SOME NOTES ON THE NUMBER OF FACTORS PROBLEM

Area of Science:

• Psychometrics
• Statistical Modeling

Background:

• The interpretation of factors in factor analysis, including components, common factors, and image factors, is crucial for understanding statistical models.
• Determining the correct number of factors is a persistent challenge in factor analysis, impacting the validity of research findings.

Purpose of the Study:

• To discuss the epistemological status of factors and their implications for factor analysis.
• To evaluate the rationales behind decision rules for determining the number of factors.
• To compare the performance of eight established and one novel rule for factor determination.

Main Methods:

• Reanalysis of 17 correlation matrices from existing literature.
• Application of nine distinct rules for determining the number of factors.
• Comparative analysis of rules based on the implied factor analytic model.

Main Results:

• The study provides a comparative analysis of various factor determination rules.
• It highlights the implications of different factor analytic models on rule performance.
• Practical implications for selecting the appropriate number of factors are discussed.

Conclusions:

• The epistemological status of factors influences the choice of factor analytic models and decision rules.
• Empirical comparison of factor determination rules offers guidance for practical application.
• Understanding the underlying model is key to effectively applying factor determination rules.