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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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| Published in: | Psychometrika 2008-12, Vol.73 (4), p.671-690 |
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| Main Authors: | , |
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| Language: | English |
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| cites | cdi_FETCH-LOGICAL-c463t-cf4150fe3f0b73a30274aa3bcac8d3d0b19d55f34da85bc99c19ec47b86e2ba43 |
| container_end_page | 690 |
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| container_title | Psychometrika |
| container_volume | 73 |
| creator | Takane, Yoshio Jung, Sunho |
| description | 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. |
| doi_str_mv | 10.1007/s11336-008-9067-y |
| format | article |
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G
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G
-fold cross validation. Illustrative examples were given to demonstrate the usefulness of the method in practical data analysis situations.</description><subject>Assessment</subject><subject>Behavioral Science and Psychology</subject><subject>Bias</subject><subject>Biological and medical sciences</subject><subject>Cross Validation</subject><subject>Data Analysis</subject><subject>Decomposition</subject><subject>Estimates</subject><subject>Expected values</subject><subject>Fundamental and applied biological sciences. Psychology</subject><subject>Humanities</subject><subject>Hypotheses</subject><subject>Law</subject><subject>Least Squares Statistics</subject><subject>Measurement Techniques</subject><subject>Multiple Regression Analysis</subject><subject>Predictor Variables</subject><subject>Psychology</subject><subject>Psychology. Psychoanalysis. Psychiatry</subject><subject>Psychology. Psychophysiology</subject><subject>Psychometrics</subject><subject>Psychometrics. Statistics. Methodology</subject><subject>Redundancy</subject><subject>Redundancy Analysis</subject><subject>Statistical Theory and Methods</subject><subject>Statistics for Social Sciences</subject><subject>Statistics. 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Psychology</topic><topic>Humanities</topic><topic>Hypotheses</topic><topic>Law</topic><topic>Least Squares Statistics</topic><topic>Measurement Techniques</topic><topic>Multiple Regression Analysis</topic><topic>Predictor Variables</topic><topic>Psychology</topic><topic>Psychology. Psychoanalysis. Psychiatry</topic><topic>Psychology. Psychophysiology</topic><topic>Psychometrics</topic><topic>Psychometrics. Statistics. Methodology</topic><topic>Redundancy</topic><topic>Redundancy Analysis</topic><topic>Statistical Theory and Methods</topic><topic>Statistics for Social Sciences</topic><topic>Statistics. Mathematics</topic><topic>Testing and Evaluation</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Takane, Yoshio</creatorcontrib><creatorcontrib>Jung, Sunho</creatorcontrib><collection>ERIC</collection><collection>ERIC (Ovid)</collection><collection>ERIC</collection><collection>ERIC</collection><collection>ERIC (Legacy Platform)</collection><collection>ERIC( SilverPlatter )</collection><collection>ERIC</collection><collection>ERIC PlusText (Legacy Platform)</collection><collection>Education Resources Information Center (ERIC)</collection><collection>ERIC</collection><collection>Pascal-Francis</collection><collection>CrossRef</collection><collection>ProQuest Social Sciences Premium Collection</collection><collection>ProQuest Central (Corporate)</collection><collection>Neurosciences Abstracts</collection><collection>ABI/INFORM Collection</collection><collection>ABI/INFORM Global (PDF only)</collection><collection>ProQuest Health & Medical Collection</collection><collection>ProQuest Central (purchase pre-March 2016)</collection><collection>ABI/INFORM Global (Alumni Edition)</collection><collection>Education Database (Alumni Edition)</collection><collection>Medical Database (Alumni Edition)</collection><collection>Psychology Database (Alumni)</collection><collection>ProQuest Pharma Collection</collection><collection>Hospital Premium Collection</collection><collection>Hospital Premium Collection (Alumni Edition)</collection><collection>ProQuest Central (Alumni) (purchase pre-March 2016)</collection><collection>ABI/INFORM Collection (Alumni Edition)</collection><collection>ProQuest Central (Alumni)</collection><collection>ProQuest Central</collection><collection>Social Science Premium Collection</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>Business Premium Collection</collection><collection>ProQuest One Community College</collection><collection>Education Collection</collection><collection>ProQuest Central Korea</collection><collection>Business Premium Collection (Alumni)</collection><collection>Health Research Premium Collection</collection><collection>ABI/INFORM Global (Corporate)</collection><collection>Health Research Premium Collection (Alumni)</collection><collection>ProQuest Central Student</collection><collection>ProQuest Business Collection (Alumni Edition)</collection><collection>ProQuest Business Collection</collection><collection>ProQuest Health & Medical Complete (Alumni)</collection><collection>ABI/INFORM Professional Advanced</collection><collection>ABI/INFORM Global</collection><collection>Education Database</collection><collection>Health & Medical Collection (Alumni Edition)</collection><collection>Medical Database</collection><collection>Psychology Database</collection><collection>ProQuest One Business</collection><collection>ProQuest One Business (Alumni)</collection><collection>ProQuest One Education</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>ProQuest One Psychology</collection><collection>ProQuest Central Basic</collection><jtitle>Psychometrika</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Takane, Yoshio</au><au>Jung, Sunho</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><ericid>EJ822829</ericid><atitle>Regularized Partial and/or Constrained Redundancy Analysis</atitle><jtitle>Psychometrika</jtitle><stitle>Psychometrika</stitle><date>2008-12-01</date><risdate>2008</risdate><volume>73</volume><issue>4</issue><spage>671</spage><epage>690</epage><pages>671-690</pages><issn>0033-3123</issn><eissn>1860-0980</eissn><coden>PSMTA2</coden><abstract>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.</abstract><cop>New York</cop><pub>Springer-Verlag</pub><doi>10.1007/s11336-008-9067-y</doi><tpages>20</tpages></addata></record> |
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| ispartof | Psychometrika, 2008-12, Vol.73 (4), p.671-690 |
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| 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 |
| title | Regularized Partial and/or Constrained Redundancy Analysis |
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