Why you cannot transform your way out of trouble for small counts
Why you cannot transform your way out of trouble for small counts
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DOI：
10.1111/biom.12728
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发表时间：
2018-03-01
期刊：
影响因子：
1.9
通讯作者：
Warton, David I.
中科院分区：
文献类型：
--
作者：
Warton, David I.
虽然数据变换是满足线性建模假设的常见策略，但理论结果表明，不能合理地期望变换能够稳定小计数的方差。在广泛的假设下，随着计数变小，表明满足 g(0)=0 的单调变换 g() 下方差与均值成正比，少数病理情况除外。建议的经验法则是，如果许多预测计数小于 1，则即使对于精心选择的转换，也不能合理地期望数据转换能够稳定方差。这一结果对于应用科学中经常实施的计数分析具有明显的意义，特别是对于生态学中的多变量分析。生态学中经常收集多变量离散数据，通常具有很大比例的零，目前广泛使用的分析方法不考虑观察之间或响应之间的方差差异。模拟表明，在这种情况下，如果采样设计不平衡，在单变量情况下，未能考虑均值-方差关系可能会产生特别严重的后果。
While data transformation is a common strategy to satisfy linear modeling assumptions, a theoretical result is used to show that transformation cannot reasonably be expected to stabilize variances for small counts. Under broad assumptions, as counts get smaller, it is shown that the variance becomes proportional to the mean under monotonic transformations g() that satisfy g(0)=0, excepting a few pathological cases. A suggested rule-of-thumb is that if many predicted counts are less than one then data transformation cannot reasonably be expected to stabilize variances, even for a well-chosen transformation. This result has clear implications for the analysis of counts as often implemented in the applied sciences, but particularly for multivariate analysis in ecology. Multivariate discrete data are often collected in ecology, typically with a large proportion of zeros, and it is currently widespread to use methods of analysis that do not account for differences in variance across observations nor across responses. Simulations demonstrate that failure to account for the mean-variance relationship can have particularly severe consequences in this context, and also in the univariate context if the sampling design is unbalanced.