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Hello, I am working with nonnormal data. I have run a LCGA two ways: (1) specifying the indicators as continuous, and (2) specifying the indicators as counts (negative binomial). I understand that the assumption of within class normality does not apply to LCGA, as the variance of the latent growth parameters are set to 0. However, I feel I am struggling to understand what changing the specification of the indicators has on the inner workings of the model. My main concerns are in regard to normality. Is it that in the continuous model  the LCGA is explaining the var/covar of a normal distribution, but in the count model  the LCGA is explaining the var/covar of a negative binomial distribution? Thanks for your help. 


Withinclass normality refers to the observed variables, not the latent ones. In the nonmixture case for continuousnormal outcomes, variances and covariances (and means) are sufficient statistics and are therefore the only quantities that the model needs to fit. In the nonmixture case for count outcomes, there are no such sufficient statistics so the model needs to be fitted to raw data. In the mixture case, there are never any such sufficient statistics but the model needs to be fitted to raw data. 


Thanks very much for the response. As an extension to your comment on withinclass normality, does this all apply to GMMs as well. Specifically, I was under the impression for GMMs that the assumptions of normality were related to the distribution of the random intercept, slope, etc. See Post 1 and 2: http://www.statmodel.com/discussion/messages/13/3364.html?1215532906 and this paper: Kreuter, F., Muthén, B., 2008. Analyzing criminal trajectory profiles: Bridging multilevel and groupbased approaches using growth mixture modeling, Journal of Quantitative Criminology. Thanks again for your guidance. 


Yes, GMMs also assume normality within class for the outcomes. It's true that this happens when both the growth factors and the residuals are normal within class  so there isn't much of a difference here. With numerical integration with respect to continuous latent variables such as growth factors, e.g. with categorical or count outcomes, the assumption of normal latent variables is explicitly made. Mplus also allows withinclass nonnormality that Mplus achieves for skewnormal and skewt. 


Thanks again. Last question (promise): If I understand correctly when the observed indicators are specified as counts (nb; negative binomial) in the GMM, the latent growth parameters are still explicitly assumed as normal. How does changing the specification of indicators from continuous to counts (nb) change the estimation of growth parameter variation? Is it just that growth parameters are now estimated with an appropriate link? Sorry if this is a broad question. Cheers. 


First question: yes. Last question: Yes. 

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