Hello, I need to fit a multivariate latent trait model with categorical outcomes as follows. I tried many standard sofware but none of them worked well. I am not sure if OpenMx can do it or not.

Prob (Y_gki <= c_l | Z_gi, U_gi)

= r_gk + (1 - r_gk)/(1 + exp(-(alpha_kl + beta_k*Z_gi + delta_k*U_gi)))

where

g = 1,2 indicating groups,

k = 1,..., K indicating K instrument items,

i indicating the subject number in each group,

so Y_gki is the response for item k from subject i in group g;

each item has a Likert scale with responses 0-5

Z_gi = (Z1_gi, Z2_gi) is 2 dimentional latent variable and assumed to follow bi-variate normal distribution

It's known that Z1 relates to first 3 instrument items and Z2 relates to the other 4 items. So beta_k can be determined.

U_gi is observed covariate.

The parameter of interest is r_gk and its MLE is needed. r_gk seeems to be a kind of guessing parameter.

Thanks a lot!!