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Hello! 1. I am running CFAs on a scale measured with three subtests. These subtests have 24 items each, thus I have 72 indicators. These itemlevel indicators are binary: the respondent was either correct or incorrect. According to the MPlus user’s guide and material I’ve found online, WLSMV is the preferred estimation method. These are my questions: a. Some people say MLE is possible. I have tried it, and it appears I have too many indicators. Is there a way to run MLE on binary data? The reason I would want to use MLE is I would like to be able to see AIC and BIC model fit statistics. Thus I would be able to compare models. b. Am I correct in that WLSMV does not produce AIC and BIC? Are there equivalent statistics that it does produce? c. Am I correct in that with WLSMV can only compare models using the DIFFTEST function, and that can only be used for nested models? Unnested models cannot be compared with WLSMV? d. Does anyone have recommendations of how to work with these models, such as alternative fit indices? 2. I will be attempting CFAs on a model which includes both binary and continuous itemlevel indicators. I will have 109 indicators. Would I have the same issues as above? Are there workarounds? Thank you very much for your help! 


First, see our FAQ: Estimator choices with categorical outcomes 1a ML is quite possible with many binary items as long as you don't have a lot of factors. Each factor implies one dimension of numerical integration so computations get slower and less precise with increasing number of dimensions. 1b Right. Chisquare/CFI fit is given. 1c Right. AIC and BIC draws on ML so are not available for WLSMV. 1d. For nonnested models you can compare say CFI values. 2. If ML can't do it, Bayes can; see FAQ 

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