1\name{llmnp}
2\alias{llmnp}
3\concept{multinomial probit}
4\concept{GHK method}
5\concept{likelihood}
6
7\title{Evaluate Log Likelihood for Multinomial Probit Model}
8
9\description{
10\code{llmnp} evaluates the log-likelihood for the multinomial probit model.
11}
12
13\usage{llmnp(beta, Sigma, X, y, r)}
14
15\arguments{
16  \item{beta }{ k x 1 vector of coefficients }
17  \item{Sigma}{ (p-1) x (p-1) covariance matrix of errors }
18  \item{X    }{ n*(p-1) x k array where X is from differenced system }
19  \item{y    }{ vector of n indicators of multinomial response (1, \ldots, p) }
20  \item{r    }{ number of draws used in GHK }
21}
22
23\details{
24  \eqn{X} is \eqn{(p-1)*n x k} matrix.  Use \code{\link{createX}} with \code{DIFF=TRUE} to create \eqn{X}. \cr
25
26  Model for each obs:  \eqn{w = Xbeta + e} with \eqn{e} \eqn{\sim}{~} \eqn{N(0,Sigma)}.
27
28  Censoring mechanism: \cr
29    if \eqn{y=j (j<p),  w_j > max(w_{-j})} and \eqn{w_j >0}    \cr
30    if \eqn{y=p,  w < 0}                   \cr
31
32   To use GHK, we must transform so that these are rectangular regions
33   e.g. if \eqn{y=1,  w_1 > 0} and \eqn{w_1 - w_{-1} > 0}.
34
35   Define \eqn{A_j} such that if \eqn{j=1,\ldots,p-1} then \eqn{A_jw = A_jmu + A_je > 0} is equivalent to \eqn{y=j}. Thus, if \eqn{y=j}, we have \eqn{A_je > -A_jmu}.  Lower truncation is \eqn{-A_jmu} and \eqn{cov = A_jSigmat(A_j)}. For \eqn{j=p}, \eqn{e < - mu}.
36}
37
38\value{Value of log-likelihood (sum of log prob of observed multinomial outcomes)}
39
40\section{Warning}{
41This routine is a utility routine that does \strong{not} check the input arguments for proper dimensions and type.
42}
43
44\author{ Peter Rossi, Anderson School, UCLA, \email{perossichi@gmail.com}.}
45
46\references{ For further discussion, see Chapters 2 and 4, \emph{Bayesian Statistics and Marketing} by Rossi, Allenby, and McCulloch. \cr \url{http://www.perossi.org/home/bsm-1}}
47
48\seealso{ \code{\link{createX}}, \code{\link{rmnpGibbs}} }
49
50\examples{
51\dontrun{ll=llmnp(beta,Sigma,X,y,r)}
52}
53
54\keyword{models}
55