0},AB_{0}^{-1})}
#'
#' The model is identified by the proper priors on the item parameters and
#' constraints placed on the ability parameters.
#'
#' As is the case with all measurement models, make sure that you have plenty
#' of free memory, especially when storing the item parameters.
#'
#' @param datamatrix The matrix of data. Must be 0, 1, or missing values. The
#' rows of \code{datamatrix} correspond to subjects and the columns correspond
#' to items.
#'
#' @param theta.constraints A list specifying possible simple equality or
#' inequality constraints on the ability parameters. A typical entry in the
#' list has one of three forms: \code{varname=c} which will constrain the
#' ability parameter for the subject named \code{varname} to be equal to c,
#' \code{varname="+"} which will constrain the ability parameter for the
#' subject named \code{varname} to be positive, and \code{varname="-"} which
#' will constrain the ability parameter for the subject named \code{varname} to
#' be negative. If x is a matrix without row names defaults names of
#' ``V1",``V2", ... , etc will be used. See Rivers (2003) for a thorough
#' discussion of identification of IRT models.
#'
#' @param burnin The number of burn-in iterations for the sampler.
#'
#' @param mcmc The number of Gibbs iterations for the sampler.
#'
#' @param thin The thinning interval used in the simulation. The number of
#' Gibbs iterations must be divisible by this value.
#'
#' @param verbose A switch which determines whether or not the progress of the
#' sampler is printed to the screen. If \code{verbose} is greater than 0 then
#' every \code{verbose}th iteration will be printed to the screen.
#'
#' @param seed The seed for the random number generator. If NA, the Mersenne
#' Twister generator is used with default seed 12345; if an integer is passed
#' it is used to seed the Mersenne twister. The user can also pass a list of
#' length two to use the L'Ecuyer random number generator, which is suitable
#' for parallel computation. The first element of the list is the L'Ecuyer
#' seed, which is a vector of length six or NA (if NA a default seed of
#' \code{rep(12345,6)} is used). The second element of list is a positive
#' substream number. See the MCMCpack specification for more details.
#'
#' @param theta.start The starting values for the subject abilities (ideal
#' points). This can either be a scalar or a column vector with dimension equal
#' to the number of voters. If this takes a scalar value, then that value will
#' serve as the starting value for all of the thetas. The default value of NA
#' will choose the starting values based on an eigenvalue-eigenvector
#' decomposition of the aggreement score matrix formed from the
#' \code{datamatrix}.
#'
#' @param alpha.start The starting values for the \eqn{\alpha}
#' difficulty parameters. This can either be a scalar or a column vector with
#' dimension equal to the number of items. If this takes a scalar value, then
#' that value will serve as the starting value for all of the alphas. The
#' default value of NA will set the starting values based on a series of probit
#' regressions that condition on the starting values of theta.
#'
#' @param beta.start The starting values for the \eqn{\beta}
#' discrimination parameters. This can either be a scalar or a column vector
#' with dimension equal to the number of items. If this takes a scalar value,
#' then that value will serve as the starting value for all of the betas. The
#' default value of NA will set the starting values based on a series of probit
#' regressions that condition on the starting values of theta.
#'
#' @param t0 A scalar parameter giving the prior mean of the subject abilities
#' (ideal points).
#'
#' @param T0 A scalar parameter giving the prior precision (inverse variance)
#' of the subject abilities (ideal points).
#'
#' @param ab0 The prior mean of \code{(alpha, beta)}. Can be either a scalar or
#' a 2-vector. If a scalar both means will be set to the passed value. The
#' prior mean is assumed to be the same across all items.
#'
#' @param AB0 The prior precision of \code{(alpha, beta)}.This can either be
#' ascalar or a 2 by 2 matrix. If this takes a scalar value, then that value
#' times an identity matrix serves as the prior precision. The prior precision
#' is assumed to be the same across all items.
#'
#' @param store.item A switch that determines whether or not to store the item
#' parameters for posterior analysis. \emph{NOTE: In situations with many
#' items storing the item parameters takes an enormous amount of memory, so
#' \code{store.item} should only be \code{FALSE} if the chain is thinned
#' heavily, or for applications with a small number of items}. By default, the
#' item parameters are not stored.
