Hypothesis Testing Using Factor Score Regression: A Comparison of Four Methods.

Area of Science:

• Statistics
• Psychometrics
• Quantitative Psychology

Background:

• Factor score regression (FSR) is crucial for analyzing latent variables.
• Existing FSR methods have limitations in accuracy and bias.
• Structural equation modeling (SEM) is a common but complex approach.

Purpose of the Study:

• To compare four FSR methods: regression, Bartlett, Skrondal & Laake, and Croon's bias-correcting method.
• To evaluate the performance of these methods against SEM.
• To introduce an extended bias-correcting method with reliable standard errors.

Main Methods:

• Analytic calculations and two Monte Carlo simulation studies were employed.
• Finite sample characteristics of each method were examined.
• Performance criteria included bias, efficiency, mean square error, standard error bias, Type I error rate, and power.

Main Results:

• The bias-correcting method with the new standard error is a suitable alternative to SEM.
• This method shows comparable bias, efficiency, MSE, power, and Type I error rate to SEM.
• It exhibits slightly higher standard error bias than SEM.

Conclusions:

• The extended bias-correcting FSR method offers a practical and accurate alternative to SEM.
• Researchers can confidently use this method for factor score analysis.
• The findings provide valuable insights for statistical modeling and psychometric research.