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Distance‐based multivariate analyses confound location and dispersion effects
Author(s) -
Warton David I.,
Wright Stephen T.,
Wang Yi
Publication year - 2012
Publication title -
methods in ecology and evolution
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.425
H-Index - 105
ISSN - 2041-210X
DOI - 10.1111/j.2041-210x.2011.00127.x
Subject(s) - multivariate statistics , variance (accounting) , statistics , pairwise comparison , multivariate analysis , econometrics , mathematics , dispersion (optics) , multivariate analysis of variance , distance matrices in phylogeny , confounding , combinatorics , economics , physics , accounting , optics
Summary 1. A critical property of count data is its mean–variance relationship, yet this is rarely considered in multivariate analysis in ecology. 2. This study considers what is being implicitly assumed about the mean–variance relationship in distance‐based analyses – multivariate analyses based on a matrix of pairwise distances – and what the effect is of any misspecification of the mean–variance relationship. 3. It is shown that distance‐based analyses make implicit assumptions that are typically out‐of‐step with what is observed in real data, which has major consequences. 4. Potential consequences of this mean–variance misspecification are: confounding location and dispersion effects in ordinations; misleading results when trying to identify taxa in which an effect is expressed; failure to detect a multivariate effect unless it is expressed in high‐variance taxa. 5. Data transformation does not solve the problem. 6. A solution is to use generalised linear models and their recent multivariate generalisations, which is shown here to have desirable properties.