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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,])
+ }
+}