Empirical Characteristics of Centering Methods for Level-I Predictor Variables in HLM

Abstract

Research has suggested that important research questions can be addressed with meaningful interpretations using hierarchical linear modeling. The proper interpretation of results, however, is invariably linked to the choice of centering for the Level-I predictor variables which produce the outcome measures for the Level-2 regression analysis. In this study, three centering methods (uncentered, group mean, and grand mean) were compared using Read93 and Lunch Status as Level-I predictor variables of ITBS94 reading test scores. The reliability estimates, or how accurately the sample estimate represents the population value, differed among the three centering methods. It was found that the group mean centering method provided the better reliability estimate. When using outcome measures based upon these three centering methods in a Level-2 analysis using two predictors, Gradrate and Percent Advdip, the group mean centering method indicated a more reliable estimate, but the grand mean centering method explained more between school variance. In fact, the gamma regression coefficients were markedly different, and the amount of variance explained was no longer consistent across the centering methods. These findings indicate that the choice of centering method for Level-I predictor variables can affect empirical findings in HLM.