#'
#' @param store.ability A switch that determines whether or not to store the
#' ability parameters for posterior analysis. \emph{NOTE: In situations with
#' many individuals storing the ability parameters takes an enormous amount of
#' memory, so \code{store.ability} should only be \code{TRUE} if the chain is
#' thinned heavily, or for applications with a small number of individuals}.
#' By default, the item parameters are stored.
#'
#' @param drop.constant.items A switch that determines whether or not items
#' that have no variation should be deleted before fitting the model. Default =
#' TRUE.
#'
#' @param ... further arguments to be passed
#'
#' @return An mcmc object that contains the sample from the posterior
#' distribution. This object can be summarized by functions provided by the
#' coda package.
#'
#' @export
#'
#' @seealso \code{\link[coda]{plot.mcmc}},\code{\link[coda]{summary.mcmc}},
#' \code{\link[MCMCpack]{MCMCirtKd}}
#'
#' @references James H. Albert. 1992. ``Bayesian Estimation of Normal Ogive
#' Item Response Curves Using Gibbs Sampling." \emph{Journal of Educational
#' Statistics}. 17: 251-269.
#'
#' Joshua Clinton, Simon Jackman, and Douglas Rivers. 2004. ``The Statistical
#' Analysis of Roll Call Data." \emph{American Political Science Review}. 98:
#' 355-370.
#'
#' Valen E. Johnson and James H. Albert. 1999. ``Ordinal Data Modeling."
#' Springer: New York.
#'
#' Andrew D. Martin, Kevin M. Quinn, and Jong Hee Park. 2011. ``MCMCpack:
#' Markov Chain Monte Carlo in R.'', \emph{Journal of Statistical Software}.
#' 42(9): 1-21. \doi{10.18637/jss.v042.i09}.
#'
#' Daniel Pemstein, Kevin M. Quinn, and Andrew D. Martin. 2007. \emph{Scythe
#' Statistical Library 1.0.} \url{http://scythe.wustl.edu.s3-website-us-east-1.amazonaws.com/}.
#'
#' Martyn Plummer, Nicky Best, Kate Cowles, and Karen Vines. 2006. ``Output
#' Analysis and Diagnostics for MCMC (CODA)'', \emph{R News}. 6(1): 7-11.
#' \url{https://CRAN.R-project.org/doc/Rnews/Rnews_2006-1.pdf}.
#'
#' Douglas Rivers. 2004. ``Identification of Multidimensional Item-Response
#' Models." Stanford University, typescript.
#'
#' @keywords models
#'
#' @examples
#'
#' \dontrun{
#' ## US Supreme Court Example with inequality constraints
#' data(SupremeCourt)
#' posterior1 <- MCMCirt1d(t(SupremeCourt),
#' theta.constraints=list(Scalia="+", Ginsburg="-"),
#' B0.alpha=.2, B0.beta=.2,
#' burnin=500, mcmc=100000, thin=20, verbose=500,
#' store.item=TRUE)
#' geweke.diag(posterior1)
#' plot(posterior1)
#' summary(posterior1)
#'
#' ## US Senate Example with equality constraints
#' data(Senate)
#' Sen.rollcalls <- Senate[,6:677]
#' posterior2 <- MCMCirt1d(Sen.rollcalls,
#' theta.constraints=list(KENNEDY=-2, HELMS=2),
#' burnin=2000, mcmc=100000, thin=20, verbose=500)
#' geweke.diag(posterior2)
#' plot(posterior2)
#' summary(posterior2)
#' }
#'
"MCMCirt1d" <-
function(datamatrix, theta.constraints=list(), burnin = 1000,
mcmc = 20000, thin=1, verbose = 0, seed = NA,
theta.start = NA, alpha.start = NA, beta.start = NA, t0 = 0,
T0 = 1, ab0=0, AB0=.25, store.item = FALSE, store.ability=TRUE,
drop.constant.items=TRUE, ... ) {
## checks
check.offset(list(...))
