Statistics

Factor analysis

Epistemology

Econometrics

Psychology

Philosophy

Measurement invariance

Structural equation modeling

Latent variable

Mathematics

Confirmatory factor analysis

Categorical variable

Property (philosophy)

Computer science

Discrete mathematics

Equivalence (formal languages)

Structural Equation Modeling A Multidisciplinary Journal

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.

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

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