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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,])
- }
-}