check.mcmc.parameters(burnin, mcmc, thin)
## check vote matrix and convert to work with C++ code
if (drop.constant.items==TRUE){
x.col.var <- apply(datamatrix, 2, var, na.rm=TRUE)
keep.inds <- x.col.var>0
keep.inds[is.na(keep.inds)] <- FALSE
datamatrix <- datamatrix[,keep.inds]
}
datamatrix <- as.matrix(datamatrix)
K <- ncol(datamatrix) # cases, bills, items, etc
J <- nrow(datamatrix) # justices, legislators, subjects, etc
if(sum(datamatrix==1 | datamatrix==0 | is.na(datamatrix)) != (J*K)) {
cat("Error: Data matrix contains elements other than 0, 1 or NA.\n")
stop("Please check data and try MCMCirt1d() again.\n",
call.=FALSE)
}
datamatrix[is.na(datamatrix)] <- 9
item.names <- colnames(datamatrix)
subject.names <- rownames(datamatrix)
## setup constraints on theta
if(length(theta.constraints) != 0) {
for (i in 1:length(theta.constraints)){
theta.constraints[[i]] <-
list(as.integer(1), theta.constraints[[i]][1])
}
}
holder <- build.factor.constraints(theta.constraints, t(datamatrix), J, 1)
theta.eq.constraints <- holder[[1]]
theta.ineq.constraints <- holder[[2]]
subject.names <- holder[[3]]
## names
item.names <- colnames(datamatrix)
if (is.null(item.names)){
item.names <- paste("item", 1:K, sep="")
}
## prior for theta
holder <- form.mvn.prior(t0, T0, 1)
t0 <- holder[[1]]
T0 <- holder[[2]]
## prior for (alpha, beta)
holder <- form.mvn.prior(ab0, AB0, 2)
ab0 <- holder[[1]]
AB0 <- holder[[2]]
## starting values for theta error checking
theta.start <- factor.score.start.check(theta.start, datamatrix,
t0, T0,
theta.eq.constraints,
theta.ineq.constraints, 1)
## starting values for (alpha, beta)
ab.starts <- matrix(NA, K, 2)
for (i in 1:K){
local.y <- datamatrix[,i]
local.y[local.y==9] <- NA
if (var(na.omit(local.y))==0){
ab.starts[i,] <- c(0,10)
}
else {
ab.starts[i,] <- coef(suppressWarnings(glm(local.y~theta.start,
family=binomial(link="probit"),
control=glm.control(
maxit=8, epsilon=1e-3)
)))
}
}
ab.starts[,1] <- -1 * ab.starts[,1] # make this into a difficulty param
## starting values for alpha and beta error checking
if (is.na(alpha.start)) {
alpha.start <- ab.starts[,1]
}
else if(is.null(dim(alpha.start))) {
alpha.start <- alpha.start * matrix(1,K,1)
}
else if((dim(alpha.start)[1] != K) || (dim(alpha.start)[2] != 1)) {
cat("Error: Starting value for alpha not conformable.\n")
stop("Please respecify and call MCMCirt1d() again.\n",
call.=FALSE)
}
if (is.na(beta.start)) {
beta.start <- ab.starts[,2]
}
else if(is.null(dim(beta.start))) {
beta.start <- beta.start * matrix(1,K,1)
}
else if((dim(beta.start)[1] != K) || (dim(beta.start)[2] != 1)) {
cat("Error: Starting value for beta not conformable.\n")
stop("Please respecify and call MCMCirt1d() again.\n",
call.=FALSE)
}
## define holder for posterior sample
if(store.item == FALSE & store.ability == TRUE) {
sample <- matrix(data=0, mcmc/thin, J)
}
else if (store.item == TRUE & store.ability == FALSE){
sample <- matrix(data=0, mcmc/thin, 2*K)
}
else if (store.item == TRUE & store.ability == TRUE){
sample <- matrix(data=0, mcmc/thin, J + 2 * K)
}
else{
cat("Error: store.item == FALSE & store.ability == FALSE.\n")
stop("Please respecify and call MCMCirt1d() again.\n",
call.=FALSE)
}
## seeds
seeds <- form.seeds(seed)
lecuyer <- seeds[[1]]
seed.array <- seeds[[2]]
lecuyer.stream <- seeds[[3]]
# call C++ code to draw sample
posterior <- .C("cMCMCirt1d",
sampledata = as.double(sample),
samplerow = as.integer(nrow(sample)),
