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Abstract:
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For multilevel data (e.g., students nested within schools), hierarchical linear models are used to examine the influence of individual (level 1) and cluster-level (level 2) covariates. Individual level exposure can have different effects at level 1 and level 2. Cluster mean centering can be used to decompose individual exposure into between-cluster (cluster means) and within-cluster (deviates from cluster means) components to estimate these different effects. A common practice in epidemiological studies is to estimate the association of a decomposed level 1 exposure of interest, while adjusting for possible confounders (at level 1 or level 2). Most methodological literature on cluster mean centering fails to provide guidance on whether level 1 confounders should also be decomposed. In practice, applied studies use various approaches: decomposing all, some, or none of the level 1 confounders. In this work, we use theoretical derivations and simulations studies to demonstrate bias in estimating the effects of a level 1 exposure of interest as a function of confounder specification in hierarchical linear models, under various scenarios.
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