FITTING MULTIVARIATE MODELS TO COMMUNITY DATA: A COMMENT ON DISTANCE-BASED REDUNDANCY ANALYSIS
Abstract
Nonparametric multivariate analysis of ecological data using permutation tests has two main challenges: (1) to partition the variability in the data according to a complex design or model, as is often required in ecological experiments, and (2) to base the analysis on a multivariate distance measure (such as the semimetric Bray-Curtis measure) that is reasonable for ecological data sets. Previous nonparametric methods have succeeded in one or other of these areas, but not in both. A recent contribution to Ecological Monographs by Legendre and Anderson, called distance-based redundancy analysis (db-RDA), does achieve both. It does this by calculating principal coordinates and subsequently correcting for negative eigenvalues, if they are present, by adding a constant to squared distances. We show here that such a correction is not necessary. Partitioning can be achieved directly from the distance matrix itself, with no corrections and no eigenanalysis, even if the distance measure used is semimetric. An ecological example is given to show the differences in these statistical methods. Empirical simulations, based on parameters estimated from real ecological species abundance data, showed that db-RDA done on multifactorial designs (using the correction) does not have type 1 error consistent with the significance level chosen for the analysis (i.e., does not provide an exact test), whereas the direct method described and advocated here does.
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For Euclidean distances computed on a single modality, MDMR is equivalent to multivariate multiple regression (MMR) using a pseudo-F statistic.
“For Euclidean distances computed on a single modality, MDMR is equivalent to multivariate multiple regression (MMR) using a pseudo-F statistic (McArdle and Anderson 2001).”
From Similarity-based multimodal regression (2024) · cites this paper as McArdle and Anderson 2001
With a univariate outcome and Euclidean distance, MDMR is equivalent to the standard regression F-statistic if appropriate degrees of freedom are accommodated.
“With a univariate outcome and Euclidean distance, it is equivalent to the standard regression F -statistic if appropriate degrees of freedom are accommodated (McArdle and Anderson 2001).”
From Similarity-based multimodal regression (2024) · cites this paper as McArdle and Anderson 2001
For a single data modality, multivariate distance matrix regression provides a distance-based framework for regression accommodating a wide range of data types.
“For a single data modality, multivariate distance matrix regression provides a distance-based framework for regression accommodating a wide range of data types.”
From Similarity-based multimodal regression (2024) · cites this paper as McArdle and Anderson, 2001
Discarding imaginary cMDS axes might lead to conservative tests.
“One solution is to discard imaginary cMDS axes; however, McArdle and Anderson (2001) show that this might lead to conservative tests.”
From Similarity-based multimodal regression (2024) · cites this paper as McArdle and Anderson (2001)
PERMANOVA was performed on the MLG abundance profile of all samples to assess impact from each of the factors listed.
“PERMANOVA39 was performed on the MLG abundance profile of all samples to assess impact from each of the factors listed (Supplementary Table 2).”
From The gut microbiome in atherosclerotic cardiovascular disease (2017) · cites this paper as [39]
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- Authors
- McArdle, B. H., & Anderson, M. J.
- Affiliations
- University of Auckland (NZ)
- Corresponding author
- Anderson, Marti J.
- ORCID
- Anderson, Marti J.
- Venue
- Ecology
- Publisher
- Wiley
- Published
- 2001-01
- Volume
- 82
- Issue
- 1
- Pages
- 290-297
- ISSN
- 0012-9658 (ISSN-L)
- OpenAlex
- W2149421543
- Cited by
- 4,001
- References
- 34
- Citations by year
- 2026: 154 · 2025: 181 · 2024: 197 · 2023: 211 · 2022: 235 · 2021: 282 · 2020: 253 · 2019: 224 · 2018: 233 · 2017: 213 · 2016: 223 · 2015: 234 · 2014: 210 · 2013: 218 · 2012: 204
- FWCI
- 23.48
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Ecology (publishedVersion)
- Funders
- University of Sydney
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Applications
- Physical Sciences › Environmental Science › Nature and Landscape Conservation › Ecology and Vegetation Dynamics Studies
- Physical Sciences › Mathematics › Statistics and Probability › Advanced Statistical Methods and Models
- Keywords
- distance-based redundancy analysis, permutation tests, Bray-Curtis distance, principal coordinates, negative eigenvalues, type I error, species abundance data
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