On the Added Value of Multiple Factor Score Estimates in Essentially Unidimensional Models

Area of Science:

• Psychometrics
• Quantitative Psychology
• Statistical Modeling

Background:

• Many psychological measures, designed for a single trait, can be analyzed using either unidimensional or correlated factor analysis (FA) models.
• Choosing between these models is crucial for accurate interpretation of measurement data.
• Existing methods may not adequately differentiate between these solutions when data fits both.

Purpose of the Study:

• To propose a novel approach for deciding between unidimensional and correlated-factor analysis (FA) solutions for measures yielding compatible data for both.
• To extend existing 'added-value' procedures to the domain of factor analysis.
• To provide researchers with a practical method for selecting the most appropriate FA model.

Main Methods:

• An extension of 'added-value' procedures for factor score estimates.
• The core principle is that multiple FA solutions are superior if their factor score estimates better measure the primary factors than unidimensional or second-order solutions.
• The approach was implemented in exploratory factor analysis software and evaluated using simulation studies and a real-data example.

Main Results:

• The proposed method provides a clear criterion for evaluating the added value of a correlated-factors solution over a unidimensional or second-order solution.
• New methodological insights were gained regarding factor indeterminacy and second-order FA.
• The simulation study demonstrated the proposed procedure's effectiveness, and a personality domain example illustrated its practical utility.

Conclusions:

• The developed FA approach offers a robust framework for distinguishing between unidimensional and correlated-factor solutions.
• This method enhances the interpretability and usefulness of factor analysis results, particularly for measures initially designed as single-trait.
• The practical implementation and validation suggest this approach can improve measurement model selection in various research fields.