Testing for nonuniform differential item functioning with multiple indicator multiple cause models
It has been found that previous studies, the MIMIC modeling approach can do a good job detecting uniform DIF in both the polytomous and dichotomous data. However, it was found that the MIMIC model could not successfully detect nonuniform DIF since they are not designed to do so.
In this research, a latent variable interaction is added to the MIMIC model (named as MIMIC-interaction models) to test for nonuniform DIF.
Question:
1. The biggest problem in this research is that there is no good solution for the interatction between continuous latent variables. The study used Mplus XWITH (ie, the latent moderated structural equations method, LMS) which assumed that the latent variables involved in the interaction are both normal. The assumption was obviously violated since in MIMIC-interaction model, the membership variable is categorical variable. Therefore, according to the result of previous study, the inflated Type-I error was expected in this study (though using the BH corrected could decrease Type-I error to near the normal rate).
Future study:
1. Using other method instead of LMS to estimate MIMIC-interaction DIF model. Some methods below may workable for the model:
(1) SEM program with product indicator methods, for example,
(2) Treated MIMIC-interaction model as an nonlinear mixed model, which can be estimated with SAS PROC NLMIXED.
2. Implement purification approach to the MIMIC-interaction.