samplecol = as.integer(ncol(sample)),
Xdata = as.integer(datamatrix),
Xrow = as.integer(nrow(datamatrix)),
Xcol = as.integer(ncol(datamatrix)),
burnin = as.integer(burnin),
mcmc = as.integer(mcmc),
thin = as.integer(thin),
lecuyer = as.integer(lecuyer),
seedarray = as.integer(seed.array),
lecuyerstream = as.integer(lecuyer.stream),
verbose = as.integer(verbose),
thetastartdata = as.double(theta.start),
thetastartrow = as.integer(nrow(theta.start)),
thetastartcol = as.integer(ncol(theta.start)),
astartdata = as.double(alpha.start),
astartrow = as.integer(length(alpha.start)),
astartcol = as.integer(1),
bstartdata = as.double(beta.start),
bstartrow = as.integer(length(beta.start)),
bstartcol = as.integer(1),
t0 = as.double(t0),
T0 = as.double(T0),
ab0data = as.double(ab0),
ab0row = as.integer(nrow(ab0)),
ab0col = as.integer(ncol(ab0)),
AB0data = as.double(AB0),
AB0row = as.integer(nrow(AB0)),
AB0col = as.integer(ncol(AB0)),
thetaeqdata = as.double(theta.eq.constraints),
thetaeqrow = as.integer(nrow(theta.eq.constraints)),
thetaeqcol = as.integer(ncol(theta.eq.constraints)),
thetaineqdata = as.double(theta.ineq.constraints),
thetaineqrow = as.integer(nrow(theta.ineq.constraints)),
thetaineqcol = as.integer(ncol(theta.ineq.constraints)),
storei = as.integer(store.item),
storea = as.integer(store.ability),
PACKAGE="MCMCpack"
)
theta.names <- paste("theta.", subject.names, sep = "")
alpha.beta.names <- paste(rep(c("alpha.","beta."), K),
rep(item.names, each = 2),
sep = "")
# put together matrix and build MCMC object to return
sample <- matrix(posterior$sampledata, posterior$samplerow,
posterior$samplecol,
byrow=FALSE)
output <- mcmc(data=sample, start=burnin+1, end=burnin+mcmc, thin=thin)
names <- NULL
if(store.ability == TRUE) {
names <- c(names, theta.names)
}
if (store.item == TRUE){
names <- c(names, alpha.beta.names)
}
varnames(output) <- names
attr(output,"title") <-
"MCMCirt1d Posterior Sample"
return(output)
}
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##########################################################################
## sample from the posterior distribution of a one-dimensional item
## response theory model in R using linked C++ code in Scythe.
##
## This software is distributed under the terms of the GNU GENERAL
## PUBLIC LICENSE Version 2, June 1991. See the package LICENSE
## file for more information.
##
## ADM and KQ 1/23/2003
## updated extensively ADM & KQ 7/28/2004
## store.ability arg added KQ 1/27/2006
##
## Copyright (C) 2003-2007 Andrew D. Martin and Kevin M. Quinn
## Copyright (C) 2007-present Andrew D. Martin, Kevin M. Quinn,
## and Jong Hee Park
##########################################################################
#' Markov Chain Monte Carlo for One Dimensional Item Response Theory Model
#'
#' This function generates a sample from the posterior distribution of a one
#' dimensional item response theory (IRT) model, with Normal priors on the
#' subject abilities (ideal points), and multivariate Normal priors on the item
#' parameters. The user supplies data and priors, and a sample from the
#' posterior distribution is returned as an mcmc object, which can be
#' subsequently analyzed with functions provided in the coda package.
#'
#' If you are interested in fitting K-dimensional item response theory models,
#' or would rather identify the model by placing constraints on the item
#' parameters, please see \code{\link[MCMCpack]{MCMCirtKd}}.
