| rhierMnlRwMixture {bayesm} | R Documentation |
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.
rhierMnlRwMixture(Data, Prior, Mcmc)
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) |
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:
plgtdatalgtdata[[i]]$ylgtdata[[i]]$XadeltabarAdmubarAmunuVncompswRkeepa 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) |
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).
Peter Rossi, Graduate School of Business, University of Chicago, Peter.Rossi@ChicagoGsb.edu.
For further discussion, see Bayesian Statistics and Marketing
by Rossi, Allenby and McCulloch, Chapter 5.
http://faculty.chicagogsb.edu/peter.rossi/research/bsm.html
##
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)
}