I am struggling with an appropriate estimator for both single and multi group CFA with data that has less than five response options (four).
I know that the recommended procedure is to treat these variables as order categorical and to use WLSMV as an estimator.
However, the fit goes way up (all models fit unrealistically good) if I use both WLSMV and a separate specification of variables as ordered and there are studies that show that conventional cut-off criteria do not apply so blindly to such a situation (Xia & Young, 2018). I see that simulation studies gauge the differences of MLR vs WMSLV for ordered categorical data but lavaan does not allow for MLR to be applied once the data are specified as ordered categorical.
Therefore, my question is, in short, what do you think about using WLSMV but still estimating intercepts (in measurement invariance)? Is the number of response scale options enough of a justification for using this estimator without saying variables are ordinal (specifying it in lavaan)?
My current strategy is to use both estimator and document the differences for single group analysis (as recommended by Sass, Schmitt, & Marsh, 2014).