The chi-square standardization, combined with Box-Cox transformation, is a valid alternative to transforming to logratios in compositional data analysis
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- dc.contributor.author Greenacre, Michael
- dc.contributor.other Universitat Pompeu Fabra. Departament d'Economia i Empresa
- dc.date.accessioned 2024-11-14T10:09:56Z
- dc.date.available 2024-11-14T10:09:56Z
- dc.date.issued 2023-01-02
- dc.date.modified 2024-11-14T10:08:50Z
- dc.description.abstract The approach to analysing compositional data with a fixed sum constraint has been dominated by the use of logratio transformations, to ensure exact subcompositional coherence and, in some situations, exact isometry as well. A problem with this approach is that data zeros, found in most applications, have to be replaced to permit the logarithmic transformation. A simpler approach is to use the chi-square standardization that is inherent in correspondence analysis. Combined with the Box-Cox power transformation, this standardization defines chi-square distances that tend to logratio distances for strictly positive data as the power parameter tends to zero, and can thus be considered equivalent to transforming to logratios. For data with zeros, a value of the power can be identified that brings the chi-square standardization as close as possible to transforming by logratios, without having to substitute the zeros. Especially in the field of high-dimensional "omics" data, this alternative presents such a high level of coherence and isometry as to be a valid, and much simpler, approach to the analysis of compositional data.
- dc.format.mimetype application/pdf*
- dc.identifier https://econ-papers.upf.edu/ca/paper.php?id=1857
- dc.identifier.citation
- dc.identifier.uri http://hdl.handle.net/10230/68648
- dc.language.iso eng
- dc.relation.ispartofseries Economics and Business Working Papers Series; 1857
- dc.rights L'accés als continguts d'aquest document queda condicionat a l'acceptació de les condicions d'ús establertes per la següent llicència Creative Commons
- dc.rights.accessRights info:eu-repo/semantics/openAccess
- dc.rights.uri http://creativecommons.org/licenses/by-nc-nd/3.0/es/
- dc.subject.keyword box-cox transformation
- dc.subject.keyword chi-square distance
- dc.subject.keyword correspondence analysis
- dc.subject.keyword isometry
- dc.subject.keyword logratios
- dc.subject.keyword procrustes analysis
- dc.subject.keyword subcompositional coherence
- dc.subject.keyword Statistics, Econometrics and Quantitative Methods
- dc.title The chi-square standardization, combined with Box-Cox transformation, is a valid alternative to transforming to logratios in compositional data analysis
- dc.title.alternative
- dc.type info:eu-repo/semantics/workingPaper