title: The impact of centering first-level predictors on individual and contextual effects in multilevel data analysis.
abstract: BACKGROUND
  Multilevel data analysis is a powerful analytical tool. Properly applying the models and correctly interpreting the findings are two interrelated general issues in using multilevel modeling (MLM). There are two specific issues when using MLM: (a) separating the individual-level effects of a predictor variable from its contextual effects and (b) centering first-level predictor variables. This can have major implications for interpreting the results at higher levels, and its impact on second-level interpretation is not always apparent.
  
  
  OBJECTIVE
  The major purposes of this article are to show how to separate organizational-level effects from individual-level effects and to show how first-level centering decisions affect the interpretation of second-level coefficients.
  
  
  METHODS
  The hierarchical linear models (HLM) are used to analyze a hypothetical data set with 385 patients nested within 10 hospitals, using uncentered, group-mean-centered, and grand-mean-centered versions of the predictor variable.
  
  
  RESULTS
  Uncentered and grand-mean-centered models are equivalent, but group-mean-centered models are not equivalent to the other two. For the grand-mean-centered and uncentered models, second-level coefficients provide correct estimates of the individual effect and the contextual effect when the contextual predictor variable is included in the second-level model. The group-mean-centered model leads to a second-level coefficient where individual-level effects are confounded with contextual-level effects.
  
  
  CONCLUSIONS
  There is no single best answer to the question of whether to use group-mean centering or grand-mean centering. The theory and specific questions to be answered should be the researcher's guide to selecting which centering approach to use. Understanding the implications of first-level centering is essential to interpreting second-level coefficients correctly.
authors.affiliation: School of Nursing, University at Buffalo, State University of New York, 920 Kimball Tower, Buffalo, NY 14214, USA. nurwu@buffalo.edu
authors.forename: Yow-Wu B
authors.initials: YW
authors.lastname: Wu
authors.forename: Powhatan J
authors.initials: PJ
authors.lastname: Wooldridge
mesh_terms: D003627:Data Interpretation, Statistical; D006760:Hospitalization; D006801:Humans; D007902:Length of Stay / Q000706:statistics & numerical data*; D016014:Linear Models