| rmnpGibbs(bayesm) | R Documentation |
rmnpGibbs implements the McCulloch/Rossi Gibbs Sampler for the multinomial probit model.
rmnpGibbs(Data, Prior, Mcmc)
Data |
list(X,y) |
Prior |
list(betabar,A,nu,V) |
Mcmc |
list(beta0,sigma0,R,keep) |
model:
w_i = X_i beta + e. e~N(0,Sigma). note: w_i, e are (p-1) x 1.
y_i = j, if w_ij > w_i-j j=1,...,p-1. w_i-j means elements of w_i other than 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
XybetabarAnuVbeta0sigma0Rkeepa 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 |
beta is not identified. beta/sqrt(Sigma_11) and Sigma/sigma_11 are. See Allenby et al or example below for details.
Peter Rossi, Graduate School of Business, University of Chicago, Peter.Rossi@ChicagoGsb.edu.
For further discussion, see Bayesian Statistics and Marketing
by Allenby, McCulloch, and Rossi, Chapter 4.
http://gsbwww.uchicago.edu/fac/peter.rossi/research/bsm.html
##
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=runif(n*(p-1),min=-1,max=1); x2=runif(n*(p-1),min=-1,max=1)
I2=diag(rep(1,p-1)); xadd=rbind(I2)
for(i in 2:n) { xadd=rbind(xadd,I2)}
X=cbind(xadd,x1,x2)
simout=simmnp(X,p,500,beta,Sigma)
R=2000
Data=list(p=p,y=simout$y,X=simout$X)
Mcmc=list(R=R,keep=1)
out=rmnpGibbs(Mcmc=Mcmc,Data=Data)
cat(" Betadraws ",fill=TRUE)
mat=apply(out$betadraw/sqrt(out$sigmadraw[,1]),2,quantile,probs=c(.01,.05,.5,.95,.99))
mat=rbind(beta,mat); rownames(mat)[1]="beta"; print(mat)
cat(" Sigmadraws ",fill=TRUE)
mat=apply(out$sigmadraw/out$sigmadraw[,1],2,quantile,probs=c(.01,.05,.5,.95,.99))
mat=rbind(as.vector(Sigma),mat); rownames(mat)[1]="sigma"; print(mat)