fit a multivariate latent trait model

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Derek's picture
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Joined: 02/11/2011

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!!

Ryne's picture
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Joined: 07/31/2009
Hi Derek, Sorry this took so

Hi Derek,

Sorry this took so long to get to.

I'm not up to date on my IRT, but this looks like a multivariate/ordinal variation on a 3PL. This should be possible in OpenMx through FIML, though I don't immediately see a clear way to specify r_gk. Peudo-guessing parameters are notoriously hard to estimate. OpenMx should be able to handle any model in which you can specify the likelihood function. If you or another of our IRT-savvy users can provide a better mapping from P(Y) to a likelihood function, optimization in OpenMx will be a little clearer.