bayesm (version 3.1-7)

rmvpGibbs: Gibbs Sampler for Multivariate Probit

Description

rmvpGibbs implements the Edwards/Allenby Gibbs Sampler for the multivariate probit model.

Usage

rmvpGibbs(Data, Prior, Mcmc)

Value

A list containing:

betadraw

\(R/keep x k\) matrix of betadraws

sigmadraw

\(R/keep x p*p\) matrix of sigma draws -- each row is the vector form of sigma

Arguments

Data

list(y, X, p)

Prior

list(betabar, A, nu, V)

Mcmc

list(R, keep, nprint, beta0 ,sigma0)

Author

Peter Rossi, Anderson School, UCLA, [email protected].

Details

Model and Priors

\(w_i = X_i\beta + e\) with \(e\) \(\sim\) N(0,\(\Sigma\)). Note: \(w_i\) is \(p x 1\).
\(y_{ij} = 1\) if \(w_{ij} > 0\), else \(y_i = 0\). \(j = 1, \ldots, p\)

beta and Sigma are not identifed. Correlation matrix and the betas divided by the appropriate standard deviation are. See reference or example below for details.

\(\beta\) \(\sim\) \(N(betabar, A^{-1})\)
\(\Sigma\) \(\sim\) \(IW(nu, V)\)

To make \(X\) matrix use createX

Argument Details

Data = list(y, X, p)

X:	\(n*p x k\) Design Matrix
y:	\(n*p x 1\) vector of 0/1 outcomes
p:	dimension of multivariate probit

Prior = list(betabar, A, nu, V) [optional]

betabar:	\(k x 1\) prior mean (def: 0)
A:	\(k x k\) prior precision matrix (def: 0.01*I)
nu:	d.f. parameter for Inverted Wishart prior (def: (p-1)+3)
V:	PDS location parameter for Inverted Wishart prior (def: nu*I)

Mcmc = list(R, keep, nprint, beta0 ,sigma0) [only R required]

R:	number of MCMC draws
keep:	MCMC thinning parameter -- keep every keepth draw (def: 1)
nprint:	print the estimated time remaining for every nprint'th draw (def: 100, set to 0 for no print)
beta0:	initial value for beta
sigma0:	initial value for sigma

References

For further discussion, see Chapter 4, Bayesian Statistics and Marketing by Rossi, Allenby, and McCulloch.

See Also

rmnpGibbs

Examples

if(nchar(Sys.getenv("LONG_TEST")) != 0) {R=2000} else {R=10}
set.seed(66)

simmvp = function(X, p, n, beta, sigma) {
  w = as.vector(crossprod(chol(sigma),matrix(rnorm(p*n),ncol=n))) + X%*%beta
  y = ifelse(w<0, 0, 1)
  return(list(y=y, X=X, beta=beta, sigma=sigma))
}

p = 3
n = 500
beta = c(-2,0,2)
Sigma = matrix(c(1, 0.5, 0.5, 0.5, 1, 0.5, 0.5, 0.5, 1), ncol=3)
k = length(beta)
I2 = diag(rep(1,p))
xadd = rbind(I2)
for(i in 2:n) { xadd=rbind(xadd,I2) }
X = xadd

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

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

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

ind = seq(from=0, by=p, length=k)
inda = 1:3
ind = ind + inda
cat(" Betadraws ", fill=TRUE)
betatilde = out$betadraw / sqrt(out$sigmadraw[,ind])
attributes(betatilde)$class = "bayesm.mat"
summary(betatilde, tvalues=beta/sqrt(diag(Sigma)))

rdraw = matrix(double((R)*p*p), ncol=p*p)
rdraw = t(apply(out$sigmadraw, 1, nmat))
attributes(rdraw)$class = "bayesm.var"
tvalue = nmat(as.vector(Sigma))
dim(tvalue) = c(p,p)
tvalue = as.vector(tvalue[upper.tri(tvalue,diag=TRUE)])
cat(" Draws of Correlation Matrix ", fill=TRUE)
summary(rdraw, tvalues=tvalue)

## plotting examples
if(0){plot(betatilde, tvalues=beta/sqrt(diag(Sigma)))}