The danger of conflating level-specific effects of control variables when primary interest lies in level-2 effects
The danger of conflating level-specific effects of control variables when primary interest lies in level-2 effects
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DOI：
10.1111/bmsp.12194
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发表时间：
2019-12-19
影响因子：
2.6
通讯作者：
Cole, David A.
中科院分区：
文献类型：
--
作者：
Rights, Jason D.;Preacher, Kristopher J.;Cole, David A.
在多水平建模文献中，方法学家广泛承认，一个水平-1变量可以有不同的群内和群间效应，如果不分解这些效应，可能会产生一个无法解释的斜率估计值，这是两者的混合。然而，方法学家指出，如果实质性的兴趣仅在于2级预测变量的影响，则在模型中包括1级变量的合并斜率是没有问题的。研究人员通常遵循这一建议，并使用不分解1级控制变量影响的方法（例如，总平均值居中）时，检查水平-2预测因子的影响。本文的主要目的是表明这是一种危险的做法。当水平1变量的水平特异性效应不同时，如果不对它们进行分解，可能会严重影响水平2预测因子斜率的估计。我们从数学上说明了为什么会出现这种情况，并强调了可能加剧这种偏见的因素。我们证实了这些研究结果与模拟，并提出了一个实证的例子，显示如何这种扭曲可以严重改变实质性的结论。我们最终建议，简单地包括水平1变量的聚类均值作为控制将缓解问题。
In the multilevel modelling literature, methodologists widely acknowledge that a level-1 variable can have distinct within-cluster and between-cluster effects, and that failing to disaggregate these can yield a slope estimate that is an uninterpretable, conflated blend of the two. Methodologists have stated, however, that including conflated slopes of level-1 variables in a model is not problematic if substantive interest lies only in effects of level-2 predictors. Researchers commonly follow this advice and use methods that do not disaggregate effects of level-1 control variables (e.g., grand mean centering) when examining effects of level-2 predictors. The primary purpose of this paper is to show that this is a dangerous practice. When level-specific effects of level-1 variables differ, failing to disaggregate them can severely bias estimation of level-2 predictor slopes. We show mathematically why this is the case and highlight factors that can exacerbate such bias. We corroborate these findings with simulations and present an empirical example, showing how such distortions can severely alter substantive conclusions. We ultimately recommend that simply including the cluster mean of the level-1 variable as a control will alleviate the problem.