I am very new to CFA and to Mplus. I will be modeling 4 latent factors with 29 categorical (5 point Likert scale items) indicators. I am using polychorics with the WLSMV estimator. I have been reading extensively about the impact of extreme non-normality on polychorics (to my understanding they are not immune to extreme skewness). While I don't expect that level of skewness to be a problem in my data, I would neverthless like to know exactly how skewed my latent factors are (if the distribution of each item appears potentially problematic to being with). Even though the literature seems to indicate that the assumption of normality of the latent factors is generally one of convenience, there also appears to be a way to test this assumption with a Chi-square.
Questions: 1) Is it the case that it is possible to test the distribution of the latent factor(s)? 2) How is this done?
Skewness is a concept related to continuous variables. Ordered categorical variables can have floor or ceiling effects when observations pile up in a lower or upper category. Categorical data methodology takes this into account. The only issue is if you get zero cells in the bivariate tables. Even with floor and ceiling effects of the factor indicators, factors may be normal. See the following paper on the website for further information:
Flora, D.B. & Curran P.J. (2004). An empirical evaluation of alternative methods of estimation for confirmatory factor analysis with ordinal data. Psychological Methods, 9, 466-491.