Abstract

Researchers must establish measurement invariance (MI) before comparing latent constructs across groups to ensure construct validity. However, traditional multi-group confirmatory factor analysis (MG-CFA) may impose overly strict equality constraints in applied settings. Alternative MI frameworks are less familiar to researchers, which limits their use. This study compares MG-CFA, alignment optimization (AO), and Bayesian approximate measurement invariance (BAMI) using archival data from the Brigham Young University Counseling and Psychological Services Client Satisfaction Survey (N = 1,278). Participants completed an exit survey after receiving individual (n = 1,063), couple (n = 83), or group (n = 132) therapy, answering 16 five-point Likert items that measure four latent factors: clarity, client satisfaction, cultural competence, and application. MG-CFA supports configural, metric, scalar, and strict invariance across therapy types; scaled χ^2 difference tests are nonsignificant, and changes in robust CFI, robust RMSEA, and SRMR stay below recommended thresholds. Under scalar invariance, couple therapy participants report higher latent clarity than individual therapy participants (ΔM = 0.299, p = .007) and higher application than group therapy participants (ΔM = 0.437, p = .007). AO identifies a small proportion of noninvariant parameters and produces similar latent mean patterns. BAMI achieves stable convergence across three prior specifications, reducing cross-group parameter differences toward zero, and estimates probabilistic credible intervals for latent mean contrasts, also producing similar latent mean patterns. Therefore, all three frameworks yield essentially similar conclusions about latent means, although they conceptualize and diagnose invariance differently. Findings suggest that approximate methods provide flexible alternatives when minor noninvariance is present in unbalanced applied datasets.

Degree

PhD

College and Department

David O. McKay School of Education; Educational Inquiry, Measurement, and Evaluation

Rights

https://lib.byu.edu/about/copyright/

Date Submitted

2026-04-17

Document Type

Dissertation

Keywords

alignment optimization, Bayesian approximate measurement invariance, client satisfaction, measurement invariance, multi-group confirmatory factor analysis

Language

english

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