

HMM with continuous indicators 

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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 classspecific 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 so much! Jim 


1) Normality is assumed within class, but not in the observed (i.e. mixed) distribution. Same for a and b. 2) Yes, repeated over the time points. 3) I think of all of them as means within classes. They can also be seen as intercepts given that they are all DVs regressed on latent class variables. Coding is not impacted. 4) No. Yes. 5) Use BIC to settle the number of classes in an LCA (LPA) for each time point. 


Thanks! And what does one do if the number of classes decided by BIC or LoMendellRubin Adjusted LRT vary across time points for the same measure (e.g., 3 classes for time 1, 4 classes for time 2)? 


If the difference in number of classes makes sense substantively, I would allow that. There is no problem in doing Markov analysis (LTA) with different number of classes at different time points. 


Thanks again! Followup 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 firstorder 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. Thanks, Jim 


Yes, you should free the intercepts as well. The contributions to the transition matrix are shown in the figure at the top of page 447 of the Version 6 UG. Here, a's are the intercepts and b's are the slopes. 


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#1c4#1] (1); [c2#2c4#2] (2); I think that is correct, but I just wanted to make sure. Thanks, Jim 


Yes. They are intercepts for c, not thresholds. 

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