rmvpGibbs {bayesm} R Documentation

## Gibbs Sampler for Multivariate Probit

### Description

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

### Usage

rmvpGibbs(Data, Prior, Mcmc)

### Arguments

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

### 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

### 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

### Author(s)

Peter Rossi, Anderson School, UCLA, perossichi@gmail.com.

### References

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

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))

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
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)))}


[Package bayesm version 3.1-6 Index]