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approximate measurement invariance, multilevel CFA, multilevel factor mixture modeling, Bayesian, alignment


With the increasing use of international survey data especially in cross-cultural and multi-national studies, establishing measurement invariance (MI) across a large number of groups in a study is essential. However, testing MI over many groups is methodologically challenging. We identified five methods for MI testing across many groups (multiple group confirmatory factor analysis, multilevel confirmatory factor analysis, multilevel factor mixture modeling, Bayesian approximate MI testing, and alignment optimization) and explicated the similarities and differences of these approaches in terms of their conceptual models and statistical procedures. A Monte Carlo study was conducted to investigate the efficacy of the five methods in detecting measurement noninvariance across many groups using various fit criteria. Generally, the five methods showed reasonable performance in identifying the level of invariance if an appropriate fit criterion was used (e.g., BIC with multilevel factor mixture modeling). Finally, general guidelines in selecting an appropriate method are provided.

Citation / Publisher Attribution

Kim, E. S., Cao, C., Wang, Y., & Nguyen, D. T. (in press). Measurement invariance testing with many groups: Empirical comparison of five approaches. Structural Equation Modeling.