CENTERING VARIABLES REFS Linear Mixed Models: Statnotes, from North Carolina State University, Public Administration Program

Mean-Centering Does Not Alleviate Collinearity Problems in Moderated Multiple Regression Models


centering variables - collinearity in interaction terms, SAS, animation, demo

Linear Mixed Models: Statnotes, from North Carolina State University, Public Administration Program: "Centering. It is customary to center data prior to running LMM or HLM. Centering means subtracting the mean, so means become zero. Two main types of centering are group mean centering and grand mean centering. For instance, in a study of PerformanceScore, there might be a PerformanceIndividualScore at level 1 and a PerformanceAgencyScore at level 2, where the latter was a mean score for all employees in an agency. The researcher might center PerformanceIndividualScore for individuals by centering on their group (agency) means, where groups were agencies, on the theory that group performance influenced individual performance and differences from the group means should therefore be the variable of interest. Or one could center each PerformanceIndividualScore on the grand mean of all such scores across agencies. Grand mean centering is preferred over group mean centering unless there is theoretical justification for the latter."

Grand mean centering often improves the interpretability of coefficients because "0" now has a meaning (ex., 0 income is mean income, whereas before centering, 0 income might be out of the range of actual observations). Group mean centering, in contrast, changes the meaning of coefficients in complex ways which make coefficients hard to interpret, as different mean values are subtracted from different sets of raw scores. As a result, with group mean centering it is not possible to recalculate output back to raw score interpretations. In essence, one is dealing with a different variable after group mean centering. Grand mean centered income, for instance, will yield different slopes but the same deviance and residual errors as uncentered raw data. Group mean centered income does not. Group mean centered income is no longer simple income but rather measures income deviation from group means. The researcher must examine his or her theoretical model and decide if that is really what was wanted for the "income" variable. As noted by Kreft, de Leeuw, and Aiken (1995), the choice of centering must be made on a theoretical rather than statistical basis, and "centering around the group mean amounts to fitting a different model from that obtained by centering around the grand mean or by using raw scores" (p. 1). Most LMM/HLM software packages support various types of automatic centering. Centering considerations are further discussed in Burton (1993) and Hoffman & Gavin (1998).