bayesm (version 1.1-2)

rmnlIndepMetrop: MCMC Algorithm for Multinomial Logit Model

Description

rmnIndepMetrop implements Independence Metropolis for the MNL.

Usage

rmnlIndepMetrop(Data, Prior, Mcmc)

Arguments

Data

list(p,y,X)

Prior

list(A,betabar) optional

Mcmc

list(R,keep,nu)

Value

• a list containing:
• betadraw
  R/keep x nvar array of beta draws
• acceptr
  acceptance rate of Metropolis draws

concept

• MCMC
• multinomial logit
• Metropolis algorithm
• bayes

Details

Model: y $\sim$ MNL(X,beta). $Pr(y=j) = exp(x_j'beta)/\sum_k{e^{x_k'beta}}$. Prior: $beta$ $\sim$ $N(betabar,A^{-1})$ list arguments contain:

• p

{number of alternatives} y{ nobs vector of multinomial outcomes (1,..., p)} X{nobs*m x nvar matrix} A{ nvar x nvar pds prior prec matrix (def: .01I)} betabar{ nvar x 1 prior mean (def: 0)} R{ number of MCMC draws} keep{ MCMC thinning parm: keep every keepth draw (def: 1)} nu{ degrees of freedom parameter for independence t density (def: 6) }

References

For further discussion, see Bayesian Statistics and Marketing by Allenby, McCulloch, and Rossi, Chapter 5. http://gsbwww.uchicago.edu/fac/peter.rossi/research/bsm.html

See Also

rhierMnlRwMixture

Examples

##

if(nchar(Sys.getenv("LONG_TEST")) != 0) {R=2000} else {R=10}

set.seed(66)
n=200; p=3; beta=c(1,-1,1.5,.5)
simout=simmnl(p,n,beta)
A=diag(c(rep(.01,length(beta)))); betabar=rep(0,length(beta))

Data=list(y=simout$y,X=simout$X,p=p); Mcmc=list(R=R,keep=1) ; Prior=list(A=A,betabar=betabar)
out=rmnlIndepMetrop(Data=Data,Prior=Prior,Mcmc=Mcmc)
cat("Betadraws ",fill=TRUE)
mat=apply(out$betadraw,2,quantile,probs=c(.01,.05,.5,.95,.99))
mat=rbind(beta,mat); rownames(mat)[1]="beta"; print(mat)