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Independence in Contingency Tables Using Simplicial Geometry

Frequently, contingency tables are generated in a multinomial sampling. Multinomial probabilities are then organized in a table assigning probabilities to each cell. A probability table can be viewed as an element in the simplex. The Aitchison geometry of the simplex identifies independent probability tables as a linear subspace. An important consequence is that, given a probability table, the nearest independent table is obtained by orthogonal projection onto the independent subspace. The nearest independent table is identified as that obtained by the product of geometric marginals, which do not coincide with the standard marginals, except in the independent case. The original probability table is decomposed into orthogonal tables, the independent and the interaction tables. The underlying model is log-linear, and a procedure to test independence of a contingency table, based on a multinomial simulation, is developed. Its performance is studied on an illustrative example

This research was supported by thegrant COST Action CRoNoS IC1408, the grant IGA PrF 2015 013 Mathematical Models of the Internal Grant Agency of the Palacky University in Olomouc and the Spanish Ministries of Science and Innovation and Economy and Competitivity under the projects CODA-RSS Ref. MTM2009-13272 and METRICS Ref. MTM2012-33236

© Communications in Statistics. Theory and Methods, 2015, vol. 44, núm. 18, p. 3978-3996

Taylor and Francis

Author: Egozcue, Juan Jose
Pawlowsky-Glahn, Vera
Templ, Matthias
Hron, Karel
Date: 2015 September 17
Abstract: Frequently, contingency tables are generated in a multinomial sampling. Multinomial probabilities are then organized in a table assigning probabilities to each cell. A probability table can be viewed as an element in the simplex. The Aitchison geometry of the simplex identifies independent probability tables as a linear subspace. An important consequence is that, given a probability table, the nearest independent table is obtained by orthogonal projection onto the independent subspace. The nearest independent table is identified as that obtained by the product of geometric marginals, which do not coincide with the standard marginals, except in the independent case. The original probability table is decomposed into orthogonal tables, the independent and the interaction tables. The underlying model is log-linear, and a procedure to test independence of a contingency table, based on a multinomial simulation, is developed. Its performance is studied on an illustrative example
This research was supported by thegrant COST Action CRoNoS IC1408, the grant IGA PrF 2015 013 Mathematical Models of the Internal Grant Agency of the Palacky University in Olomouc and the Spanish Ministries of Science and Innovation and Economy and Competitivity under the projects CODA-RSS Ref. MTM2009-13272 and METRICS Ref. MTM2012-33236
Format: application/pdf
ISSN: 0361-0926 (versió paper)
1532-415X (versió electrònica)
Document access: http://hdl.handle.net/10256/13740
Language: eng
Publisher: Taylor and Francis
Collection: MICINN/PN 2010-2012/MTM2009-13272
MINECO/PN 2013-2015/MTM2012-33236
Reproducció digital del document publicat a: http://dx.doi.org/10.1080/03610926.2013.824980
Articles publicats (D-IMA)
Is part of: © Communications in Statistics. Theory and Methods, 2015, vol. 44, núm. 18, p. 3978-3996
Rights: Tots els drets reservats
Subject: Anàlisi multivariable
Multivariate analysis
Euclides, Elements d’
Euclid’s Elements
Geometria plana
Geometry, Plane
Title: Independence in Contingency Tables Using Simplicial Geometry
Type: info:eu-repo/semantics/article
Repository: DUGiDocs

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