BMLogit {Baldur}R Documentation

Bayesian multinomial logit model

Description

BMLogit produces iid draws from the posterior density of a Bayesian multinomial logit model with a multivariate normal prior.

Usage

BMLogit(y,X,alpha,mu,P,draws,Prec=FALSE,A=FALSE)

Arguments

y n*m Matrix with counts for the m (m>=2) alternatives.
X n*k Matrix with the values for the independent variables
alpha n*m Matrix added to the utilities of the various alternatives
mu (k(m-1))*1 Prior Mean Vector
P k(m-1)*k(m-1) Prior Precision Matrix (must be Positive definite)
draws Number of desired draws from the posterior density
Prec Optional logical argument with default Prec=FALSE. If argument is set to TRUE, the matrix P is treated as a prior precision matrix.
A Optional logical argument with default A=FALSE. If argument is set to TRUE, the function returns not only the simulated draws from the posterior density but also a vector with information related to the acceptance rate for the underlying accept/reject procedure (see below).

Details

Makes use of the likelihood subgradient density accept/reject procedure of Nygren and Nygren (2006) in order to generate iid samples from the posterior density of a Bayesian multinomial logit model. If the posterior density is close to multivariate normal, then the expected number of draws should be approximately equal to $(2/sqrt{pi})^{k(m-1)}$.

Value

If A=FALSE, a matrix beta. If A=TRUE, a list containing the matrix beta and a matrix Accept.:

beta draws*k(m-1) matrix with the iid draws for the model parameters.
Accept draws*1 matrix with the number of candidates for each draw that were required before acceptance in the accept/reject procedure.

Author(s)

Kjell Nygren knygren@us.imshealth.com

Examples


data(Contraceptives,package="Baldur")

y<-as.matrix(Contraceptives[1:7,1:3])
X<-matrix(1,nrow=7,ncol=3)
X[,2]<-Contraceptives[,5]
X[,3]<-Contraceptives[,5]*Contraceptives[,5]

mu<-matrix(0,nrow=6,ncol=1)
alpha<-matrix(0,nrow=7,ncol=3)
P<-100*diag(6)

draws<-1000

set.seed(666)
system.time(sim<-BMLogit(y,X,alpha,mu,P,draws))
[Package Baldur version 0.0-0 Index]