title: Centering Predictor Variables in Three-Level Contextual Models.
abstract: Hierarchical data are becoming increasingly complex, often involving more than two levels. Centering decisions in multilevel models are closely tied to substantive hypotheses and require researchers to be clear and cautious about their choices. This study investigated the implications of group mean centering (i.e., centering within context; CWC) and grand mean centering (CGM) of predictor variables in three-level contextual models. The goals were to (a) determine equivalencies in the means and variances across the centering options and (b) use the algebraic relationships between the centering choices to clarify the interpretation of the estimated parameters. We provide recommendations to assist the researcher in making centering decisions for analysis of three-level contextual models.
authors.affiliation: a College of Human Medicine, Michigan State University.
authors.forename: Ahnalee M
authors.initials: AM
authors.lastname: Brincks
authors.affiliation: b University of California , Los Angeles.
authors.forename: Craig K
authors.initials: CK
authors.lastname: Enders
authors.affiliation: c Department of Psychology , University of Miami.
authors.forename: Maria M
authors.initials: MM
authors.lastname: Llabre
authors.affiliation: c Department of Psychology , University of Miami.
authors.forename: Rebecca J
authors.initials: RJ
authors.lastname: Bulotsky-Shearer
authors.affiliation: d Miller School of Medicine, University of Miami.
authors.forename: Guillermo
authors.initials: G
authors.lastname: Prado
authors.affiliation: d Miller School of Medicine, University of Miami.
authors.forename: Daniel J
authors.initials: DJ
authors.lastname: Feaster
mesh_terms: D000465:Algorithms; D002652:Child Behavior; D002675:Child, Preschool; D003627:Data Interpretation, Statistical; D003657:Decision Making; D018479:Early Intervention, Educational; D005260:Female; D006801:Humans; D016014:Linear Models; D008297:Male; D015999:Multivariate Analysis; D011581:Psychological Tests; D012919:Social Behavior
keywords: Multilevel modeling; centering; hierarchical linear modeling