Why you cannot transform your way out of trouble for small counts

Why you cannot transform your way out of trouble for small counts IntroductionIn modern statistics, count data are conventionally analyzed by specifying a distributional assumption that implies a mean–variance relationship, typically done via generalized linear models (McCullagh and Nelder, ) and its various extensions. However, many applied researchers with little statistical training persist with the older approach of transforming data and fitting a linear model assuming equal variance. Indeed, transformation is the only method of dealing with heteroscedasticity that is taught in most introductory statistics courses, and is still occasionally advocated in the applied literature (Ives, ).A particular motivation for revisiting this issue is the analysis of multivariate abundance data in ecology (Warton et al., ) as in Table . Counts of the abundance of different taxonomic groups are recorded at different sites, and we are primarily interested in making simultaneous inferences across many taxonomic groups in a community, concerning the effect of some site treatment. A key property for the purpose of this article is that the response variable is discrete with many zeros, since not every taxon is observed at every site. While extensions of the generalized linear model have recently been proposed by several authors (Warton, ; Ovaskainen et al., ; Hui et al., ), the convention in http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Biometrics Wiley

Why you cannot transform your way out of trouble for small counts

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Publisher
Wiley Subscription Services, Inc., A Wiley Company
Copyright
© 2018, The International Biometric Society
ISSN
0006-341X
eISSN
1541-0420
D.O.I.
10.1111/biom.12728
Publisher site
See Article on Publisher Site

Abstract

IntroductionIn modern statistics, count data are conventionally analyzed by specifying a distributional assumption that implies a mean–variance relationship, typically done via generalized linear models (McCullagh and Nelder, ) and its various extensions. However, many applied researchers with little statistical training persist with the older approach of transforming data and fitting a linear model assuming equal variance. Indeed, transformation is the only method of dealing with heteroscedasticity that is taught in most introductory statistics courses, and is still occasionally advocated in the applied literature (Ives, ).A particular motivation for revisiting this issue is the analysis of multivariate abundance data in ecology (Warton et al., ) as in Table . Counts of the abundance of different taxonomic groups are recorded at different sites, and we are primarily interested in making simultaneous inferences across many taxonomic groups in a community, concerning the effect of some site treatment. A key property for the purpose of this article is that the response variable is discrete with many zeros, since not every taxon is observed at every site. While extensions of the generalized linear model have recently been proposed by several authors (Warton, ; Ovaskainen et al., ; Hui et al., ), the convention in

Journal

BiometricsWiley

Published: Jan 1, 2018

Keywords: ; ; ; ;

References

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