bayesm (version 2.2-1)

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
• loglike
  R/keep vector of loglike values for each draw
• 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*p 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 Rossi, Allenby and McCulloch, Chapter 5. http://faculty.chicagogsb.edu/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)

simmnl= function(p,n,beta) {
  #   note: create X array with 2 alt.spec vars
  k=length(beta)
  X1=matrix(runif(n*p,min=-1,max=1),ncol=p)
  X2=matrix(runif(n*p,min=-1,max=1),ncol=p)
  X=createX(p,na=2,nd=NULL,Xd=NULL,Xa=cbind(X1,X2),base=1)
  Xbeta=X%*%beta # now do probs
  p=nrow(Xbeta)/n
  Xbeta=matrix(Xbeta,byrow=TRUE,ncol=p)
  Prob=exp(Xbeta)
  iota=c(rep(1,p))
  denom=Prob%*%iota
  Prob=Prob/as.vector(denom)
  # draw y
  y=vector("double",n)
  ind=1:p
  for (i in 1:n) 
        { yvec=rmultinom(1,1,Prob[i,]); y[i]=ind%*%yvec }
   return(list(y=y,X=X,beta=beta,prob=Prob))
}

simout=simmnl(p,n,beta)

Data1=list(y=simout$y,X=simout$X,p=p); Mcmc1=list(R=R,keep=1)
out=rmnlIndepMetrop(Data=Data1,Mcmc=Mcmc1)

cat("Summary of beta draws",fill=TRUE)
summary(out$betadraw,tvalues=beta)

if(0){
## plotting examples
plot(out$betadraw)
}