Understanding the Consequences of Collinearity for Multilevel Models: The Importance of Disaggregation Across Levels

Multivariate Behav Res. 2024 May 9:1-23. doi: 10.1080/00273171.2024.2315549. Online ahead of print.

Abstract

In multilevel models, disaggregating predictors into level-specific parts (typically accomplished via centering) benefits parameter estimates and their interpretations. However, the importance of level-specificity has been sparsely addressed in multilevel literature concerning collinearity. In this study, we develop novel insights into the interactivity of centering and collinearity in multilevel models. After integrating the broad literatures on centering and collinearity, we review level-specific and conflated correlations in multilevel data. Next, by deriving formal relationships between predictor collinearity and multilevel model estimates, we demonstrate how the consequences of collinearity change across different centering specifications and identify data characteristics that may exacerbate or mitigate those consequences. We show that when all or some level-1 predictors are uncentered, slope estimates can be greatly biased by collinearity. Disaggregation of all predictors eliminates the possibility that fixed effect estimates will be biased due to collinearity alone; however, under some data conditions, collinearity is associated with biased standard errors and random effect (co)variance estimates. Finally, we illustrate the importance of disaggregation for diagnosing collinearity in multilevel data and provide recommendations for the use of level-specific collinearity diagnostics. Overall, the necessity of disaggregation for identifying and managing collinearity's consequences in multilevel models is clarified in novel ways.

Keywords: Collinearity; centering; correlation; hierarchical linear models; multicollinearity; multilevel models.