rhierMnlRwMixture {bayesm}R Documentation

MCMC Algorithm for Hierarchical Multinomial Logit with Mixture of Normals Heterogeneity

Description

rhierMnlRwMixture is a MCMC algorithm for a hierarchical multinomial logit with a mixture of normals heterogeneity distribution. This is a hybrid Gibbs Sampler with a RW Metropolis step for the MNL coefficients for each panel unit.

Usage

rhierMnlRwMixture(Data, Prior, Mcmc)

Arguments

Data list(p,lgtdata,Z) ( Z is optional)
Prior list(a,deltabar,Ad,mubar,Amu,nu,V,ncomp) (all but ncomp are optional)
Mcmc list(s,w,R,keep) (R required)

Details

Model:
y_i ~ MNL(X_i,beta_i). i=1,..., length(lgtdata). theta_i is nvar x 1.

beta_i= ZDelta[i,] + u_i.
Note: here ZDelta refers to Z%*%D, ZDelta[i,] is ith row of this product.
Delta is an nz x nvar array.

u_i ~ N(mu_{ind},Sigma_{ind}). ind ~ multinomial(pvec).

Priors:
pvec ~ dirichlet (a)
delta= vec(Delta) ~ N(deltabar,A_d^{-1})
mu_j ~ N(mubar,Sigma_j (x) Amu^{-1})
Sigma_j ~ IW(nu,V)

Lists contain:

Value

a list containing:

Deltadraw R/keep x nz*nvar matrix of draws of Delta, first row is initial value
betadraw nlgt x nvar x R/keep array of draws of betas
nmix list of 3 components, probdraw, NULL, compdraw
loglike log-likelihood for each kept draw (length R/keep)

Note

More on probdraw component of nmix list:
R/keep x ncomp matrix of draws of probs of mixture components (pvec)
More on compdraw component of return value list:

Note: Z should not include an intercept and is centered for ease of interpretation.

Be careful in assessing prior parameter, Amu. .01 is too small for many applications. See Rossi et al, chapter 5 for full discussion.

Note: as of version 2.0-2 of bayesm, the fractional weight parameter has been changed to a weight between 0 and 1. w is the fractional weight on the normalized pooled likelihood. This differs from what is in Rossi et al chapter 5, i.e.

like_i^(1-w) x like_pooled^((n_i/N)*w)

Large R values may be required (>20,000).

Author(s)

Peter Rossi, Graduate School of Business, University of Chicago, Peter.Rossi@ChicagoGsb.edu.

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

rmnlIndepMetrop

Examples

##
if(nchar(Sys.getenv("LONG_TEST")) != 0) {R=10000} else {R=10}

set.seed(66)
p=3                                # num of choice alterns
ncoef=3  
nlgt=300                           # num of cross sectional units
nz=2
Z=matrix(runif(nz*nlgt),ncol=nz)
Z=t(t(Z)-apply(Z,2,mean))          # demean Z
ncomp=3                                # no of mixture components
Delta=matrix(c(1,0,1,0,1,2),ncol=2)
comps=NULL
comps[[1]]=list(mu=c(0,-1,-2),rooti=diag(rep(1,3)))
comps[[2]]=list(mu=c(0,-1,-2)*2,rooti=diag(rep(1,3)))
comps[[3]]=list(mu=c(0,-1,-2)*4,rooti=diag(rep(1,3)))
pvec=c(.4,.2,.4)

simmnlwX= function(n,X,beta) {
  ##  simulate from MNL model conditional on X matrix
  k=length(beta)
  Xbeta=X%*%beta
  j=nrow(Xbeta)/n
  Xbeta=matrix(Xbeta,byrow=TRUE,ncol=j)
  Prob=exp(Xbeta)
  iota=c(rep(1,j))
  denom=Prob%*%iota
  Prob=Prob/as.vector(denom)
  y=vector("double",n)
  ind=1:j
  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))
}

## simulate data
simlgtdata=NULL
ni=rep(50,300)
for (i in 1:nlgt) 
{  betai=Delta%*%Z[i,]+as.vector(rmixture(1,pvec,comps)$x)
   Xa=matrix(runif(ni[i]*p,min=-1.5,max=0),ncol=p)
   X=createX(p,na=1,nd=NULL,Xa=Xa,Xd=NULL,base=1)
   outa=simmnlwX(ni[i],X,betai)
   simlgtdata[[i]]=list(y=outa$y,X=X,beta=betai)
}

## plot betas
if(0){
## set if(1) above to produce plots
bmat=matrix(0,nlgt,ncoef)
for(i in 1:nlgt) {bmat[i,]=simlgtdata[[i]]$beta}
par(mfrow=c(ncoef,1))
for(i in 1:ncoef) hist(bmat[,i],breaks=30,col="magenta")
}

##   set parms for priors and Z
Prior1=list(ncomp=5)

keep=5
Mcmc1=list(R=R,keep=keep)
Data1=list(p=p,lgtdata=simlgtdata,Z=Z)

out=rhierMnlRwMixture(Data=Data1,Prior=Prior1,Mcmc=Mcmc1)

cat("Summary of Delta draws",fill=TRUE)
summary(out$Deltadraw,tvalues=as.vector(Delta))
cat("Summary of Normal Mixture Distribution",fill=TRUE)
summary(out$nmix)

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


[Package bayesm version 2.1-2 Index]