I would like to extend ex 8.12 for continuous DVs:
1) Is there a normality assumption for the observed continuous DVs if I use a) MLR, b) the Bayesian estimator?
2) You suggested elsewhere to reference item means instead of thresholds in class-specific model statements for continuous DVs. To be specific, for indicator u1 and latent variable c1 (3 classes), would the code be: %c1#1% [u1] (3); %c1#2% [u1] (4); %c1#3% [u1] (5);
3) Would the first latent variable in the markov chain have a mean to reference whereas subsequent variables in the chain would have an intercept (b/c they're predicted)? Would I still refer to all of the means/intercepts in the same way (as above) when coding the measurement model?
4) Would it be problematic for the 1st order AR paths to vary across time intervals (c1 -> c2 =/ c2 -> c3); the gap btwn my 1st and 2nd assessment was 4 months, whereas the gap btwn my 2nd and 3rd assessment was 9 months. Would this mean I will have 2 transition matrices (w/3 time periods)?
5) How do you recommend determining the "correct" number of classes for the latent categorical variable(s)? Do you estimate the HMM with different numbers of classes and compare model fits, test LPAs with different # of classes at each time point, or something else?
Thanks again! Follow-up on a previous question: you mentioned earlier it was OK for AR paths to vary across time points in the HMM (e.g., if time points are measured across different intervals). I was wondering, if I were to free the AR paths, should I also free the latent category intercepts?
In the manual, it states "the transition matrices are held equal over time. This is done by placing (1) after the bracket statement for the intercepts of c2, c3, c4, and by placing (2) after each of the ON statements that represent the first-order Markov relationships."
Could you expand on this a little (i.e., the differential contributions of the intercepts and the AR paths on the transition matrices)? What does it mean to the transition matrices to free the paths but not the intercepts, free the paths and the intercepts, or free the intercepts but not the paths.
Thank you, that makes sense. And if I wanted to model example 8.12 but with a 3 category latent class measurement model (as opposed to a 2 category latent class), I would set the latent class thresholds as:
%OVERALL% [c2#1-c4#1] (1); [c2#2-c4#2] (2);
I think that is correct, but I just wanted to make sure.