#'
#' \code{MCMCirt1d} simulates from the posterior distribution using standard
#' Gibbs sampling using data augmentation (a Normal draw for the subject
#' abilities, a multivariate Normal draw for the item parameters, and a
#' truncated Normal draw for the latent utilities). The simulation proper is
#' done in compiled C++ code to maximize efficiency. Please consult the coda
#' documentation for a comprehensive list of functions that can be used to
#' analyze the posterior sample.
#'
#' The model takes the following form. We assume that each subject has an
#' subject ability (ideal point) denoted \eqn{\theta_j} and that each
#' item has a difficulty parameter \eqn{\alpha_i} and discrimination
#' parameter \eqn{\beta_i}. The observed choice by subject \eqn{j}
#' on item \eqn{i} is the observed data matrix which is \eqn{(I \times
#' J)}. We assume that the choice is dictated by an unobserved
#' utility:
#'
#' \deqn{z_{i,j} = -\alpha_i + \beta_i \theta_j + \varepsilon_{i,j}}
#'
#'
#' Where the errors are assumed to be distributed standard Normal.
#' The parameters of interest are the subject abilities (ideal points)
#' and the item parameters.
#'
#' We assume the following priors. For the subject abilities (ideal points):
#'
#' \deqn{\theta_j \sim \mathcal{N}(t_{0},T_{0}^{-1})}
#'
#' For the item parameters, the prior is:
#'
#' \deqn{\left[\alpha_i, \beta_i \right]' \sim \mathcal{N}_2 (ab_{0},AB_{0}^{-1})}
#'
#' The model is identified by the proper priors on the item parameters and
#' constraints placed on the ability parameters.
#'
#' As is the case with all measurement models, make sure that you have plenty
#' of free memory, especially when storing the item parameters.
#'
#' @param datamatrix The matrix of data. Must be 0, 1, or missing values. The
#' rows of \code{datamatrix} correspond to subjects and the columns correspond
#' to items.
#'
#' @param theta.constraints A list specifying possible simple equality or
#' inequality constraints on the ability parameters. A typical entry in the
#' list has one of three forms: \code{varname=c} which will constrain the
#' ability parameter for the subject named \code{varname} to be equal to c,
#' \code{varname="+"} which will constrain the ability parameter for the
#' subject named \code{varname} to be positive, and \code{varname="-"} which
#' will constrain the ability parameter for the subject named \code{varname} to
#' be negative. If x is a matrix without row names defaults names of
#' ``V1",``V2", ... , etc will be used. See Rivers (2003) for a thorough
#' discussion of identification of IRT models.
#'
#' @param burnin The number of burn-in iterations for the sampler.
#'
#' @param mcmc The number of Gibbs iterations for the sampler.
#'
#' @param thin The thinning interval used in the simulation. The number of
#' Gibbs iterations must be divisible by this value.
#'
#' @param verbose A switch which determines whether or not the progress of the
#' sampler is printed to the screen. If \code{verbose} is greater than 0 then
#' every \code{verbose}th iteration will be printed to the screen.
#'
#' @param seed The seed for the random number generator. If NA, the Mersenne
#' Twister generator is used with default seed 12345; if an integer is passed
#' it is used to seed the Mersenne twister. The user can also pass a list of
#' length two to use the L'Ecuyer random number generator, which is suitable
#' for parallel computation. The first element of the list is the L'Ecuyer
#' seed, which is a vector of length six or NA (if NA a default seed of
#' \code{rep(12345,6)} is used). The second element of list is a positive
#' substream number. See the MCMCpack specification for more details.
#'
#' @param theta.start The starting values for the subject abilities (ideal
#' points). This can either be a scalar or a column vector with dimension equal
#' to the number of voters. If this takes a scalar value, then that value will
#' serve as the starting value for all of the thetas. The default value of NA
#' will choose the starting values based on an eigenvalue-eigenvector
#' decomposition of the aggreement score matrix formed from the
#' \code{datamatrix}.
#'
#' @param alpha.start The starting values for the \eqn{\alpha}
#' difficulty parameters. This can either be a scalar or a column vector with
#' dimension equal to the number of items. If this takes a scalar value, then
#' that value will serve as the starting value for all of the alphas. The
#' default value of NA will set the starting values based on a series of probit
#' regressions that condition on the starting values of theta.
