Testing for Factorial Invariance in the Context of Construct Validation

This article describes the logic and procedures behind testing for factorial invariance across groups in the context of construct validation. The procedures include testing for configural, measurement, and structural invariance in the framework of multiple-group confirmatory factor analysis (CFA). The forward (sequential constraint imposition) approach to testing for factorial invariance is described and illustrated for the cases of first-order and second-order CFA models; computer codes in Mplus are provided. Computations of the Satorra-Bentler scaled chi-square difference, used in testing for factorial invariance under lack of multivariate normality, are also described. Some points of caution related to testing and interpreting measurement invariance are provided as well.