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