Dear WinBUGS users:
Does anyone have any experience in modeling a multivariate probit model?
(I have three equations).
The model I wrote, which is pasted below, fails because there is no check
that the correlation matrix be positive definite.
I read the Barnard, Meng, McCulloch article in Statistica Sinica, which
gives me the solution to my problem.
But I am stuck when I try to translate the Barnard, Meng, McCulloch
solution into the WinBUGS language structure.
I would truly appreciate any help that would push me in the right
direction.
Best regards,
giacomo
### Trivariate probit model
model {
for (i in 1:1000) {
Y[i,1] <- y1[i]
Y[i,2] <- y2[i]
Y[i,3] <- y3[i]
z[i,1:3] ~ dmnorm(eta[i,1:3],tau[1:3,1:3])I(L[i,1:3],U[i,1:3])
for (j in 1:3) {
L[i,j] <- -50*equals(Y[i,j],0)
U[i,j] <- 50*equals(Y[i,j],1)
eta[i,j] <- b[j,1] + b[j,2]*x2[i] + b[j,3]*x3[i]
}
}
sigma[1,2] <- rho[1]
sigma[2,1] <- rho[1]
sigma[1,3] <- rho[2]
sigma[3,1] <- rho[2]
sigma[2,3] <- rho[3]
sigma[3,2] <- rho[3]
for (k in 1:3) {
rho[k] ~ dunif(-1,1)
}
sigma[1,1] <- 1
sigma[2,2] <- 1
sigma[3,3] <- 1
tau[1:3,1:3] <- inverse(sigma[,])
for (j in 1:3) {
for (k in 1:3) {
b[j,k] ~ dnorm(0,.01)
}
}
}
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