Bell Andrew, Jones Kelvyn, Fairbrother Malcolm
1Sheffield Methods Institute, University of Sheffield, 219 Portobello, Sheffield, S1 4DP UK.
2School of Geographical Sciences, University of Bristol, University Road, Bristol, BS8 1SS UK.
Qual Quant. 2018;52(5):2031-2036. doi: 10.1007/s11135-017-0593-5. Epub 2017 Nov 7.
Kelley et al. argue that group-mean-centering covariates in multilevel models is dangerous, since-they claim-it generates results that are biased and misleading. We argue instead that what is dangerous is Kelley et al.'s unjustified assault on a simple statistical procedure that is enormously helpful, if not vital, in analyses of multilevel data. Kelley et al.'s arguments appear to be based on a faulty algebraic operation, and on a simplistic argument that parameter estimates from models with mean-centered covariates must be wrong merely because they are different than those from models with uncentered covariates. They also fail to explain why researchers should dispense with mean-centering when it is central to the estimation of fixed effects models-a common alternative approach to the analysis of clustered data, albeit one increasingly incorporated within a random effects framework. Group-mean-centering is, in short, no more dangerous than any other statistical procedure, and should remain a normal part of multilevel data analyses where it can be judiciously employed to good effect.
凯利等人认为，在多层次模型中对协变量进行组均值中心化是危险的，因为他们声称这会产生有偏差且具误导性的结果。相反，我们认为危险的是凯利等人对一个简单统计程序的无端抨击，这个统计程序在多层次数据分析中即便不是至关重要，也是非常有帮助的。凯利等人的论点似乎基于一个错误的代数运算，以及一个过于简单化的观点，即认为来自协变量均值中心化模型的参数估计一定是错误的，仅仅因为它们与来自协变量未中心化模型的参数估计不同。他们也未能解释为什么研究人员在固定效应模型估计（这是分析聚类数据的一种常见替代方法，尽管它越来越多地被纳入随机效应框架）的核心环节中应该摒弃均值中心化。简而言之，组均值中心化并不比任何其他统计程序更危险，并且在多层次数据分析中，如果能明智地运用，它应该仍然是正常的一部分且能产生良好效果。
