Identification of Factor Scores by Regression with External Variables in Exploratory Factor Analysis

Area of Science:

• Statistics
• Psychometrics
• Data Analysis

Background:

• Factor analysis (FA) models are characterized by factor score indeterminacy.
• Existing methods struggle with unique determination of factor scores and parameter estimation.

Purpose of the Study:

• Introduce Regression-based Factor Exploration (RFE) for unique factor score determination.
• Develop Clustering-based Factor Exploration (CFE) as a variant of RFE for improved clustering.
• Evaluate the performance and efficiency of the proposed methods.

Main Methods:

• RFE minimizes a loss function balancing FA and multivariate regression using a tuning parameter.
• CFE generalizes RFE's penalty term for factor score clustering.
• Simulation studies and real data examples are used for evaluation.

Main Results:

• RFE uniquely determines factor scores and estimates FA parameters simultaneously.
• CFE demonstrates superior accuracy in creating cluster structures compared to existing methods.
• Proposed methods accurately recover parameter matrices from error-contaminated data with lower computational cost.

Conclusions:

• RFE and CFE offer novel solutions to factor score indeterminacy in FA.
• The methods provide interpretable results and are relevant to existing factor score estimation techniques.
• These procedures enhance accuracy and computational efficiency in factor analysis.