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KAISER CRITERION IN FACTOR MODELS
Changhu Wang1, Jianhua Guo1, Yanyuan Ma1
1Northeast Normal University and Pennsylvania State University.
Acta Mathematica Sinica, English Series
|April 2, 2026
Summary
Determining the correct number of factors in factor models remains challenging. This study identifies the precise conditions on the loading matrix for eigenvalue methods to accurately estimate the number of factors.
Area of Science:
- Statistics
- Econometrics
- Machine Learning
Background:
- Factor models are widely used but determining the number of factors is an unresolved statistical problem.
- A common heuristic involves counting eigenvalues greater than one, assuming this equals the true factor number.
Purpose of the Study:
- To investigate the relationship between the number of eigenvalues greater than one and the true number of factors.
- To establish the necessary and sufficient conditions for these two numbers to be equal in factor analysis.
Main Methods:
- Theoretical analysis of factor model properties.
- Derivation of conditions based on the loading matrix characteristics.
- Examination of the impact of model error on factor number estimation.
Main Results:
- The equality between the number of eigenvalues greater than one and the true number of factors is shown to depend exclusively on the properties of the loading matrix.
- Specific conditions are derived that guarantee the accuracy of this eigenvalue-based heuristic.
Conclusions:
- The study provides a rigorous theoretical foundation for selecting the number of factors using eigenvalues.
- Understanding the role of the loading matrix and model error is crucial for accurate factor number determination in statistical modeling.
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