Recent Advances in Visualizing Multivariate Linear Models
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 th...
- Autores:
-
Friendly, Michael
Sigal, Matthew
- Tipo de recurso:
- Article of journal
- Fecha de publicación:
- 2014
- Institución:
- Universidad Nacional de Colombia
- Repositorio:
- Universidad Nacional de Colombia
- Idioma:
- spa
- OAI Identifier:
- oai:repositorio.unal.edu.co:unal/66555
- Acceso en línea:
- https://repositorio.unal.edu.co/handle/unal/66555
http://bdigital.unal.edu.co/67583/
- Palabra clave:
- 51 Matemáticas / Mathematics
31 Colecciones de estadística general / Statistics
Graphics
Multivariate Analysis
Software
Visualization
Análisis multivariado
Gráficas
Software
Visualización
- Rights
- openAccess
- License
- Atribución-NoComercial 4.0 Internacional
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Recent Advances in Visualizing Multivariate Linear Models |
| title |
Recent Advances in Visualizing Multivariate Linear Models |
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Recent Advances in Visualizing Multivariate Linear Models 51 Matemáticas / Mathematics 31 Colecciones de estadística general / Statistics Graphics Multivariate Analysis Software Visualization Análisis multivariado Gráficas Software Visualización |
| title_short |
Recent Advances in Visualizing Multivariate Linear Models |
| title_full |
Recent Advances in Visualizing Multivariate Linear Models |
| title_fullStr |
Recent Advances in Visualizing Multivariate Linear Models |
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Recent Advances in Visualizing Multivariate Linear Models |
| title_sort |
Recent Advances in Visualizing Multivariate Linear Models |
| dc.creator.fl_str_mv |
Friendly, Michael Sigal, Matthew |
| dc.contributor.author.spa.fl_str_mv |
Friendly, Michael Sigal, Matthew |
| dc.subject.ddc.spa.fl_str_mv |
51 Matemáticas / Mathematics 31 Colecciones de estadística general / Statistics |
| topic |
51 Matemáticas / Mathematics 31 Colecciones de estadística general / Statistics Graphics Multivariate Analysis Software Visualization Análisis multivariado Gráficas Software Visualización |
| dc.subject.proposal.spa.fl_str_mv |
Graphics Multivariate Analysis Software Visualization Análisis multivariado Gráficas Software Visualización |
| description |
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, and the development of generalizations of influence measures and diagnostic plots for MLMs (in the mvinfluence package). |
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2014 |
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2014-07-01 |
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2019-07-03T02:21:50Z |
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2019-07-03T02:21:50Z |
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Artículo de revista |
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http://purl.org/coar/resource_type/c_2df8fbb1 |
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ISSN: 2389-8976 |
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https://repositorio.unal.edu.co/handle/unal/66555 |
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ISSN: 2389-8976 |
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spa |
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spa |
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https://revistas.unal.edu.co/index.php/estad/article/view/47934 |
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Universidad Nacional de Colombia Revistas electrónicas UN Revista Colombiana de Estadística Revista Colombiana de Estadística |
| dc.relation.references.spa.fl_str_mv |
Friendly, Michael and Sigal, Matthew (2014) Recent Advances in Visualizing Multivariate Linear Models. Revista Colombiana de Estadística, 37 (2Spe). pp. 261-283. ISSN 2389-8976 |
| dc.rights.spa.fl_str_mv |
Derechos reservados - Universidad Nacional de Colombia |
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Atribución-NoComercial 4.0 Internacional |
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http://creativecommons.org/licenses/by-nc/4.0/ |
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Universidad Nacional de Colombia - Sede Bogotá - Facultad de Ciencias - Departamento de Estadística |
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Atribución-NoComercial 4.0 InternacionalDerechos reservados - Universidad Nacional de Colombiahttp://creativecommons.org/licenses/by-nc/4.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Friendly, Michaela710a281-df13-4403-92ae-f5f1dfd9efd2300Sigal, Matthew14b5e041-e0aa-4002-ad8e-d6ff6851360e3002019-07-03T02:21:50Z2019-07-03T02:21:50Z2014-07-01ISSN: 2389-8976https://repositorio.unal.edu.co/handle/unal/66555http://bdigital.unal.edu.co/67583/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, and the development of generalizations of influence measures and diagnostic plots for MLMs (in the mvinfluence package).Este artículo hace una revisión de los desarrollos recientes en métodos de visualización (implementados en R) para la comprensión e interpretación de los efectos de los predictores en modelos lineales multivariados (MLMs) de la forma Y = XB + U y sus extensiones recientes. Comenzamos con una descripción y ejemplos de los gráficos de Hipótesis- Error (HE), (utilizando el paquete heplots) en los cuales los tests multivariados son visualizados vía elipsoides en 2D, 3D o todas las vistas pareadas de las matrices de sumas de cuadrados y productos (SSP por sus siglas en inglés) de Hipótesis y Error. Las gráficas HE permiten pruebas de significancia visuales: un término es significativo en el test de Roy si y solo si su elipsoide H es proyectado fuera del elipsoide E. Estas ideas se extienden a diseños de medidas repetidas en el contexto multivariado. Cuando el rango de la matriz de hipótesis para un término es mayor a 2, estos efectos pueden ser visualizados en un espacio canónico de rango reducido vía el paquete candisc, que a su vez también permite nuevos gráficos para problemas de correlación canónica. Finalmente, se discuten algunas áreas de investigación en desarrollo: la extensión de estos métodos a MLMs robustos, generalizaciones de las medidas de influencia y gráficas de diagnóstico para MLMs (en el paquete mvinfluence).application/pdfspaUniversidad Nacional de Colombia - Sede Bogotá - Facultad de Ciencias - Departamento de Estadísticahttps://revistas.unal.edu.co/index.php/estad/article/view/47934Universidad Nacional de Colombia Revistas electrónicas UN Revista Colombiana de EstadísticaRevista Colombiana de EstadísticaFriendly, Michael and Sigal, Matthew (2014) Recent Advances in Visualizing Multivariate Linear Models. Revista Colombiana de Estadística, 37 (2Spe). pp. 261-283. ISSN 2389-897651 Matemáticas / Mathematics31 Colecciones de estadística general / StatisticsGraphicsMultivariate AnalysisSoftwareVisualizationAnálisis multivariadoGráficasSoftwareVisualizaciónRecent Advances in Visualizing Multivariate Linear ModelsArtículo de revistainfo:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501http://purl.org/coar/resource_type/c_2df8fbb1http://purl.org/coar/version/c_970fb48d4fbd8a85Texthttp://purl.org/redcol/resource_type/ARTORIGINAL47934-235017-1-PB.pdfapplication/pdf1046001https://repositorio.unal.edu.co/bitstream/unal/66555/1/47934-235017-1-PB.pdfc225373f28fa0a74c3750063ab761ef5MD51THUMBNAIL47934-235017-1-PB.pdf.jpg47934-235017-1-PB.pdf.jpgGenerated Thumbnailimage/jpeg5121https://repositorio.unal.edu.co/bitstream/unal/66555/2/47934-235017-1-PB.pdf.jpgc1913d4438d4f8cdd7ba05fb9fd4842eMD52unal/66555oai:repositorio.unal.edu.co:unal/665552023-05-25 23:03:11.45Repositorio Institucional Universidad Nacional de Colombiarepositorio_nal@unal.edu.co |