#'
#' @param beta.start The starting values for the \eqn{\beta}
#' discrimination parameters. This can either be a scalar or a column vector
#' with dimension equal to the number of items. If this takes a scalar value,
#' then that value will serve as the starting value for all of the betas. The
#' default value of NA will set the starting values based on a series of probit
#' regressions that condition on the starting values of theta.
#'
#' @param t0 A scalar parameter giving the prior mean of the subject abilities
#' (ideal points).
#'
#' @param T0 A scalar parameter giving the prior precision (inverse variance)
#' of the subject abilities (ideal points).
#'
#' @param ab0 The prior mean of \code{(alpha, beta)}. Can be either a scalar or
#' a 2-vector. If a scalar both means will be set to the passed value. The
#' prior mean is assumed to be the same across all items.
#'
#' @param AB0 The prior precision of \code{(alpha, beta)}.This can either be
#' ascalar or a 2 by 2 matrix. If this takes a scalar value, then that value
#' times an identity matrix serves as the prior precision. The prior precision
#' is assumed to be the same across all items.
#'
#' @param store.item A switch that determines whether or not to store the item
#' parameters for posterior analysis. \emph{NOTE: In situations with many
#' items storing the item parameters takes an enormous amount of memory, so
#' \code{store.item} should only be \code{FALSE} if the chain is thinned
#' heavily, or for applications with a small number of items}. By default, the
#' item parameters are not stored.
#'
#' @param store.ability A switch that determines whether or not to store the
#' ability parameters for posterior analysis. \emph{NOTE: In situations with
#' many individuals storing the ability parameters takes an enormous amount of
#' memory, so \code{store.ability} should only be \code{TRUE} if the chain is
#' thinned heavily, or for applications with a small number of individuals}.
#' By default, the item parameters are stored.
#'
#' @param drop.constant.items A switch that determines whether or not items
#' that have no variation should be deleted before fitting the model. Default =
#' TRUE.
#'
#' @param ... further arguments to be passed
#'
#' @return An mcmc object that contains the sample from the posterior
#' distribution. This object can be summarized by functions provided by the
#' coda package.
#'
#' @export
#'
#' @seealso \code{\link[coda]{plot.mcmc}},\code{\link[coda]{summary.mcmc}},
#' \code{\link[MCMCpack]{MCMCirtKd}}
#'
#' @references James H. Albert. 1992. ``Bayesian Estimation of Normal Ogive
#' Item Response Curves Using Gibbs Sampling." \emph{Journal of Educational
#' Statistics}. 17: 251-269.
#'
#' Joshua Clinton, Simon Jackman, and Douglas Rivers. 2004. ``The Statistical
#' Analysis of Roll Call Data." \emph{American Political Science Review}. 98:
#' 355-370.
#'
#' Valen E. Johnson and James H. Albert. 1999. ``Ordinal Data Modeling."
#' Springer: New York.
#'
#' Andrew D. Martin, Kevin M. Quinn, and Jong Hee Park. 2011. ``MCMCpack:
#' Markov Chain Monte Carlo in R.'', \emph{Journal of Statistical Software}.
#' 42(9): 1-21. \doi{10.18637/jss.v042.i09}.
#'
#' Daniel Pemstein, Kevin M. Quinn, and Andrew D. Martin. 2007. \emph{Scythe
#' Statistical Library 1.0.} \url{http://scythe.wustl.edu.s3-website-us-east-1.amazonaws.com/}.
#'
#' Martyn Plummer, Nicky Best, Kate Cowles, and Karen Vines. 2006. ``Output
#' Analysis and Diagnostics for MCMC (CODA)'', \emph{R News}. 6(1): 7-11.
#' \url{https://CRAN.R-project.org/doc/Rnews/Rnews_2006-1.pdf}.
#'
#' Douglas Rivers. 2004. ``Identification of Multidimensional Item-Response
#' Models." Stanford University, typescript.
