#################################################################################
# Bayesian model selection and statistical modeling 
# Chapman & Hall/CRC Taylor and Francis Group 
#
# Bayesian model selection and statistical modeling 
# Chapman & Hall/CRC Taylor and Francis Group 
#
# Chapter6: Section6.1.1
#
# Multinomial probit models
#
# Author : Tomohiro Ando
#
################################################################################
library(MNP)
library(MCMCpack)

# Dutch voting behavior data

data(Nethvote)

n <- nrow(Nethvote)

fit <- mnp(vote~distPvdA+distVVD+distCDA+income+age, data = Nethvote, 
p.var = 10000, 
p.df = 10, 
n.draws = 101000, 
burnin = 1000, 
thin = 100, 
verbose = TRUE)

p <- 3*6
V <- var((fit$param)[,-(p+1)])

A <- diag(10000,p)

S <- summary.mnp(fit)

M <- as.vector((S$coef)[,1])

LogLike <- (-p/2)*log(2*pi)+(-1/2)*log(det(A))-sum( M%*%solve(A)%*%M )/2

nu <- 10+1

SS <- as.vector((S$cov)[,1])
K <- diag(1,4)
K[2,2] <- SS[1]
K[2,3] <- K[3,2] <- SS[2]
K[2,4] <- K[4,2] <- SS[3]
K[3,3] <- SS[4]
K[3,4] <- K[4,3] <- SS[5]
K[4,4] <- K[4,4] <- SS[6]

Prior <- lndIWishart(nu, diag(1,4), K)

Margianllikelihood <- LogLike+Prior+p/2*log(2*pi)-log(n)*p/2-log(det(V))/2

print(Margianllikelihood)