Partial correlations in compositional data analysis

Partial correlations quantify linear association between two variables while adjusting for the influence of the remaining variables. They form the backbone for graphical models and are readily obtained from the inverse of the covariance matrix. For compositional data, the covariance structure is spe...

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Detalles Bibliográficos
Autor: Erb, Ionas
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2020
País:España
Institución:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
Repositorio:Recercat. Dipósit de la Recerca de Catalunya
OAI Identifier:oai:recercat.cat:10230/52884
Acceso en línea:http://hdl.handle.net/10230/52884
http://dx.doi.org/10.1016/j.acags.2020.100026
Access Level:acceso abierto
Palabra clave:Anàlisi de dades
Correlació parcial
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spelling Partial correlations in compositional data analysisErb, IonasAnàlisi de dadesCorrelació parcialPartial correlations quantify linear association between two variables while adjusting for the influence of the remaining variables. They form the backbone for graphical models and are readily obtained from the inverse of the covariance matrix. For compositional data, the covariance structure is specified from log ratios of variables, which implies changes in the definition and interpretation of partial correlations. In the present work, we elucidate how results derived by Aitchison (1986) lead to a natural definition of partial correlation that has a number of advantages over current measures of association. For this, we show that the residuals of log-ratios between a variable with a reference, when adjusting for all remaining variables including the reference, are reference-independent. Since the reference itself can be controlled for, correlations between residuals are defined for the variables directly without the necessity to explicitly specify the reference (as it is implicit in the variables that are partialled out). Thus, perhaps surprisingly, partial correlations do not have the problems commonly found with measures of pairwise association on compositional data. They are well-defined between two variables, are properly scaled, and allow for negative association. By design, they are subcompositionally incoherent, but they share this property with conventional partial correlations (where results change when adjusting for the influence of fewer variables). We discuss the reference-dependence of the multiple correlation coefficient as well as partial correlations that are obtained after effective library-size normalizations. We also determine the partial variances and correlations on two previously studied data sets and compare with symmetric balance correlations and the proportionality coefficient.Elsevier202220222020info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfapplication/pdfhttp://hdl.handle.net/10230/52884http://dx.doi.org/10.1016/j.acags.2020.100026reponame:Recercat. Dipósit de la Recerca de Catalunyainstname:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)Inglés© 2020 Ionas Erb. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/)https://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessoai:recercat.cat:10230/528842026-05-29T05:05:01Z
dc.title.none.fl_str_mv Partial correlations in compositional data analysis
title Partial correlations in compositional data analysis
spellingShingle Partial correlations in compositional data analysis
Erb, Ionas
Anàlisi de dades
Correlació parcial
title_short Partial correlations in compositional data analysis
title_full Partial correlations in compositional data analysis
title_fullStr Partial correlations in compositional data analysis
title_full_unstemmed Partial correlations in compositional data analysis
title_sort Partial correlations in compositional data analysis
dc.creator.none.fl_str_mv Erb, Ionas
author Erb, Ionas
author_facet Erb, Ionas
author_role author
dc.subject.none.fl_str_mv Anàlisi de dades
Correlació parcial
topic Anàlisi de dades
Correlació parcial
description Partial correlations quantify linear association between two variables while adjusting for the influence of the remaining variables. They form the backbone for graphical models and are readily obtained from the inverse of the covariance matrix. For compositional data, the covariance structure is specified from log ratios of variables, which implies changes in the definition and interpretation of partial correlations. In the present work, we elucidate how results derived by Aitchison (1986) lead to a natural definition of partial correlation that has a number of advantages over current measures of association. For this, we show that the residuals of log-ratios between a variable with a reference, when adjusting for all remaining variables including the reference, are reference-independent. Since the reference itself can be controlled for, correlations between residuals are defined for the variables directly without the necessity to explicitly specify the reference (as it is implicit in the variables that are partialled out). Thus, perhaps surprisingly, partial correlations do not have the problems commonly found with measures of pairwise association on compositional data. They are well-defined between two variables, are properly scaled, and allow for negative association. By design, they are subcompositionally incoherent, but they share this property with conventional partial correlations (where results change when adjusting for the influence of fewer variables). We discuss the reference-dependence of the multiple correlation coefficient as well as partial correlations that are obtained after effective library-size normalizations. We also determine the partial variances and correlations on two previously studied data sets and compare with symmetric balance correlations and the proportionality coefficient.
publishDate 2020
dc.date.none.fl_str_mv 2020
2022
2022
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/10230/52884
http://dx.doi.org/10.1016/j.acags.2020.100026
url http://hdl.handle.net/10230/52884
http://dx.doi.org/10.1016/j.acags.2020.100026
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.rights.none.fl_str_mv https://creativecommons.org/licenses/by-nc-nd/4.0/
info:eu-repo/semantics/openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-nd/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Elsevier
publisher.none.fl_str_mv Elsevier
dc.source.none.fl_str_mv reponame:Recercat. Dipósit de la Recerca de Catalunya
instname:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
instname_str Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
reponame_str Recercat. Dipósit de la Recerca de Catalunya
collection Recercat. Dipósit de la Recerca de Catalunya
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