Recent Advances in Visualizing Multivariate Linear Models
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| Format: | Artículo científico |
| Langue: | en |
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Universidad Nacional de Colombia
2014
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| _version_ | 1876423897701679104 |
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| author | Michael Friendly |
| author_facet | Michael Friendly |
| contents | Recent Advances in Visualizing Multivariate Linear Models Michael Friendly Matthew Sigal Física, Astronomía y Matemáticas Graphics Software Visualization Multivariate Analysis This paper reviews our work in the development of visualization methods (implemented in R ) for understanding and interpreting the effects of predictors in multivariate linear models (MLMs) of the form Y = XB + U , and some of their recent extensions. We begin with a description of and examples from the Hypothesis-error (HE) plots framework (utilizing the heplots package), wherein multivariate tests can be visualized via ellipsoids in 2D, 3D or all pairwise views for the Hypothesis and Error Sum of Squares and Products (SSP) matrices used in hypothesis tests. Such HE plots provide visual tests of significance: a term is significant by Roy’s test if and only if its H ellipsoid projects somewhere outside the E ellipsoid. These ideas extend naturally to repeated measures designs in the multivariate context. When the rank of the hypothesis matrix for a term exceeds 2, these effects can also be visualized in a reduced-rank canonical space via the candisc package, which also provides new data plots for canonical correlation problems. Finally, we discuss some recent work-in-progress: the extension of these methods to robust MLMs, development of generalizations of influence measures and diagnostic plots for MLMs (in the mvinfluence package). 2014 artículo científico 0120-1751 https://www.redalyc.org/articulo.oa?id=89933712003 en http://www.redalyc.org/revista.oa?id=899 Revista Colombiana de Estadística application/pdf Universidad Nacional de Colombia Revista Colombiana de Estadística (Colombia) Num.2 Vol.37 |
| format | Artículo científico |
| id | redalyc_89933712003 |
| institution | Redalyc |
| language | en |
| publishDate | 2014 |
| publisher | Universidad Nacional de Colombia |
| spellingShingle | Recent Advances in Visualizing Multivariate Linear Models Michael Friendly Física, Astronomía y Matemáticas Graphics Software Visualization Multivariate Analysis Recent Advances in Visualizing Multivariate Linear Models Michael Friendly Matthew Sigal Física, Astronomía y Matemáticas Graphics Software Visualization Multivariate Analysis This paper reviews our work in the development of visualization methods (implemented in R ) for understanding and interpreting the effects of predictors in multivariate linear models (MLMs) of the form Y = XB + U , and some of their recent extensions. We begin with a description of and examples from the Hypothesis-error (HE) plots framework (utilizing the heplots package), wherein multivariate tests can be visualized via ellipsoids in 2D, 3D or all pairwise views for the Hypothesis and Error Sum of Squares and Products (SSP) matrices used in hypothesis tests. Such HE plots provide visual tests of significance: a term is significant by Roy’s test if and only if its H ellipsoid projects somewhere outside the E ellipsoid. These ideas extend naturally to repeated measures designs in the multivariate context. When the rank of the hypothesis matrix for a term exceeds 2, these effects can also be visualized in a reduced-rank canonical space via the candisc package, which also provides new data plots for canonical correlation problems. Finally, we discuss some recent work-in-progress: the extension of these methods to robust MLMs, development of generalizations of influence measures and diagnostic plots for MLMs (in the mvinfluence package). 2014 artículo científico 0120-1751 https://www.redalyc.org/articulo.oa?id=89933712003 en http://www.redalyc.org/revista.oa?id=899 Revista Colombiana de Estadística application/pdf Universidad Nacional de Colombia Revista Colombiana de Estadística (Colombia) Num.2 Vol.37 |
| title | Recent Advances in Visualizing Multivariate Linear Models |
| topic | Física, Astronomía y Matemáticas Graphics Software Visualization Multivariate Analysis |
| url | https://www.redalyc.org/articulo.oa?id=89933712003 |