Regularized Partial and/or Constrained Redundancy Analysis

Methods of incorporating a ridge type of regularization into partial redundancy analysis (PRA), constrained redundancy analysis (CRA), and partial and constrained redundancy analysis (PCRA) were discussed. The usefulness of ridge estimation in reducing mean square error (MSE) has been recognized in...

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Bibliographic Details
Published in:Psychometrika 2008-12, Vol.73 (4), p.671-690
Main Authors: Takane, Yoshio, Jung, Sunho
Format: Article
Language:English
Subjects:
Assessment
Behavioral Science and Psychology
Bias
Biological and medical sciences
Cross Validation
Data Analysis
Decomposition
Estimates
Expected values
Fundamental and applied biological sciences. Psychology
Humanities
Hypotheses
Law
Least Squares Statistics
Measurement Techniques
Multiple Regression Analysis
Predictor Variables
Psychology
Psychology. Psychoanalysis. Psychiatry
Psychology. Psychophysiology
Psychometrics
Psychometrics. Statistics. Methodology
Redundancy
Redundancy Analysis
Statistical Theory and Methods
Statistics for Social Sciences
Statistics. Mathematics
Testing and Evaluation
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Summary:Methods of incorporating a ridge type of regularization into partial redundancy analysis (PRA), constrained redundancy analysis (CRA), and partial and constrained redundancy analysis (PCRA) were discussed. The usefulness of ridge estimation in reducing mean square error (MSE) has been recognized in multiple regression analysis for some time, especially when predictor variables are nearly collinear, and the ordinary least squares estimator is poorly determined. The ridge estimation method was extended to PRA, CRA, and PCRA, where the reduced rank ridge estimates of regression coefficients were obtained by minimizing the ridge least squares criterion. It was shown that in all cases they could be obtained in closed form for a fixed value of ridge parameter. An optimal value of the ridge parameter is found by G -fold cross validation. Illustrative examples were given to demonstrate the usefulness of the method in practical data analysis situations.
ISSN:0033-3123
1860-0980
DOI:10.1007/s11336-008-9067-y