The Trade-Off Between Factor Score Determinacy and the Preservation of Inter-Factor Correlations

Area of Science:

• Psychometrics
• Statistical modeling

Background:

• Regression factor score predictors offer maximum factor score determinacy.
• These predictors, however, do not preserve the inter-correlations of the original factors.
• Correlation-preserving factor score predictors have been developed to address this limitation.

Purpose of the Study:

• To investigate the trade-off between factor score determinacy and the bias of inter-correlations.
• To determine the conditions under which this trade-off occurs.
• To propose an alternative to default regression factor score predictors.

Main Methods:

• Algebraic considerations were used to analyze the relationship between factor score determinacy and inter-correlation bias.
• A simulation study was conducted to empirically investigate the trade-off.
• The study compared regression factor score predictors with correlation-preserving factor score predictors.

Main Results:

• A trade-off exists: higher factor score determinacy is associated with greater bias in inter-correlations, and vice versa.
• Under certain conditions, small gains in factor score determinacy with regression predictors lead to significant bias in inter-correlations.
• Correlation-preserving predictors can avoid substantial inter-correlation bias without a significant loss of factor score determinacy.

Conclusions:

• The default use of regression factor score predictors may lead to biased inter-correlations.
• Researchers should consider using correlation-preserving factor score predictors to mitigate inter-correlation bias.
• Evaluating the balance between factor score determinacy and inter-correlation accuracy is recommended for robust factor analysis.