Measurement equivalence: A non-technical primer on categorical multi-group confirmatory factor analysis in school psychology

Evidence-based interventions (EBIs) have become a central component of school psychology research and practice, but EBIs are dependent upon the availability and use of evidence-based assessments (EBAs) with diverse student populations. Multi-group confirmatory factor analysis (MG-CFA) is an analytical tool that can be used to examine the validity and measurement equivalence/invariance of scores across diverse groups. The objective of this article is to provide a conceptual and procedural overview of categorical MG-CFA, as well as an illustrated example based on data from the Social and Academic Behavior Risk Screener (SABRS) - a tool designed for use in school-based interventions. This article serves as a non-technical primer on the topic of MG-CFA with ordinal (rating scale) data and does so through the framework of examining equivalence of measures used for EBIs within multi-tiered models - an understudied topic. To go along with the illustrated example, we have provided supplementary files that include sample data, Mplus input code, and an annotated guide for understanding the input code (http://dx.doi.org/10.1016/j.jsp.2016.11.002). Data needed to reproduce analyses in this article are available as supplemental materials (online only) in the Appendix of this article.