# Calibration and Individual Differences
# provide r[i,j], the probability estimate of ith person on jth question
# monitor delta[i] (calibration) and sigma[i] (expertise) for ith person
# and p[j] inferred grounds truth for jth question

model{
  for (i in 1:ns){
    delta[i] ~ dbeta(5,1)
    lambda[i] <- pow(sigma[i],-2)
    sigma[i] ~ dunif(0,1)
    for (j in 1:nq){
      psi[i,j] <- psitmp[j]*delta[i]
      r[i,j] ~ dnorm(exp(psi[i,j])/(1+exp(psi[i,j])),lambda[i])
    }
  }
  for (j in 1:nq){
    p[j] ~ dbeta(1,1)
    psitmp[j] <- log(p[j]/(1-p[j]))
  }
}