1\name{llnhlogit} 2\alias{llnhlogit} 3\concept{multinomial logit} 4\concept{non-homothetic utility} 5 6\title{Evaluate Log Likelihood for non-homothetic Logit Model} 7 8\description{ 9\code{llnhlogit} evaluates log-likelihood for the Non-homothetic Logit model. 10} 11 12\usage{llnhlogit(theta, choice, lnprices, Xexpend)} 13 14\arguments{ 15 \item{theta }{ parameter vector (see details section) } 16 \item{choice }{ \eqn{n x 1} vector of choice (1,\ldots,p) } 17 \item{lnprices}{ \eqn{n x p} array of log-prices} 18 \item{Xexpend }{ \eqn{n x d} array of vars predicting expenditure } 19} 20 21\details{ 22 Non-homothetic logit model, \eqn{Pr(i) = exp(tau v_i) / sum_j exp(tau v_j)} \cr 23 24 \eqn{v_i = alpha_i - e^{kappaStar_i}u^i - lnp_i} \cr 25 tau is the scale parameter of extreme value error distribution.\cr 26 \eqn{u^i} solves \eqn{u^i = psi_i(u^i)E/p_i}.\cr 27 \eqn{ln(psi_i(U)) = alpha_i - e^{kappaStar_i}U}. \cr 28 \eqn{ln(E) = gamma'Xexpend}.\cr 29 30 Structure of theta vector: \cr 31 alpha: \eqn{p x 1} vector of utility intercepts.\cr 32 kappaStar: \eqn{p x 1} vector of utility rotation parms expressed on natural log scale. \cr 33 gamma: \eqn{k x 1} -- expenditure variable coefs.\cr 34 tau: \eqn{1 x 1} -- logit scale parameter.\cr 35} 36 37\value{Value of log-likelihood (sum of log prob of observed multinomial outcomes).} 38 39\section{Warning}{ 40This routine is a utility routine that does \strong{not} check the input arguments for proper dimensions and type. 41} 42 43\author{Peter Rossi, Anderson School, UCLA, \email{perossichi@gmail.com}.} 44 45\references{For further discussion, see Chapter 4, \emph{Bayesian Statistics and Marketing} by Rossi, Allenby, and McCulloch. \cr \url{http://www.perossi.org/home/bsm-1}} 46 47\seealso{\code{\link{simnhlogit}}} 48 49\examples{ 50N=1000; p=3; k=1 51theta = c(rep(1,p), seq(from=-1,to=1,length=p), rep(2,k), 0.5) 52lnprices = matrix(runif(N*p), ncol=p) 53Xexpend = matrix(runif(N*k), ncol=k) 54simdata = simnhlogit(theta, lnprices, Xexpend) 55 56## evaluate likelihood at true theta 57llstar = llnhlogit(theta, simdata$y, simdata$lnprices, simdata$Xexpend) 58} 59 60\keyword{models}