Gibbs Sampler for Multivariate Probit
rmvpGibbs implements the Edwards/Allenby Gibbs Sampler for the multivariate probit model.
rmvpGibbs(Data, Prior, Mcmc)
Data |
list(y, X, p) |
Prior |
list(betabar, A, nu, V) |
Mcmc |
list(R, keep, nprint, beta0 ,sigma0) |
w_i = X_iβ + e with e ~ N(0,Σ). Note: w_i is p x 1.
y_{ij} = 1 if w_{ij} > 0, else y_i = 0. j = 1, …, 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.
β ~ N(betabar, A^{-1})
Σ ~ IW(nu, V)
To make X matrix use createX
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 |
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 |
Peter Rossi, Anderson School, UCLA, perossichi@gmail.com.
For further discussion, see Chapter 4, Bayesian Statistics and Marketing by Rossi, Allenby, and McCulloch.
http://www.perossi.org/home/bsm-1
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)))}Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.