Exploring the Relationship between two Compositions using Canonical Correlation Analys
dc.contributor.author
dc.date.accessioned
2017-03-16T09:32:50Z
dc.date.available
2017-03-16T09:32:50Z
dc.date.issued
2016
dc.identifier.issn
1854-0031
dc.identifier.uri
dc.description.abstract
The aim of this article is to describe a method for relating two compositions which
combines compositional data analysis and canonical correlation analysis (CCA),
and to examine its main statistical properties. We use additive log-ratio (alr)
transformation on both compositions and apply standard CCA to the transformed
data. We show that canonical variates are themselves log-ratios and log-contrasts.
The first pair of canonical variates can be interpreted as the log-contrast of a
composition that has the maximum correlation with a log-contrast of the other
composition. The second pair can be interpreted as the log-contrast of a
composition that has the maximum correlation with a log-contrast of the other
composition, under the restriction that they are uncorrelated with the first pair, and
so on.
Using properties from changes of basis, we prove that both canonical
correlations and canonical variates are invariant to the choice of divisors in alr
transformation. We show how to implement the analysis and interpret the results
by means of an illustration from the social sciences field using data from Kolb’s
Learning Style Inventory and Boyatzis’ Philosophical Orientation Questionnaire,
which distribute a fixed total score among several learning modes and
philosophical orientations
dc.description.sponsorship
The authors would like to acknowledge the support provided by Spanish Health Ministry Grant CB06/02/1002 funding the research group “Epidemiology and Public Health (CIBERESP)”; Catalan Autonomous Government Consolidated Research Group Grants 2014SGR551 and 2014SGR582 funding the research groups “Compositional and Spatial Data Analysis (COSDA)” and “Leadership Development Research Centre (GLEAD)”; Spanish Economy and Competitiveness Ministry grants MINECO/FEDER-EU MTM2015-65016-C2-1-R and EDU2015-68610-R funding the projects “Compositional Data Analysis and RElated meThOdS (CODA-RETOS)” and “Assessing Individual and Team Entrepreneurial Potential”; and University of Girona grants MPCUdG2016/069 and MPCUdG2016/098
dc.format.mimetype
application/pdf
dc.language.iso
eng
dc.publisher
University of Ljubljana. Faculty of Social Sciences
dc.relation
info:eu-repo/grantAgreement/MINECO//MTM2015-65016-C2-1-R/ES/ANALISIS DE DATOS COMPOSICIONALES Y METODOS RELACIONADOS/
dc.relation.isformatof
Reproducció digital del document publicat a: http://www.stat-d.si/mz/Articles.html
dc.relation.ispartof
© Metodološki zvezki, 2016, vol. 13, núm. 2, p. 131-150
dc.relation.ispartofseries
Articles publicats (D-IMA)
dc.rights
Tots els drets reservats
dc.subject
dc.title
Exploring the Relationship between two Compositions using Canonical Correlation Analys
dc.type
info:eu-repo/semantics/article
dc.rights.accessRights
info:eu-repo/semantics/openAccess
dc.embargo.terms
Cap
dc.type.version
info:eu-repo/semantics/publishedVersion
dc.identifier.idgrec
026161
dc.contributor.funder
dc.relation.ProjectAcronym