Neglected biological patterns in the residuals A behavioural ecologist's guide to co-operating with heteroscedasticity
Neglected biological patterns in the residuals A behavioural ecologist's guide to co-operating with heteroscedasticity
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DOI：
10.1007/s00265-011-1254-7
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发表时间：
2011-12-01
影响因子：
2.3
通讯作者：
Nakagawa, Shinichi
中科院分区：
文献类型：
--
作者：
Cleasby, Ian R.;Nakagawa, Shinichi
线性回归模型的基本假设之一是误差具有恒定方差（即，homoscedastic）。当这个假设被违反时，回归的标准误差可能会有偏差和不一致，这意味着相关的p值和95%置信区间不能被信任。同方差的假设是出于统计原因而不是生物原因;在大多数真实的数据集中，可能存在某种形式的异方差。然而，一项对行为生态学文献的调查显示，只有约5%的文章明确提到了异方差性，剩下95%的文章显然没有异方差性。这些结果强烈表明，异方差的患病率是广泛的行为生态学内的报告。本文的目的是提高行为生态学家之间的异方差性的认识。使用局部的例子，从行为生态学领域，如两性异形和动物的个性，我们强调考虑异方差的生物学重要性。我们还强调，研究人员应该更加关注他们的数据的方差，并考虑哪些因素可能导致异方差。此外，我们还介绍了一些处理异方差的简单方法。我们关注的两种方法是：（1）在广义最小二乘（GLS）框架内引入方差函数来模拟异方差的函数形式;（2）异方差一致性标准误差（HCSE）估计，当异方差的函数形式未知时可以使用。通过案例研究，我们展示了这两种方法如何影响线性回归模型的输出。最后，我们希望更多的研究人员将异方差视为正在研究的特定生物过程的额外信息的重要来源，而不是统计分析的障碍。
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.