Robust principal component analysis for compositional tables
© 2020 Informa UK Limited, trading as Taylor & Francis Group.
| Publié dans: | Journal of applied statistics. - 1991. - 48(2021), 2 vom: 17., Seite 214-233 |
|---|---|
| Auteur principal: | |
| Autres auteurs: | , , |
| Format: | Article en ligne |
| Langue: | English |
| Publié: |
2021
|
| Accès à la collection: | Journal of applied statistics |
| Sujets: | Journal Article Compositional data compositional table independence table interaction table pivot coordinates robust principal component analysis |
| Résumé: | © 2020 Informa UK Limited, trading as Taylor & Francis Group. A data table arranged according to two factors can often be considered a compositional table. An example is the number of unemployed people, split according to gender and age classes. Analyzed as compositions, the relevant information consists of ratios between different cells of such a table. This is particularly useful when analyzing several compositional tables jointly, where the absolute numbers are in very different ranges, e.g. if unemployment data are considered from different countries. Within the framework of the logratio methodology, compositional tables can be decomposed into independent and interactive parts, and orthonormal coordinates can be assigned to these parts. However, these coordinates usually require some prior knowledge about the data, and they are not easy to handle for exploring the relationships between the given factors. Here we propose a special choice of coordinates with direct relation to centered logratio (clr) coefficients, which are particularly useful for an interpretation in terms of the original cells of the tables. With these coordinates, robust principal component analysis (rPCA) is performed for dimension reduction, allowing to investigate relationships between the factors. The link between orthonormal coordinates and clr coefficients enables to apply rPCA, which would otherwise suffer from the singularity of clr coefficients |
|---|---|
| Description: | Date Revised 16.07.2022 published: Electronic-eCollection Citation Status PubMed-not-MEDLINE |
| ISSN: | 0266-4763 |
| DOI: | 10.1080/02664763.2020.1722078 |