A1 Vertaisarvioitu alkuperäisartikkeli tieteellisessä lehdessä
On the distribution of isometric log-ratio coordinates under extra-multinomial count data
Tekijät: Kartiosuo, Noora; Virta, Joni; Nevalainen, Jaakko; Raitakari, Olli; Auranen, Kari
Kustantaja: Springer Science and Business Media LLC
Kustannuspaikka: NEW YORK
Julkaisuvuosi: 2025
Journal: Statistical Papers
Tietokannassa oleva lehden nimi: Statistical Papers
Lehden akronyymi: STAT PAP
Artikkelin numero: 113
Vuosikerta: 66
Numero: 5
Sivujen määrä: 30
ISSN: 0932-5026
eISSN: 1613-9798
DOI: https://doi.org/10.1007/s00362-025-01732-8
Verkko-osoite: https://doi.org/10.1007/s00362-025-01732-8
Rinnakkaistallenteen osoite: https://research.utu.fi/converis/portal/detail/Publication/499223265
Compositional data can be mapped from the simplex to the Euclidean space through the isometric log-ratio (ilr) transformation. When the underlying counts follow a multinomial distribution, the distribution of the ensuing ilr coordinates has been shown to be asymptotically multivariate normal. We derive conditions under which the asymptotic normality of the ilr coordinates holds under a compound multinomial distribution inducing overdispersion in the counts. We derive a normal approximation and investigate its practical applicability under extra-multinomial variation using a simulation study under the Dirichlet-multinomial distribution. The approximation works well, except with a small total count or high amount of overdispersion. Our work is motivated by microbiome data, which exhibit extra-multinomial variation and are increasingly treated as compositions. We conclude that if empirical data analysis relies on the normality of ilr coordinates, it may be advisable to choose a taxonomic level with less sparsity so that the distribution of taxon-specific class probabilities remains unimodal.
Ladattava julkaisu This is an electronic reprint of the original article. |  |
Julkaisussa olevat rahoitustiedot:
Open Access funding provided by University of Turku (including Turku University Central Hospital). Open Access funding provided by University of Turku (including Turku University Central Hospital). NK has been financially supported by Emil Aaltonen Foundation, Alfred Kordelin Foundation, Finnish Cultural Foundation and the MATTI programme in The University of Turku Graduate School (UTUGS). The work of JV was supported by Research Council of Finland, Grants 347501, 353769 and 368494.
