Multiple-Group Invariance with Categorical Outcomes Using Updated Guidelines: An Illustration Using M plus and the lavaan/semTools Packages

Meaningful comparisons of means or relationships between latent constructs across groups require evidence that measurement is equivalent across the studied groups– a property known as measurement equivalence or invariance (ME/I). Methods typically involve an evaluation of increasingly stringent models via confirmatory factor analysis, a typical assumption of which is continuous observed variables. When that assumption is not met – as is often the case in many surveys – alternative methods that directly model the categorical nature of the data exist. Although well established, categorical ME/I models pose a number of complexities and various recommendations for their evaluation. To that end, we describe the current state of categorical ME/I and demonstrate an up-to-date method for model identification and invariance testing. In the tutorial, we exemplify a common approach to establishing ME/I via multiple-group confirmatory factor analysis using Mplus and the lavaan and semTools packages in R.