I was testing several factor models using CFA and used WLSMV estimator for categorical indicators. I have established a model that provided the best description for the data.
Now I am trying to test this model in terms of Measurement Invariance (across gender). I have some example output for Mplus where I can test configural, metric, and scalar models. However, I am not sure if I should (or NOT) include WLSMV estimator while testing for MI or not... Please help.
Witold, for categorical data WLSMV would be an option. Previous research
suggests that WLSMV commonly performs better than ML with fewer than five response categories:
Rhemtulla, M., Brosseau-Liard, P. & Savalei, V. (2012). When can categorical variables be treated as continuous? A comparison of robust continuous and categorical SEM estimation methods in non-ideal conditions. Psychological Methods, 17, 354-373.
There is in article in the journal Structural Equation Modeling in which measurement invariance was tested using MLR and WLSMV:
Sass, D.A., Schmitt, T.A., & Marsh, H.W. (2014) Evaluating Model Fit With Ordered Categorical Data Within a Measurement Invariance Framework: A Comparison of Estimators. Structural Equation Modeling, 21 (2), 167-180. DOI: 10.1080/10705511.2014.882658
Kind regards,
Karin
Witold, for categorical data WLSMV would be an option. Previous research
suggests that WLSMV commonly performs better than ML with fewer than five response categories:
Rhemtulla, M., Brosseau-Liard, P. & Savalei, V. (2012). When can categorical variables be treated as continuous? A comparison of robust continuous and categorical SEM estimation methods in non-ideal conditions. Psychological Methods, 17, 354-373.
There is in article in the journal Structural Equation Modeling in which measurement invariance was tested using MLR and WLSMV:
Sass, D.A., Schmitt, T.A., & Marsh, H.W. (2014) Evaluating Model Fit With Ordered Categorical Data Within a Measurement Invariance Framework: A Comparison of Estimators. Structural Equation Modeling, 21 (2), 167-180. DOI: 10.1080/10705511.2014.882658
Kind regards,
Karin
Since your measurement model was chosen using WLSMV, measurement invariance should be tested using the same estimation method. I can't find a reason why not. On the contrary, if another method (ML/MLR) is used instead, the fit indices, e.g. for for configural invariance, probably won't be within acceptable limits.
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