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\name{rmnlIndepMetrop}
\alias{rmnlIndepMetrop}
\concept{MCMC}
\concept{multinomial logit}
\concept{Metropolis algorithm}
\concept{bayes}
\title{MCMC Algorithm for Multinomial Logit Model}
\description{
\code{rmnlIndepMetrop} implements Independence Metropolis algorithm for the multinomial logit (MNL) model.
}
\usage{rmnlIndepMetrop(Data, Prior, Mcmc)}
\arguments{
\item{Data }{list(y, X, p)}
\item{Prior}{list(A, betabar)}
\item{Mcmc }{list(R, keep, nprint, nu)}
}
\details{
\subsection{Model and Priors}{
y \eqn{\sim}{~} MNL(X, \eqn{\beta}) \cr
\eqn{Pr(y=j) = exp(x_j'\beta)/\sum_k{e^{x_k'\beta}}}
\eqn{\beta} \eqn{\sim}{~} \eqn{N(betabar, A^{-1})}
}
\subsection{Argument Details}{
\emph{\code{Data = list(y, X, p)}}
\tabular{ll}{
\code{y: } \tab \eqn{n x 1} vector of multinomial outcomes (1, \ldots, p) \cr
\code{X: } \tab \eqn{n*p x k} matrix \cr
\code{p: } \tab number of alternatives
}
\emph{\code{Prior = list(A, betabar)} [optional]}
\tabular{ll}{
\code{A: } \tab \eqn{k x k} prior precision matrix (def: 0.01*I) \cr
\code{betabar: } \tab \eqn{k x 1} prior mean (def: 0)
}
\emph{\code{Mcmc = list(R, keep, nprint, nu)} [only \code{R} required]}
\tabular{ll}{
\code{R: } \tab number of MCMC draws \cr
\code{keep: } \tab MCMC thinning parameter -- keep every \code{keep}th draw (def: 1) \cr
\code{nprint: } \tab print the estimated time remaining for every \code{nprint}'th draw (def: 100, set to 0 for no print) \cr
\code{nu: } \tab d.f. parameter for independent t density (def: 6)
}
}
}
\value{
A list containing:
\item{betadraw }{\eqn{R/keep x k} matrix of beta draws}
\item{loglike }{\eqn{R/keep x 1} vector of log-likelihood values evaluated at each draw}
\item{acceptr }{acceptance rate of Metropolis draws}
}
\author{Peter Rossi, Anderson School, UCLA, \email{perossichi@gmail.com}.}
\references{For further discussion, see Chapter 3, \emph{Bayesian Statistics and Marketing} by Rossi, Allenby, and McCulloch.}
\seealso{ \code{\link{rhierMnlRwMixture}} }
\examples{
if(nchar(Sys.getenv("LONG_TEST")) != 0) {R=2000} else {R=10}
set.seed(66)
simmnl = function(p, n, beta) {
## note: create X array with 2 alt.spec vars
k = length(beta)
X1 = matrix(runif(n*p,min=-1,max=1), ncol=p)
X2 = matrix(runif(n*p,min=-1,max=1), ncol=p)
X = createX(p, na=2, nd=NULL, Xd=NULL, Xa=cbind(X1,X2), base=1)
Xbeta = X\%*\%beta
## now do probs
p = nrow(Xbeta) / n
Xbeta = matrix(Xbeta, byrow=TRUE, ncol=p)
Prob = exp(Xbeta)
iota = c(rep(1,p))
denom = Prob\%*\%iota
Prob = Prob / as.vector(denom)
## draw y
y = vector("double",n)
ind = 1:p
for (i in 1:n) {
yvec = rmultinom(1, 1, Prob[i,])
y[i] = ind\%*\%yvec
}
return(list(y=y, X=X, beta=beta, prob=Prob))
}
n = 200
p = 3
beta = c(1, -1, 1.5, 0.5)
simout = simmnl(p,n,beta)
Data1 = list(y=simout$y, X=simout$X, p=p)
Mcmc1 = list(R=R, keep=1)
out = rmnlIndepMetrop(Data=Data1, Mcmc=Mcmc1)
cat("Summary of beta draws", fill=TRUE)
summary(out$betadraw, tvalues=beta)
## plotting examples
if(0){plot(out$betadraw)}
}
\keyword{models}
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