#'
#' @keywords models
#'
#' @examples
#'
#' \dontrun{
#' ## US Supreme Court Example with inequality constraints
#' data(SupremeCourt)
#' posterior1 <- MCMCirt1d(t(SupremeCourt),
#' theta.constraints=list(Scalia="+", Ginsburg="-"),
#' B0.alpha=.2, B0.beta=.2,
#' burnin=500, mcmc=100000, thin=20, verbose=500,
#' store.item=TRUE)
#' geweke.diag(posterior1)
#' plot(posterior1)
#' summary(posterior1)
#'
#' ## US Senate Example with equality constraints
#' data(Senate)
#' Sen.rollcalls <- Senate[,6:677]
#' posterior2 <- MCMCirt1d(Sen.rollcalls,
#' theta.constraints=list(KENNEDY=-2, HELMS=2),
#' burnin=2000, mcmc=100000, thin=20, verbose=500)
#' geweke.diag(posterior2)
#' plot(posterior2)
#' summary(posterior2)
#' }
#'
"MCMCirt1d" <-
function(datamatrix, theta.constraints=list(), burnin = 1000,
mcmc = 20000, thin=1, verbose = 0, seed = NA,
theta.start = NA, alpha.start = NA, beta.start = NA, t0 = 0,
T0 = 1, ab0=0, AB0=.25, store.item = FALSE, store.ability=TRUE,
drop.constant.items=TRUE, ... ) {
## checks
check.offset(list(...))
check.mcmc.parameters(burnin, mcmc, thin)
## check vote matrix and convert to work with C++ code
if (drop.constant.items==TRUE){
x.col.var <- apply(datamatrix, 2, var, na.rm=TRUE)
keep.inds <- x.col.var>0
keep.inds[is.na(keep.inds)] <- FALSE
datamatrix <- datamatrix[,keep.inds]
}
datamatrix <- as.matrix(datamatrix)
K <- ncol(datamatrix) # cases, bills, items, etc
J <- nrow(datamatrix) # justices, legislators, subjects, etc
if(sum(datamatrix==1 | datamatrix==0 | is.na(datamatrix)) != (J*K)) {
cat("Error: Data matrix contains elements other than 0, 1 or NA.\n")
stop("Please check data and try MCMCirt1d() again.\n",
call.=FALSE)
}
datamatrix[is.na(datamatrix)] <- 9
item.names <- colnames(datamatrix)
subject.names <- rownames(datamatrix)
## setup constraints on theta
if(length(theta.constraints) != 0) {
for (i in 1:length(theta.constraints)){
theta.constraints[[i]] <-
list(as.integer(1), theta.constraints[[i]][1])
}
}
holder <- build.factor.constraints(theta.constraints, t(datamatrix), J, 1)
theta.eq.constraints <- holder[[1]]
theta.ineq.constraints <- holder[[2]]
subject.names <- holder[[3]]
## names
item.names <- colnames(datamatrix)
if (is.null(item.names)){
item.names <- paste("item", 1:K, sep="")
}
## prior for theta
holder <- form.mvn.prior(t0, T0, 1)
t0 <- holder[[1]]
T0 <- holder[[2]]
## prior for (alpha, beta)
holder <- form.mvn.prior(ab0, AB0, 2)
ab0 <- holder[[1]]
AB0 <- holder[[2]]
## starting values for theta error checking
theta.start <- factor.score.start.check(theta.start, datamatrix,
t0, T0,
theta.eq.constraints,
theta.ineq.constraints, 1)
## starting values for (alpha, beta)
ab.starts <- matrix(NA, K, 2)
for (i in 1:K){
local.y <- datamatrix[,i]
local.y[local.y==9] <- NA
if (var(na.omit(local.y))==0){
ab.starts[i,] <- c(0,10)
}
else {
ab.starts[i,] <- coef(suppressWarnings(glm(local.y~theta.start,
family=binomial(link="probit"),
control=glm.control(
maxit=8, epsilon=1e-3)
)))
}
}
ab.starts[,1] <- -1 * ab.starts[,1] # make this into a difficulty param
## starting values for alpha and beta error checking
if (is.na(alpha.start)) {
alpha.start <- ab.starts[,1]
}
else if(is.null(dim(alpha.start))) {
alpha.start <- alpha.start * matrix(1,K,1)
}
