How does your umx handle categorical data? Does it handle ordinal and unordered categories in the same way and what estimator is it using?
umx implements a thresholded latent variable approach to handle ordinal data. This uses a standard latent variable estimating the parameter via FIML, and a thresholds matrix, allowing umx to map scores on this latent variable onto the ordinal variable levels, and move (estimate) the thresholds around (keeping them in order) to a most likely locations.
While a binary ordinal variable can be regarded as categorical, there are some important differences. If we were to run analyses by race, or country of birth, then there isn't an obvious ordering to the different categories. In this case, it may be better to treat the different categories as different groups in a multiple group model. That way it becomes possible to test for heterogeneity of every one of the model parameters across the groups.
So I think the OP may have been asking a different question, although since you are one and the same perhaps not...
I put the question up based on a user query direct from email.
Good point about building the right model
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