I am testing a longitudinal cross-lagged model with both ordinal (with four categories) and continuous variables. My sample size is very big (N > 10,000) and my variables are not normally distributed. Is it ok to use maximum likelihood estimation for such a model?
The answer to that seemingly simple question has many layers of complexity. First, what do you mean by ML when you have ordinal and continuous variables? Do you mean treating all variables as continuous? Or do you mean specifying the ordinal ones as categorical? The latter can also be done using ML. Second, in the latter ML analysis the mediating ordinal variables (say time 2 vbles) are treated as continuous when they are used as predictors. WLSMV and Bayes can instead use their continuous latent response variables which might be a better alternative. See also our FAQ:
No because you need more information for the weight matrix of WLS to get SEs and chi-square. With only a correlation matrix, you can pretend the variables are continuous and use ULS without SEs and chi-2.