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Understanding the Consequences of Collinearity for Multilevel Models: The Importance of Disaggregation Across Levels
Haley E Yaremych1, Kristopher J Preacher1
1Department of Psychology & Human Development, Vanderbilt University.
Multivariate Behavioral Research
|May 9, 2024
Summary
Disaggregating predictors in multilevel models is crucial for understanding collinearity. Proper centering prevents bias in slope estimates, but careful diagnostics are still needed for standard errors and random effects.
Area of Science:
- Multilevel modeling
- Statistical analysis
- Quantitative psychology
Background:
- Centering predictors in multilevel models aids parameter interpretation.
- The impact of collinearity on multilevel models, especially concerning predictor centering, is under-explored.
Purpose of the Study:
- To investigate the interplay between predictor centering and collinearity in multilevel models.
- To offer novel insights into how centering strategies affect collinearity's consequences.
Main Methods:
- Integration of literature on centering and collinearity.
- Derivation of formal relationships between collinearity and multilevel model estimates.
- Analysis of level-specific and conflated correlations.
Main Results:
- Uncentered level-1 predictors can lead to significant slope estimate bias due to collinearity.
- Complete predictor disaggregation removes fixed effect bias from collinearity but may affect standard errors and random effects.
- Collinearity's impact varies with centering choices and data characteristics.
Conclusions:
- Disaggregation is essential for accurate collinearity diagnosis in multilevel data.
- Recommendations are provided for using level-specific collinearity diagnostics.
- The study clarifies the necessity of disaggregation for managing collinearity in multilevel models.
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