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# lsat.jags example from classic-bugs examples in JAGS
# See http://sourceforge.net/projects/mcmc-jags/files/Examples/2.x/
var
response[R,T], m[R], culm[R], alpha[T], a[T], theta[N], r[N,T],
p[N,T], beta, theta.new, p.theta[T], p.item[R,T], P.theta[R];
data {
for (j in 1:culm[1]) {
r[j, ] <- response[1, ];
}
for (i in 2:R) {
for (j in (culm[i - 1] + 1):culm[i]) {
r[j, ] <- response[i, ];
}
}
}
model {
# 2-parameter Rasch model
for (j in 1:N) {
for (k in 1:T) {
probit(p[j,k]) <- delta[k]*theta[j] - eta[k];
r[j,k] ~ dbern(p[j,k]);
}
theta[j] ~ dnorm(0,1);
}
# Priors
for (k in 1:T) {
eta[k] ~ dnorm(0,0.0001);
e[k] <- eta[k] - mean(eta[]); # sum-to-zero constraint
delta[k] ~ dnorm(0,1) T(0,); # constrain variance to 1, slope +ve
d[k] <- delta[k]/pow(prod(delta), 1/T); # PRODUCT_k (d_k) = 1
g[k] <- e[k]/d[k]; # equivalent to B&A's threshold parameters
}
# Compute probability of response pattern i, for later use in computing G^2
theta.new ~ dnorm(0,1); # ability parameter for random student
for(k in 1:T) {
probit(p.theta[k]) <- delta[k]*theta.new - eta[k];
for(i in 1:R) {
p.item[i,k] <- p.theta[k]^response[i,k] * (1-p.theta[k])^(1-response[i,k]);
}
}
for(i in 1:R) {
P.theta[i] <- prod(p.item[i,])
}
}
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