49 lines
1.4 KiB
Plaintext
49 lines
1.4 KiB
Plaintext
# 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,])
|
|
}
|
|
}
|