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Hello, I am running a 4factor CFA using both binary and continuous indicators (ML estimation). Three of the latent factors have continuous indicators while one latent factor has a set of binary indicators. I am interested in the overall fit of the model. The output, however, only gives relative fit indices (the H0 value for 2loglikelihood model comparisons, AIC, BIC) and a chisquare test that appears to be valid for only the categorical portion of the model ("ChiSquare Test of Model Fit for the Binary and Categorical Outcomes"). I am concerned that, although this model may fit better than an alternative (nested) model (e.g., a 3 factor model), the overall fit to the data may be lousy. Is there a means of obtaining an index of absolute fit (e.g., TLI, CFI, RMSEA, Chisquare) for the overall model using both continuous and categorical predictors? If not, how do you suggest I evaluate overall model fit in this case? 


If you want overall fit measures, you can use the default estimator WLSMV for categorical outcomes for CFA. It sounds like you are using maximum likelihood. 

Frank Martin posted on Tuesday, September 02, 2008  10:40 am



To followup on this question. Is it permissible to have a latent factor with two continuous indicators and one categorical (binary) indicator? Are there any major issues or concerns? I will use a WLS estimator. For the structural model, the latent will be an endogenous variable. Several exogenous variables will be included that are continuous or categorical. Thanks. 


Yes, a factor can have a combination of categorical and continuous indicators. This is not problematic. I would use WLSMV. 

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