Packard Gary C
Department of Biology, Colorado State University, Fort Collins, CO 80523, USA.
Zoology (Jena). 2017 Aug;123:115-120. doi: 10.1016/j.zool.2017.07.005. Epub 2017 Jul 19.
Logarithmic transformation is often assumed to be necessary in allometry to accommodate the kind of variation that accompanies multiplicative growth by plants and animals; and the traditional approach to allometric analysis is commonly believed to have important application even when the bivariate distribution of interest is curvilinear on the logarithmic scale. Here I examine four arguments that have been tendered in support of these perceptions. All the arguments are based on misunderstandings about the traditional method for allometric analysis and/or on a lack of familiarity with newer methods of nonlinear regression. Traditional allometry actually has limited utility because it can be used only to fit a two-parameter power equation that assumes lognormal, heteroscedastic error on the original scale. In contrast, nonlinear regression can fit two- and three-parameter power equations with differing assumptions about structure for error directly to untransformed data. Nonlinear regression should be preferred to the traditional method in future allometric analyses.
在异速生长研究中，通常认为对数变换是必要的，以适应动植物乘法生长所伴随的那种变化；并且，即使感兴趣的双变量分布在对数尺度上是曲线的，传统的异速生长分析方法通常也被认为具有重要应用。在此，我审视了为支持这些观点而提出的四个论据。所有这些论据都基于对传统异速生长分析方法的误解和/或对更新的非线性回归方法缺乏了解。传统异速生长分析实际上效用有限，因为它只能用于拟合一个双参数幂方程，该方程假设在原始尺度上存在对数正态、异方差误差。相比之下，非线性回归可以直接对未变换的数据拟合具有不同误差结构假设的双参数和三参数幂方程。在未来的异速生长分析中，非线性回归应优于传统方法。
