Group-mean-centering independent variables in multi-level models is dangerous

Group-mean centering of independent variables in multi-level models is widely practiced and widely recommended. For example, in cross-national studies of educational performance, family background is scored as a deviation from the country mean for student's family background. We argue that this is usually a serious mis-specification, introducing bias and random measurement error with all their attendant vices. We examine five diverse examples of "real world" analyses using large, high quality datasets on topics of broad interest in the social sciences. In all of them, consistent with much (but not all) of the technical literature, group-mean centering substantially distorts results. Moreover the distortions are large, substantively important differences pointing towards seriously incorrect interpretations of important social processes. We therefore recommend that group-mean centering be abandoned.