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

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
• multicollinearity
• correlation
• multilevel models
• hierarchical linear models
• centering

Article information

Conflict of Interest Disclosure: Each author signed a form for disclosure of potential conflicts of interest. No authors reported any financial or other conflicts of interest in relation to the work described.

Ethical Principles: The authors affirm having followed professional ethical guidelines in preparing this work. These guidelines include obtaining informed consent from human participants, maintaining ethical treatment and respect for the rights of human or animal participants, and ensuring the privacy of participants and their data, such as ensuring that individual participants cannot be identified in reported results or from publicly available original or archival data.

Funding: This material is based upon work supported by the National Science Foundation Graduate Research Fellowship under [Grant No. 1937963]. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.

Role of the Funders/Sponsors: None of the funders or sponsors of this research had any role in the design and conduct of the study; collection, management, analysis, and interpretation of data; preparation, review, or approval of the manuscript; or decision to submit the manuscript for publication.

Acknowledgments: The ideas and opinions expressed herein are those of the authors alone, and endorsement by the authors’ institution or the National Science Foundation is not intended and should not be inferred.

Data availability statement: Code for data generation is available in the Online Code Supplement.

Notes

1 See Snijders and Bosker (2012), section 3.6.2, for greater detail.

2 Throughout this paper, full information maximum likelihood (FIML) estimation is synonymous with maximum likelihood estimation (MLE), as the two are equivalent in this case.

Additional information

Funding

This material is based upon work supported by the National Science Foundation Graduate Research Fellowship under [Grant No. 1937963].