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

J Sch Psychol. 2017 Feb;60:65-82. doi: 10.1016/j.jsp.2016.11.002. Epub 2017 Jan 3.


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 ( Data needed to reproduce analyses in this article are available as supplemental materials (online only) in the Appendix of this article.

Keywords: Bias; Categorical; Diversity; Equivalence; Factor analysis; Invariance; Measurement; SABRS; School psychology.

MeSH terms

  • Adolescent
  • Adolescent Behavior*
  • Child
  • Child Behavior*
  • Factor Analysis, Statistical*
  • Humans
  • Psychology, Educational / methods*
  • Psychometrics / methods*
  • Social Behavior*