Neglected biological patterns in the residuals |
| |
Authors: | Ian R Cleasby Shinichi Nakagawa |
| |
Institution: | (1) Department of Animal and Plant Sciences, University of Sheffield, Western Bank, Sheffield, S10 2TN, UK;(2) Department of Zoology, University of Otago, 340 Great King Street, PO Box 56, Dunedin, New Zealand |
| |
Abstract: | One of the fundamental assumptions underlying linear regression models is that the errors have a constant variance (i.e.,
homoscedastic). When this assumption is violated, standard errors from a regression can be biased and inconsistent, meaning
that the associated p values and 95% confidence intervals cannot be trusted. The assumption of homoscedasticity is made for statistical reasons
rather than biological reasons; in most real datasets, some form of heteroscedasticity is likely to exist. However, a survey
of the behavioural ecology literature showed that only about 5% of articles explicitly mentioned heteroscedasticity, leaving
95% of articles in which heteroscedasticity was apparently absent. These results strongly indicate that the prevalence of
heteroscedasticity is widely under-reported within behavioural ecology. The aim of this article is to raise awareness of heteroscedasticity
amongst behavioural ecologists. Using topical examples from fields in behavioural ecology such as sexual dimorphism and animal
personality, we highlight the biological importance of considering heteroscedasticity. We also emphasize that researchers
should pay closer attention to the variance in their data and consider what factors could cause heteroscedasticity. In addition,
we introduce some simple methods of dealing with heteroscedasticity. The two methods we focus on are: (1) incorporating variance
functions within a generalised least squares (GLS) framework to model the functional form of heteroscedasticity and; (2) heteroscedasticity-consistent
standard error (HCSE) estimators, which can be used when the functional form of heteroscedasticity is unknown. Using case
studies, we show how both methods can influence the output from linear regression models. Finally, we hope that more researchers
will consider heteroscedasticity as an important source of additional information about the particular biological process
being studied, rather than an impediment to statistical analysis. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|