Empirical selection of referent variables: Comparing multiple-indicator multiple-cause-interaction modeling and moderated nonlinear factor analysis.

The fulfillment of measurement invariance/equivalence is considered a prerequisite for meaningfully proceeding with substantive cross-group comparisons. In the multiple-group confirmatory factor analysis approach, one model identification issue has unfortunately received little attention: the specification of a referent variable in the test of measurement invariance. A multiple-indicator multiple-cause (MIMIC) model with moderated effects (i.e., MIMIC-interaction modeling; Woods & Grimm, 2011) and a moderated nonlinear factor analysis (MNLFA; Bauer, 2017) model for detecting uniform and nonuniform measurement inequivalences in tandem were proposed to identify credible referent variables. The performance of two search strategies, constrained and free baseline models, and MIMIC-interaction and MNLFA methodologies were evaluated in a Monte Carlo simulation. Effects of different configurations of the number of inequivalent variables, type and magnitude of inequivalence, magnitude of group differences in factor means and variances, and sample size in combination with each search strategy were determined. Results showed that the constrained baseline model strategy generally outperformed the free baseline model strategy for identifying credible referent variables, functioning well when up to one-third of the observed variables were noninvariant. Moreover, MNLFA performed better than MIMIC-interaction modeling for the selection of referent variables across nearly all conditions investigated in the study. The superiority of MNLFA over MIMIC-interaction modeling was specifically evident in the models with relatively small samples, large between-group latent variance differences, or a combination of both. An empirical example was presented to demonstrate the applicability of MNLFA with the constrained baseline model strategy for referent variable selection. (PsycInfo Database Record (c) 2025 APA, all rights reserved).