A 1 factor model for continuous outcomes (linear model) using Type = General or else using EFA 1 1 yields as expected the exact same likelihood. BUT, surprisingly, when the obsered variables are treated as categorical (dichotomous), I find that Mplus gives two different Maximum Likilihood values across the two.
The code for comparison is below. If I drop the categorical are commands, they yield the identical likelihood values, but with the categorical are they are different. Why? shouldn't they be the same since it is the same model? Maybe EFA is not using the logit link?
***CFA version****; categorical are alcdep1-alcdep7 alcab1 alcab2 alcab4; analysis: estimator = ml; model: f by alcdep1* alcdep2 -alcdep7 alcab1 alcab2 alcab4; f@1;
***EFA version***; categorical are alcdep1-alcdep7 alcab1 alcab2 alcab4 ; analysis: type = efa 1 1; estimator = ml;