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Evaluating Change in Adjusted R-Square and R-Square Indices: A Latent Variable Method Application
Tenko Raykov1, Christine DiStefano2
1Michigan State University, E. Lansing, MI, USA.
Educational and Psychological Measurement
|April 15, 2025
Summary
This study introduces a new method for estimating the difference in adjusted R-square for nested linear models. This approach provides more comprehensive information for model selection than traditional R-square change tests.
Area of Science:
- Statistics
- Econometrics
- Psychometrics
Background:
- Nested linear models are frequently used in statistical analysis.
- Model selection often relies on R-square change statistics and significance tests.
- Existing methods for comparing adjusted R-square offer limited information.
Purpose of the Study:
- To present a novel procedure for interval estimation of the difference in adjusted R-square for nested linear models.
- To provide a more informative alternative to standard R-square change statistics.
- To facilitate robust model selection in empirical research.
Main Methods:
- Develops a procedure for calculating confidence intervals for the difference in adjusted R-square.
- The method also yields confidence intervals for standard R-square and adjusted R-square for individual models.
- The procedure is designed for easy implementation with common statistical software.
Main Results:
- The interval estimate for the adjusted R-square difference offers a more informative assessment than traditional significance tests.
- The method provides simultaneous confidence intervals for related R-square measures.
- Numerical examples demonstrate the practical application and utility of the procedure.
Conclusions:
- The proposed interval estimation procedure for adjusted R-square difference is a valuable tool for model selection.
- It complements and enhances traditional R-square change statistics by providing richer information.
- The method is applicable to educational and psychological research, aiding in the selection of superior nested linear models.
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