The danger of conflating level-specific effects of control variables when primary interest lies in level-2 effects.

Abstract

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.