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\name{rhierBinLogit}
\alias{rhierBinLogit}
\concept{bayes}
\concept{MCMC}
\concept{hierarchical models}
\concept{binary logit}
\title{MCMC Algorithm for Hierarchical Binary Logit}
\description{
\bold{This function has been deprecated. Please use \code{rhierMnlRwMixture} instead.}
\code{rhierBinLogit} implements an MCMC algorithm for hierarchical binary logits with a normal heterogeneity distribution. This is a hybrid sampler with a RW Metropolis step for unit-level logit parameters.
\code{rhierBinLogit} is designed for use on choice-based conjoint data with partial profiles. The Design matrix is based on differences of characteristics between two alternatives. See Appendix A of \emph{Bayesian Statistics and Marketing} for details.
}
\usage{rhierBinLogit(Data, Prior, Mcmc)}
\arguments{
\item{Data }{list(lgtdata, Z)}
\item{Prior}{list(Deltabar, ADelta, nu, V)}
\item{Mcmc }{list(R, keep, sbeta)}
}
\details{
\subsection{Model and Priors}{
\eqn{y_{hi} = 1} with \eqn{Pr = exp(x_{hi}'\beta_h) / (1+exp(x_{hi}'\beta_h)} and \eqn{\beta_h} is \eqn{nvar x 1} \cr
\eqn{h = 1, \ldots, length(lgtdata)} units (or "respondents" for survey data)
\eqn{\beta_h} = ZDelta[h,] + \eqn{u_h} \cr
Note: here ZDelta refers to \code{Z\%*\%Delta} with ZDelta[h,] the \eqn{h}th row of this product\cr
Delta is an \eqn{nz x nvar} array
\eqn{u_h} \eqn{\sim}{~} \eqn{N(0, V_{beta})}. \cr
\eqn{delta = vec(Delta)} \eqn{\sim}{~} \eqn{N(vec(Deltabar), V_{beta}(x) ADelta^{-1})}\cr
\eqn{V_{beta}} \eqn{\sim}{~} \eqn{IW(nu, V)}
}
\subsection{Argument Details}{
\emph{\code{Data = list(lgtdata, Z)} [\code{Z} optional]}
\tabular{ll}{
\code{lgtdata: } \tab list of lists with each cross-section unit MNL data \cr
\code{lgtdata[[h]]$y:} \tab \eqn{n_h x 1} vector of binary outcomes (0,1) \cr
\code{lgtdata[[h]]$X:} \tab \eqn{n_h x nvar} design matrix for h'th unit \cr
\code{Z: } \tab \eqn{nreg x nz} mat of unit chars (def: vector of ones)
}
\emph{\code{Prior = list(Deltabar, ADelta, nu, V)} [optional]}
\tabular{ll}{
\code{Deltabar:} \tab \eqn{nz x nvar} matrix of prior means (def: 0) \cr
\code{ADelta: } \tab prior precision matrix (def: 0.01I) \cr
\code{nu: } \tab d.f. parameter for IW prior on normal component Sigma (def: nvar+3) \cr
\code{V: } \tab pds location parm for IW prior on normal component Sigma (def: nuI)
}
\emph{\code{Mcmc = list(R, keep, sbeta)} [only \code{R} required]}
\tabular{ll}{
\code{R: } \tab number of MCMC draws \cr
\code{keep: } \tab MCMC thinning parm -- keep every \code{keep}th draw (def: 1) \cr
\code{sbeta: } \tab scaling parm for RW Metropolis (def: 0.2)
}
}
}
\value{
A list containing:
\item{Deltadraw }{ \eqn{R/keep x nz*nvar} matrix of draws of Delta}
\item{betadraw }{ \eqn{nlgt x nvar x R/keep} array of draws of betas}
\item{Vbetadraw }{ \eqn{R/keep x nvar*nvar} matrix of draws of Vbeta}
\item{llike }{ \eqn{R/keep x 1} vector of log-like values}
\item{reject }{ \eqn{R/keep x 1} vector of reject rates over nlgt units}
}
\note{Some experimentation with the Metropolis scaling paramter (\code{sbeta}) may be required.}
\author{Peter Rossi, Anderson School, UCLA, \email{perossichi@gmail.com}.}
\references{For further discussion, see Chapter 5, \emph{Bayesian Statistics and Marketing} by Rossi, Allenby, and McCulloch.}
\examples{
if(nchar(Sys.getenv("LONG_TEST")) != 0) {R=10000} else {R=10}
set.seed(66)
nvar = 5 ## number of coefficients
nlgt = 1000 ## number of cross-sectional units
nobs = 10 ## number of observations per unit
nz = 2 ## number of regressors in mixing distribution
Z = matrix(c(rep(1,nlgt),runif(nlgt,min=-1,max=1)), nrow=nlgt, ncol=nz)
Delta = matrix(c(-2, -1, 0, 1, 2, -1, 1, -0.5, 0.5, 0), nrow=nz, ncol=nvar)
iota = matrix(1, nrow=nvar, ncol=1)
Vbeta = diag(nvar) + 0.5*iota\%*\%t(iota)
lgtdata=NULL
for (i in 1:nlgt) {
beta = t(Delta)\%*\%Z[i,] + as.vector(t(chol(Vbeta))\%*\%rnorm(nvar))
X = matrix(runif(nobs*nvar), nrow=nobs, ncol=nvar)
prob = exp(X\%*\%beta) / (1+exp(X\%*\%beta))
unif = runif(nobs, 0, 1)
y = ifelse(unif<prob, 1, 0)
lgtdata[[i]] = list(y=y, X=X, beta=beta)
}
Data1 = list(lgtdata=lgtdata, Z=Z)
Mcmc1 = list(R=R)
out = rhierBinLogit(Data=Data1, Mcmc=Mcmc1)
cat("Summary of Delta draws", fill=TRUE)
summary(out$Deltadraw, tvalues=as.vector(Delta))
cat("Summary of Vbeta draws", fill=TRUE)
summary(out$Vbetadraw, tvalues=as.vector(Vbeta[upper.tri(Vbeta,diag=TRUE)]))
if(0){
## plotting examples
plot(out$Deltadraw,tvalues=as.vector(Delta))
plot(out$betadraw)
plot(out$Vbetadraw,tvalues=as.vector(Vbeta[upper.tri(Vbeta,diag=TRUE)]))
}
}
\seealso{ \code{\link{rhierMnlRwMixture}} }
\keyword{ models}
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