ML vs WLSMV: which is better for categorical data and why? I was wondering which is a better estimator to use for categorical data: ML or WLSMV. I saw on a discussion on the Mplus website that they recommend WLSMV for categorical data but didn't explain why. Does anyone know specifically why ML doesn't work as well?
Preferably, I am looking for a reference that compares these two estimation approaches, but have not been able to locate one after hours of searching.
Thank you for sharing your knowledge and experience!
 A: In one medical research paper, Proitsi et al. (2009) write:

"The WLSMV is a robust estimator which does not assume normally
  distributed variables and provides the best option for modelling
  categorical or ordered data (Brown, 2006)".

For your convenience, I'm including the cited reference in the reference list below (I use APA format):
Brown, T. (2006). Confirmatory factor analysis for applied research. New York: Guildford.
Proitsi, P., Hamilton, G., Tsolaki, M., Lupton, M., Daniilidou, M., Hollingworth, P., ..., Powell, J. F. (2009, in press). A multiple indicators multiple causes (MIMIC) model of behavioural and psychological symptoms in dementia (BPSD). Neurobiology Aging. doi:10.1016/j.neurobiolaging.2009.03.005
I hope this is helpful and answers your question.
A: The most obvious reason for choosing one over the other would be the kind of fit indices you need. The WLSMV will give you CFI, TLI and RMSEA, which will help you evaluate the fit of a given model. If you need to compare non-nested models, you would need AIC and/or BIC, which aren't available with WLSMV and categorical data. The opposite is true of ML (again, only when dealing with categorical data). 
I'm not sure why they recommend WLSMV on the Mplus website, but if you are comparing nested models, the WLSMV is probably the most convenient as it will allow you to both (1) evalute whether the models provide adequate fit to the data (e.g. CFI > .90 and RMSEA < .5), and (2) use a chi2 difference test to see which models provides the best fit out of a number of competing models.
