Non-parametric testing of differences between groups in compositional data sets

J. Palarea-Albaladejo, N. Štefelová, J. A. Martín-Fernández

Multivariate data accounting for relative parts of some whole are known as compositional data (CoDa). Drawing on the most elemental units of information in CoDa, the pairwise logratios, a test to compare group centres is introduced building on Welch’s t-statistics. They are computed for all logratios and all pairs of groups, and re-expressed as normalised standard normal quantiles to enable comparability. The resulting basic dissimilarities are aggregated into an overall dissimilarity measure used as input into a permutational significance test. A weighting parameter allows to emphasise differences at the individual pairwise logratio level, which contributes to increase the sensitivity of the test. This is applicable to groups according to an external factor and to e.g. subsets linked to zero patterns in the data. A simulation study shows its comparative performance in a range of scenarios. Finally, the use is illustrated in a comparison of physical activity patterns by age group.

Keywords: Compositional data, logratio analysis, permutation test, group comparison

Análisis Multivariante
June 12, 2025  7:00 PM
MR 1

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