Independence in Contingency Tables Using Simplicial Geometry
dc.contributor.author
dc.date.accessioned
2017-03-15T11:15:01Z
dc.date.available
2017-03-15T11:15:01Z
dc.date.issued
2015-09-17
dc.identifier.issn
0361-0926
dc.identifier.uri
dc.description.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
dc.description.sponsorship
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
dc.format.mimetype
application/pdf
dc.language.iso
eng
dc.publisher
Taylor and Francis
dc.relation
info:eu-repo/grantAgreement/MICINN//MTM2009-13272/ES/Analisis Estadistico De Datos Composicionales Y Otros Datos Con Espacio Muestral Restringido/
info:eu-repo/grantAgreement/MINECO//MTM2012-33236/ES/METODOS ESTADISTICOS EN ESPACIOS RESTRINGIDOS/
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Reproducció digital del document publicat a: http://dx.doi.org/10.1080/03610926.2013.824980
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© Communications in Statistics. Theory and Methods, 2015, vol. 44, núm. 18, p. 3978-3996
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Articles publicats (D-IMA)
dc.rights
Tots els drets reservats
dc.subject
dc.title
Independence in Contingency Tables Using Simplicial Geometry
dc.type
info:eu-repo/semantics/article
dc.rights.accessRights
info:eu-repo/semantics/embargoedAccess
dc.embargo.terms
Cap
dc.date.embargoEndDate
info:eu-repo/date/embargoEnd/2026-01-01
dc.type.version
info:eu-repo/semantics/publishedVersion
dc.identifier.doi
dc.identifier.idgrec
023754
dc.contributor.funder
dc.relation.ProjectAcronym
dc.identifier.eissn
1532-415X