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Updated: Mar 1, 2026
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More efficient parameter estimates for factor analysis of ordinal variables by ridge generalized least squares
Ke-Hai Yuan1, Ge Jiang1, Ying Cheng1
1Department of Psychology, University of Notre Dame, Indiana, USA.
Summary
New ridge generalized least squares (GLS) methods improve factor analysis for ordinal data, offering more accurate parameter estimates than existing techniques like least squares (LS) and diagonally weighted least squares (DWLS). These advancements enhance the analysis of psychological data collected via Likert scales.
Area of Science:
- Psychometrics
- Statistical Modeling
Background:
- Likert-type scales are common in psychology, but traditional analysis methods struggle with skewed data.
- Factor analysis of ordinal data is best performed on polychoric correlation matrices.
- Existing methods like generalized least squares (GLS) with asymptotically correct weight matrices (AGLS), least squares (LS), and diagonally weighted least squares (DWLS) have limitations.
Purpose of the Study:
- To introduce novel ridge GLS methods for factor analysis of ordinal data.
- To address the gap between theoretical recommendations and practical application in ordinal data factor analysis.
- To improve the accuracy and efficiency of parameter estimation in factor analysis of Likert-type data.
Main Methods:
- Development of ridge GLS methods for polychoric correlation matrices.
- Monte Carlo simulations to compare ridge GLS with existing methods (LS, DWLS, AGLS).
- Application of methods to a real-data example.
Main Results:
- Ridge GLS methods consistently yield more accurate parameter estimates across various sample sizes compared to LS, DWLS, and AGLS.
- Real-data analysis shows ridge GLS estimates are 9-20% more efficient than existing methods.
- Rescaled test statistics and sandwich-type standard errors demonstrate good performance with ridge GLS.
Conclusions:
- Ridge GLS represents a significant advancement for factor analysis of ordinal data.
- The proposed methods offer superior accuracy and efficiency, particularly for skewed Likert-scale data.
- Ridge GLS methods bridge the gap between statistical theory and practical application in psychometric analysis.
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