12.6 Generate data according to the logit–logit latent trait model of Bartholomew(1987). There are 100 subjects and P = 5 binary items and Q = 1 factor. The generating program is model{ for (h in 1:100) {for (j in 1:5){x[h,j]∼ dbern (p[h,j])

logit(p[h,j])<− kappa[j] + lambda[j]*F[h]|

F[h]<−logit(y[h]); y[h]∼ dunif(0, 1)||

with parameter values list(kappa = c(−1,−1, 0, 1, 1), lambda = c(2, 2, 1, 0.5, 0.5)).

Using only the X[100, 5] binary values so generated, re-estimate the κ and λ parameters.

This may involve constrained priors on λ to ensure that the direction of F is identified.