Nested model comparisons between common factors and composites

Area of Science:

• Psychological Measurement
• Structural Equation Modeling
• Psychometrics

Background:

• Reflective Confirmatory Factor Analysis (CFA) is the dominant measurement model in psychological research.
• Formative measurement models are increasingly recognized as theoretically appropriate for certain psychological data.
• Existing structural equation modeling (SEM) frameworks lack direct specification for formative composites.

Purpose of the Study:

• To demonstrate the theoretical and empirical nesting structure of reflective CFA, formative Henseler-Ogasawara confirmatory composite analysis, and formative pseudo-indicator models within SEM.
• To evaluate the utility of nested model comparison techniques, specifically the chi-square difference test and RMSEA (RMSEA_D), for distinguishing between reflective and formative measurement models.
• To provide practical guidance and empirical examples for researchers on selecting and comparing measurement models.

Main Methods:

• Specification of three nested measurement models within a structural equation modeling (SEM) framework: reflective CFA, formative Henseler-Ogasawara confirmatory composite analysis, and formative pseudo-indicator model.
• Theoretical and empirical demonstration of the hierarchical relationship between these models when the structural component is saturated.
• A simulation study to assess the performance of chi-square difference tests and RMSEA_D in discriminating between reflective and formative models under varying conditions (sample size, indicator weights, external correlations).

Main Results:

• The reflective CFA, formative Henseler-Ogasawara confirmatory composite analysis, and formative pseudo-indicator models are demonstrated to be nested within each other under saturated structural conditions.
• Chi-square difference tests and RMSEA_D show potential for reliably distinguishing between reflective and formative measurement models, though performance varies with sample size, indicator weights, and construct correlations.
• Empirical examples illustrate the application of nested model comparison tools for practical differentiation between reflective and formative measurement approaches.

Conclusions:

• Reflective and formative measurement models can be formally compared within a unified SEM framework using nested model comparison techniques.
• Researchers can leverage statistical tests like the chi-square difference test to empirically validate the choice between reflective and formative measurement models.
• The findings support the broader adoption and rigorous evaluation of formative measurement models in psychological research where theoretically justified.