Two-part modeling: combination of LCA and LPA

[Yingyi Lin]

Hi Statalists,

I was trying to do a two-part modeling for my dataset, in which observed vars are zero-inflated. I followed the steps in this publication: Kim (2009) Two-Part Factor Mixture Modeling: Application to an Aggressive Behavior Measurement Instrument. Basically, here's what I did:

1) Step 1: based on my raw data, I created dichotomous vars: v1_d, v2_d, v3_d; and then I created continuous vars, wherein 0s are treated missing, so I have v1_c, v2_c, v3_c

2) Step 2: EFA and LCA for dichotomous data

3) Step 3: EFA and LPA for continuous data

4) Step 4: EFA for the combination of dichotomous and continuous data identified the best two-part model with 2 factors from dichotomous data, and 1 factor from continuous data, and here is my codes:

gsem ( F1 -> v1_d v2_d v3_d, logit) ( F2 ->  v4_d v5_d v6_d, logit) ( F3 -> v1_c v2_c v3_c v4_c v5_c v6_c) ///
, nocapslatent nonrtolerance  latent(F1 F2 F3) cov(F1*F2 F1*F3 F3*F2) difficult

5) Step 5: as suggested in the publication, "the latent classes can be added to the two-part model (i.e. the model I identified in step 4) and correlated if necessary". However, I am not quite sure how to do that in Stata codes. Is it possible to identify separate classes from different factors in the SAME model? If so, how should I write the Stata codes? Any though/comments would be much appreciated!

Thank-you in advance,
Yingyi

[Weiwen Ng]

I haven't read the article deeply and I'm not familiar with their notation, but I believe the authors you cited were basically proposing a zero-inflated factor mixture model. That is, there's one class that are structural zeroes (as you might see in zero-inflated count models), and then the second class follows some other sort of response process. For example, zero inflated IRT models are now a thing; the structural zero class can be thought of as non-pathological (i.e. if it's a model for depression, the structural zero class aren't at risk for depression at all). They were proposing a more general factor model.

Unfortunately, Stata does not currently support models with both continuous and categorical latent variables. Your F variables are continuous. Your latent classes would be categorical. Ergo, you can't fit the desired model in Stata 15. I believe they're looking at adding support for this type of model in Stata 16.

That is a bit of a pity, because in Stata 15, gsem can handle zero-inflation through the family(pointmass 0) option.

[Yingyi Lin]

Thank-you for the info Weiwen, I guess I would just go for Mplus then, and that's the software they used in the paper!

Yingyi