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Mixing compositions and other scales

Theory of compositional data analysis is often focused on the composition only. However in practical applications we often treat a composition together with covariables with some other scale. This contribution systematically gathers and develop statistical tools for this situation. For instance, for the graphical display of the dependence of a composition with a categorical variable, a colored set of ternary diagrams might be a good idea for a first look at the data, but it will fast hide important aspects if the composition has many parts, or it takes extreme values. On the other hand colored scatterplots of ilr components could not be very instructive for the analyst, if the conventional, black-box ilr is used. Thinking on terms of the Euclidean structure of the simplex, we suggest to set up appropriate projections, which on one side show the compositional geometry and on the other side are still comprehensible by a non-expert analyst, readable for all locations and scales of the data. This is e.g. done by defining special balance displays with carefully- selected axes. Following this idea, we need to systematically ask how to display, explore, describe, and test the relation to complementary or explanatory data of categorical, real, ratio or again compositional scales. This contribution shows that it is sufficient to use some basic concepts and very few advanced tools from multivariate statistics (principal covariances, multivariate linear models, trellis or parallel plots, etc.) to build appropriate procedures for all these combinations of scales. This has some fundamental implications in their software implementation, and how might they be taught to analysts not already experts in multivariate analysis

Geologische Vereinigung; Institut d鈥橢stad铆stica de Catalunya; International Association for Mathematical Geology; C脿tedra Llu铆s Santal贸 d鈥橝plicacions de la Matem脿tica; Generalitat de Catalunya, Departament d鈥橧nnovaci贸, Universitats i Recerca; Ministerio de Educaci贸n y Ciencia; Ingenio 2010.

Universitat de Girona. Departament d鈥橧nform脿tica i Matem脿tica Aplicada

Manager: Daunis-i-Estadella, Pepus
Mart铆n Fern谩ndez, Josep Antoni
Other contributions: Universitat de Girona. Departament d鈥橧nform脿tica i Matem脿tica Aplicada
Author: Boogaart, K. Gerald van den
Tolosana Delgado, Raimon
Date: 2008 May 30
Abstract: Theory of compositional data analysis is often focused on the composition only. However in practical applications we often treat a composition together with covariables with some other scale. This contribution systematically gathers and develop statistical tools for this situation. For instance, for the graphical display of the dependence of a composition with a categorical variable, a colored set of ternary diagrams might be a good idea for a first look at the data, but it will fast hide important aspects if the composition has many parts, or it takes extreme values. On the other hand colored scatterplots of ilr components could not be very instructive for the analyst, if the conventional, black-box ilr is used. Thinking on terms of the Euclidean structure of the simplex, we suggest to set up appropriate projections, which on one side show the compositional geometry and on the other side are still comprehensible by a non-expert analyst, readable for all locations and scales of the data. This is e.g. done by defining special balance displays with carefully- selected axes. Following this idea, we need to systematically ask how to display, explore, describe, and test the relation to complementary or explanatory data of categorical, real, ratio or again compositional scales. This contribution shows that it is sufficient to use some basic concepts and very few advanced tools from multivariate statistics (principal covariances, multivariate linear models, trellis or parallel plots, etc.) to build appropriate procedures for all these combinations of scales. This has some fundamental implications in their software implementation, and how might they be taught to analysts not already experts in multivariate analysis
Geologische Vereinigung; Institut d鈥橢stad铆stica de Catalunya; International Association for Mathematical Geology; C脿tedra Llu铆s Santal贸 d鈥橝plicacions de la Matem脿tica; Generalitat de Catalunya, Departament d鈥橧nnovaci贸, Universitats i Recerca; Ministerio de Educaci贸n y Ciencia; Ingenio 2010.
Format: application/pdf
Citation: Boogaart, K.G.; Tolosana Delgado, R. 鈥橫ixing compositions and other scales鈥 a CODAWORK鈥08. Girona: La Universitat, 2008 [consulta: 14 maig 2008]. Necessita Adobe Acrobat. Disponible a Internet a: http://hdl.handle.net/10256/743
Document access: http://hdl.handle.net/10256/743
Language: eng
Publisher: Universitat de Girona. Departament d鈥橧nform脿tica i Matem脿tica Aplicada
Rights: Tots els drets reservats
Subject: An脿lisi de regressi贸
Models matem脿tics
Title: Mixing compositions and other scales
Type: info:eu-repo/semantics/conferenceObject
Repository: DUGiDocs

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