Empirical selection of referent variables: Comparing multiple-indicator multiple-cause-interaction modeling and...

Area of Science:

• Psychometrics
• Statistical Modeling
• Cross-Cultural Psychology

Background:

• Measurement invariance is essential for valid cross-group comparisons in statistical analyses.
• Selecting an appropriate referent variable in multiple-group confirmatory factor analysis (CFA) is a critical yet often overlooked identification issue.

Purpose of the Study:

• To evaluate methods for identifying credible referent variables in measurement invariance testing.
• To compare the performance of constrained versus free baseline models and MIMIC-interaction versus MNLFA methodologies.

Main Methods:

• A Monte Carlo simulation was employed to assess the performance of different strategies and models.
• Evaluated factors included the number and type of noninvariant variables, group differences in latent means/variances, and sample size.
• Compared constrained and free baseline models, and MIMIC-interaction and MNLFA for referent variable selection.

Main Results:

• The constrained baseline model strategy generally outperformed the free baseline model strategy for identifying referent variables.
• Moderated Nonlinear Factor Analysis (MNLFA) demonstrated superior performance over MIMIC-interaction modeling in referent variable selection across most conditions.
• MNLFA's superiority was particularly pronounced with small sample sizes or large between-group latent variance differences.

Conclusions:

• The constrained baseline model strategy is recommended for referent variable selection, especially when a proportion of variables may be noninvariant.
• MNLFA is a more robust method than MIMIC-interaction modeling for selecting referent variables, particularly in challenging conditions.
• The study provides practical guidance for researchers on selecting referent variables to ensure accurate cross-group comparisons.