Centering or Not Centering in Multilevel Models? The Role of the Group Mean and the Assessment of Group Effects

Abstract

In multilevel regression, centering the model variables produces effects that are different and sometimes unexpected compared with those in traditional regression analysis. In this article, the main contributions in terms of meaning, assumptions, and effects underlying a multilevel centering solution are reviewed, emphasizing advantages and critiques of this approach. In addition, in the spirit of Manski, contextual and correlated effects in a multilevel framework are defined to detect group effects. It is shown that the decision of centering in a multilevel analysis depends on the way the variables are centered, on whether the model has been specified with or without cross-level terms and group means, and on the purposes of the specific analysis.

Disfluent Responses to Job Interview Questions and What They Entail

“…We thus modeled candidates as a random effect. We centered the predictors using the grand mean centering method (Hox, 2002;Paccagnella, 2006;West, Aiken, & Krull, 1996). We first calculated a null model, with candidates modeled as random effect but no predictors.…”

First signs of transition: The parallel decline of early baptism and early mortality in the province of Padua (northeast Italy), 1816‒1870

“…We tend to consider these cases to be the result of an error in the transcription of the information rather than real cases of omission of baptism. 24 For an extensive description of the technique of centering predictor variables in multilevel models, see Paccagnella (2006) and Enders and Tofighi (2007). Including in the model as explanatory variables both the mean (or median) value and the individual value (rather than the difference between individual value and mean (or median), the estimations of regression coefficients are systematically biased, as the two explanatory variables are systematically correlated.…”

An Overview of Classroom Composition Research on Social-Emotional Outcomes: Introduction to the Special Issue

“…To reduce problems of collinearity between the individual characteristic and the compositional characteristic (aggregated individual data), several authors proposed to center variables (e.g., Algina & Swaminathan, 2011;Enders & Tofighi, 2007;Hox, 2010). In general, the decision between grand-mean (i.e., individual difference from the overall mean) or group-mean (i.e., individual difference from the corresponding group mean) centering should be based on content considerations and on the aim of the analyses (Lüdtke, Robitzsch, Trauwein, & Kunter, 2009;Paccagnella, 2006). Group-mean centering is often recommended in the case of "within-group effects," such as the "frog-pond" effect (Davis, 1966) or the aforementioned BFLPE.…”