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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.