Dimension Reduction for Multivariate Response Data
This article concerns the analysis of multivariate response data with multivariate regressors. Methods for reducing the dimensionality of response variables are developed, with the goal of preserving as much regression information as possible. We note parallels between this goal and the goal of slic...
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| Veröffentlicht in: | Journal of the American Statistical Association 2003-03, Vol.98 (461), p.99-109 |
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| container_title | Journal of the American Statistical Association |
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| creator | Li, Ker-Chau Aragon, Yve Shedden, Kerby Thomas Agnan, C |
| description | This article concerns the analysis of multivariate response data with multivariate regressors. Methods for reducing the dimensionality of response variables are developed, with the goal of preserving as much regression information as possible. We note parallels between this goal and the goal of sliced inverse regression, which intends to reduce the regressor dimension in a univariate regression while preserving as much regression information as possible. A detailed discussion is given for the case where the response is a curve measured at fixed points. The problem in this setting is to select basis functions for fitting an aggregate of curves. We propose that instead of focusing on goodness of fit, attention should be shifted to the problem of explaining the variation of the curves in terms of the regressor variables. A data-adaptive basis searching method based on dimension reduction theory is proposed. Simulation results and an application to a climatology problem are given. |
| doi_str_mv | 10.1198/016214503388619139 |
| format | Article |
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Methods for reducing the dimensionality of response variables are developed, with the goal of preserving as much regression information as possible. We note parallels between this goal and the goal of sliced inverse regression, which intends to reduce the regressor dimension in a univariate regression while preserving as much regression information as possible. A detailed discussion is given for the case where the response is a curve measured at fixed points. The problem in this setting is to select basis functions for fitting an aggregate of curves. We propose that instead of focusing on goodness of fit, attention should be shifted to the problem of explaining the variation of the curves in terms of the regressor variables. A data-adaptive basis searching method based on dimension reduction theory is proposed. Simulation results and an application to a climatology problem are given.</description><identifier>ISSN: 0162-1459</identifier><identifier>EISSN: 1537-274X</identifier><identifier>DOI: 10.1198/016214503388619139</identifier><identifier>CODEN: JSTNAL</identifier><language>eng</language><publisher>Alexandria: Taylor & Francis</publisher><subject>Canonical correlation ; Correlation ; Data analysis ; Datasets ; Dimensionality ; Dimensionality reduction ; Effective dimension reduction space ; Eigenvalues ; Eigenvectors ; Functional data analysis ; Linear regression ; Mathematical vectors ; Parsimony ; Principal component analysis ; Principal components analysis ; Regression analysis ; Sliced inverse regression ; Space ; Standard deviation ; Statistical methods ; Statistics ; Theory and Methods ; Variables</subject><ispartof>Journal of the American Statistical Association, 2003-03, Vol.98 (461), p.99-109</ispartof><rights>American Statistical Association 2003</rights><rights>Copyright 2003 American Statistical Association</rights><rights>Copyright American Statistical Association Mar 2003</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c410t-fc71ba4e42dfbf8bde4c0e15b91a67a0984fec267370a414b7e6ab42462b9f7b3</citedby><cites>FETCH-LOGICAL-c410t-fc71ba4e42dfbf8bde4c0e15b91a67a0984fec267370a414b7e6ab42462b9f7b3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://www.jstor.org/stable/pdf/30045198$$EPDF$$P50$$Gjstor$$H</linktopdf><linktohtml>$$Uhttps://www.jstor.org/stable/30045198$$EHTML$$P50$$Gjstor$$H</linktohtml><link.rule.ids>314,780,784,803,832,27922,27923,58015,58019,58248,58252,59645,60434</link.rule.ids></links><search><creatorcontrib>Li, Ker-Chau</creatorcontrib><creatorcontrib>Aragon, Yve</creatorcontrib><creatorcontrib>Shedden, Kerby</creatorcontrib><creatorcontrib>Thomas Agnan, C</creatorcontrib><title>Dimension Reduction for Multivariate Response Data</title><title>Journal of the American Statistical Association</title><description>This article concerns the analysis of multivariate response data with multivariate regressors. Methods for reducing the dimensionality of response variables are developed, with the goal of preserving as much regression information as possible. We note parallels between this goal and the goal of sliced inverse regression, which intends to reduce the regressor dimension in a univariate regression while preserving as much regression information as possible. A detailed discussion is given for the case where the response is a curve measured at fixed points. The problem in this setting is to select basis functions for fitting an aggregate of curves. We propose that instead of focusing on goodness of fit, attention should be shifted to the problem of explaining the variation of the curves in terms of the regressor variables. A data-adaptive basis searching method based on dimension reduction theory is proposed. Simulation results and an application to a climatology problem are given.</description><subject>Canonical correlation</subject><subject>Correlation</subject><subject>Data analysis</subject><subject>Datasets</subject><subject>Dimensionality</subject><subject>Dimensionality reduction</subject><subject>Effective dimension reduction space</subject><subject>Eigenvalues</subject><subject>Eigenvectors</subject><subject>Functional data analysis</subject><subject>Linear regression</subject><subject>Mathematical vectors</subject><subject>Parsimony</subject><subject>Principal component analysis</subject><subject>Principal components analysis</subject><subject>Regression analysis</subject><subject>Sliced inverse regression</subject><subject>Space</subject><subject>Standard deviation</subject><subject>Statistical methods</subject><subject>Statistics</subject><subject>Theory and 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Methods for reducing the dimensionality of response variables are developed, with the goal of preserving as much regression information as possible. We note parallels between this goal and the goal of sliced inverse regression, which intends to reduce the regressor dimension in a univariate regression while preserving as much regression information as possible. A detailed discussion is given for the case where the response is a curve measured at fixed points. The problem in this setting is to select basis functions for fitting an aggregate of curves. We propose that instead of focusing on goodness of fit, attention should be shifted to the problem of explaining the variation of the curves in terms of the regressor variables. A data-adaptive basis searching method based on dimension reduction theory is proposed. 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| ispartof | Journal of the American Statistical Association, 2003-03, Vol.98 (461), p.99-109 |
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| source | JSTOR Mathematics & Statistics; Jstor Complete Legacy; Taylor & Francis:Master (3349 titles) |
| subjects | Canonical correlation Correlation Data analysis Datasets Dimensionality Dimensionality reduction Effective dimension reduction space Eigenvalues Eigenvectors Functional data analysis Linear regression Mathematical vectors Parsimony Principal component analysis Principal components analysis Regression analysis Sliced inverse regression Space Standard deviation Statistical methods Statistics Theory and Methods Variables |
| title | Dimension Reduction for Multivariate Response Data |
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