rmnpGibbs {bayesm}R Documentation

Gibbs Sampler for Multinomial Probit

Description

rmnpGibbs implements the McCulloch/Rossi Gibbs Sampler for the multinomial probit model.

Usage

rmnpGibbs(Data, Prior, Mcmc)

Arguments

Data list(p, y, X)
Prior list(betabar,A,nu,V) (optional)
Mcmc list(beta0,sigma0,R,keep) (R required)

Details

model:
w_i = X_iβ + e. e ~ N(0,Sigma). note: w_i, e are (p-1) x 1.
y_i = j, if w_{ij} > max(0,w_{i,-j}) j=1,...,p-1. w_{i,-j} means elements of w_i other than the jth.
y_i = p, if all w_i < 0.

priors:
beta ~ N(betabar,A^{-1})
Sigma ~ IW(nu,V)

to make up X matrix use createX with DIFF=TRUE.

List arguments contain

Value

a list containing:

betadraw R/keep x k array of betadraws
sigmadraw R/keep x (p-1)*(p-1) array of sigma draws – each row is in vector form

Note

beta is not identified. beta/sqrt(sigma_{11}) and Sigma/sigma_{11} are. See Allenby et al or example below for details.

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 4.
http://faculty.chicagogsb.edu/peter.rossi/research/bsm.html

See Also

rmvpGibbs

Examples

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

set.seed(66)
p=3
n=500
beta=c(-1,1,1,2)
Sigma=matrix(c(1,.5,.5,1),ncol=2)
k=length(beta)
X1=matrix(runif(n*p,min=0,max=2),ncol=p); X2=matrix(runif(n*p,min=0,max=2),ncol=p)
X=createX(p,na=2,nd=NULL,Xa=cbind(X1,X2),Xd=NULL,DIFF=TRUE,base=p)

simmnp= function(X,p,n,beta,sigma) {
  indmax=function(x) {which(max(x)==x)}
  Xbeta=X%*%beta
  w=as.vector(crossprod(chol(sigma),matrix(rnorm((p-1)*n),ncol=n)))+ Xbeta
  w=matrix(w,ncol=(p-1),byrow=TRUE)
  maxw=apply(w,1,max)
  y=apply(w,1,indmax)
  y=ifelse(maxw < 0,p,y)
  return(list(y=y,X=X,beta=beta,sigma=sigma))
}

simout=simmnp(X,p,500,beta,Sigma)

Data1=list(p=p,y=simout$y,X=simout$X)
Mcmc1=list(R=R,keep=1)

out=rmnpGibbs(Data=Data1,Mcmc=Mcmc1)

cat(" Summary of Betadraws ",fill=TRUE)
betatilde=out$betadraw/sqrt(out$sigmadraw[,1])
attributes(betatilde)$class="bayesm.mat"
summary(betatilde,tvalues=beta)

cat(" Summary of Sigmadraws ",fill=TRUE)
sigmadraw=out$sigmadraw/out$sigmadraw[,1]
attributes(sigmadraw)$class="bayesm.var"
summary(sigmadraw,tvalues=as.vector(Sigma[upper.tri(Sigma,diag=TRUE)]))

if(0){
## plotting examples
plot(betatilde,tvalues=beta)
}

[Package bayesm version 2.2-2 Index]