ON EXTENSION ANALYSIS AND ITS RELATION TO CORRELATIONS BETWEEN VARIABLES AND FACTOR SCORES

Area of Science:

• Psychometrics
• Statistical Analysis
• Multivariate Statistics

Background:

• Factor analysis is a common statistical technique used to identify underlying latent variables from observed variables.
• Understanding the relationship between core and extension variables is crucial for comprehensive data interpretation.
• Existing methods may not fully capture the correlations between excluded variables and derived factor scores.

Purpose of the Study:

• To develop matrix algebra algorithms for calculating correlations between extension variables and direct method factor scores.
• To provide equations for extension analysis applicable to oblique factors and specific rotation methods.
• To enhance the interpretability of factor analysis by including excluded variables.

Main Methods:

• Development of matrix algebra algorithms tailored for factor score correlation.
• Formulation of specific equations for extension analysis.
• Application to scenarios involving oblique factors and primary factor or reference vector rotation methods.

Main Results:

• Successful derivation of algorithms and equations for correlating extension variables with factor scores.
• Demonstration of applicability to oblique factor solutions.
• Validation of methods for primary factor and reference vector rotation techniques.

Conclusions:

• The developed algorithms offer a robust method for assessing the relationship between excluded and included variables in factor analysis.
• These findings extend the utility of factor analysis by providing a quantitative link to extension variables.
• The approach facilitates a more complete understanding of the factor structure and its implications.