I want to analyze a multilevel multidimensional model in WinBUGS. the model is as below (N=2362 students responding to K=45 items of a test, students are nested within J=116 schools):
- model{
- #responses
- for(i in 1:N){
- for(j in 1:K){
- logit(p[i,j])<- a1[j]*t[i,1]+a2[j]*t[i,2]-b[j]
- y[i,j]~dbern(p[i,j] }#for j
- t[i,1:2]~dmnorm(mu[sc,1:2],tau.p[1:2,1:2])
- }#for i
- #school level
- for(j in 1:J){
- mu[j,1:2]~dmnorm(m[j,1:2],tau.s[1:2,1:2])
- }#for j of school
- #priors
- for(j in 1:J){
- m[j,1:2]~dmnorm(m0[1:2],cov[1:2,1:2])
- #m0=c(0,0) #cov=diag(2)
- }
- tau.p[1:2,1:2]~dwish(cov[1:2,1:2],2)
- tau.s[1:2,1:2]~dwish(cov[1:2,1:2],2)
- sigma.p[1:2,1:2]<-inverse(tau.p[,])
- sigma.s[1:2,1:2]<-inverse(tau.s[,])
- s2p<-sum(sigma.p[,])
- s2s<-sum(sigma.s[,])
- rho<-(s2s)/(s2s+s2p)
- a1[1]~dlnorm(0,4)
- a2[1]<-0
- b[1]~dnorm(0,1)
- for(s in 2:K) {
- a1~dlnorm(0,4)
- a2~dlnorm(0,4)
- b~dnorm(0,1)
- }#for s of items
- }#for model
Also see next post


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