The Implications of Centering in a Three-Level Multilevel Model

Hierarchical data are becoming increasingly complex, often involving more than two levels. This study investigated the implications of centering within context (CWC) and grand mean centering (CGM) in three distinct three-level models. The goals were to (1) determine equivalencies in the means and variances across the centering options, (2) identify the algebraic relationships between the three-level contextual models, and (3) clarify the interpretation of the estimated parameters. Artificial datasets were used for illustration. Centering decisions in multilevel models are closely tied to substantive hypotheses and require researchers to be clear and cautious about their choices. This work is designed to assist the researcher in making centering decisions for analysis of three-level hierarchical data