else if((dim(alpha.start)[1] != K) || (dim(alpha.start)[2] != 1)) {
cat("Error: Starting value for alpha not conformable.\n")
stop("Please respecify and call MCMCirt1d() again.\n",
call.=FALSE)
}
if (is.na(beta.start)) {
beta.start <- ab.starts[,2]
}
else if(is.null(dim(beta.start))) {
beta.start <- beta.start * matrix(1,K,1)
}
else if((dim(beta.start)[1] != K) || (dim(beta.start)[2] != 1)) {
cat("Error: Starting value for beta not conformable.\n")
stop("Please respecify and call MCMCirt1d() again.\n",
call.=FALSE)
}
## define holder for posterior sample
if(store.item == FALSE & store.ability == TRUE) {
sample <- matrix(data=0, mcmc/thin, J)
}
else if (store.item == TRUE & store.ability == FALSE){
sample <- matrix(data=0, mcmc/thin, 2*K)
}
else if (store.item == TRUE & store.ability == TRUE){
sample <- matrix(data=0, mcmc/thin, J + 2 * K)
}
else{
cat("Error: store.item == FALSE & store.ability == FALSE.\n")
stop("Please respecify and call MCMCirt1d() again.\n",
call.=FALSE)
}
## seeds
seeds <- form.seeds(seed)
lecuyer <- seeds[[1]]
seed.array <- seeds[[2]]
lecuyer.stream <- seeds[[3]]
# call C++ code to draw sample
posterior <- .C("cMCMCirt1d",
sampledata = as.double(sample),
samplerow = as.integer(nrow(sample)),
samplecol = as.integer(ncol(sample)),
Xdata = as.integer(datamatrix),
Xrow = as.integer(nrow(datamatrix)),
Xcol = as.integer(ncol(datamatrix)),
burnin = as.integer(burnin),
mcmc = as.integer(mcmc),
thin = as.integer(thin),
lecuyer = as.integer(lecuyer),
seedarray = as.integer(seed.array),
lecuyerstream = as.integer(lecuyer.stream),
verbose = as.integer(verbose),
thetastartdata = as.double(theta.start),
thetastartrow = as.integer(nrow(theta.start)),
thetastartcol = as.integer(ncol(theta.start)),
astartdata = as.double(alpha.start),
astartrow = as.integer(length(alpha.start)),
astartcol = as.integer(1),
bstartdata = as.double(beta.start),
bstartrow = as.integer(length(beta.start)),
bstartcol = as.integer(1),
t0 = as.double(t0),
T0 = as.double(T0),
ab0data = as.double(ab0),
ab0row = as.integer(nrow(ab0)),
ab0col = as.integer(ncol(ab0)),
AB0data = as.double(AB0),
AB0row = as.integer(nrow(AB0)),
AB0col = as.integer(ncol(AB0)),
thetaeqdata = as.double(theta.eq.constraints),
thetaeqrow = as.integer(nrow(theta.eq.constraints)),
thetaeqcol = as.integer(ncol(theta.eq.constraints)),
thetaineqdata = as.double(theta.ineq.constraints),
thetaineqrow = as.integer(nrow(theta.ineq.constraints)),
thetaineqcol = as.integer(ncol(theta.ineq.constraints)),
storei = as.integer(store.item),
storea = as.integer(store.ability),
PACKAGE="MCMCpack"
)
theta.names <- paste("theta.", subject.names, sep = "")
alpha.beta.names <- paste(rep(c("alpha.","beta."), K),
rep(item.names, each = 2),
sep = "")
# put together matrix and build MCMC object to return
sample <- matrix(posterior$sampledata, posterior$samplerow,
posterior$samplecol,
byrow=FALSE)
output <- mcmc(data=sample, start=burnin+1, end=burnin+mcmc, thin=thin)
names <- NULL
if(store.ability == TRUE) {
names <- c(names, theta.names)
}
if (store.item == TRUE){
names <- c(names, alpha.beta.names)
}
varnames(output) <- names
attr(output,"title") <-
"MCMCirt1d Posterior Sample"
return(output)
}
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