rmnpGibbs {bayesm} | R Documentation |
rmnpGibbs
implements the McCulloch/Rossi Gibbs Sampler for the multinomial probit model.
rmnpGibbs(Data, Prior, Mcmc)
Data |
list(p, y, X) |
Prior |
list(betabar,A,nu,V) (optional) |
Mcmc |
list(beta0,sigma0,R,keep) (R required) |
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
p
y
X
betabar
A
nu
V
beta0
sigma0
R
keep
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 |
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 Rossi, Allenby and McCulloch, Chapter 4.
http://gsbwww.uchicago.edu/fac/peter.rossi/research/bsm.html
## 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=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) 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)