Linear association in compositional data analysis
With compositional data, ordinary covariation indices, designed for real random variables, fail to describe dependence. There is a need for compositional alternatives to covariance and correlation. Based on the Euclidean structure of the simplex, called Aitchison geometry, compositional association...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2018 |
| 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:10256/15874 |
| Acceso en línea: | http://hdl.handle.net/10256/15874 |
| Access Level: | acceso abierto |
| Palabra clave: | Anàlisi multivariable Multivariate analysis Anàlisi de regressió Regression analysis |
| Sumario: | With compositional data, ordinary covariation indices, designed for real random variables, fail to describe dependence. There is a need for compositional alternatives to covariance and correlation. Based on the Euclidean structure of the simplex, called Aitchison geometry, compositional association is identified to a linear restriction of the sample space when a log-contrast is constant. In order to simplify interpretation, a sparse and simple version of compositional association is defined in terms of balances which are constant across the sample. It is called b-association. This kind of association of compositional variables is extended to association between groups of compositional variables. In practice, exact b-association seldom occurs, and measures of degree of b-association are reviewed based on those previously proposed. Also, some techniques for testing b-association are studied. These techniques are applied to available oral microbiome data to illustrate both their advantages and difficulties. Both testing and measurements of b-association appear to be quite sensitive to heterogeneities in the studied populations and to outliers |
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