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Area of Science:

  • Multilevel modeling
  • Statistical analysis
  • Hierarchical data analysis

Background:

  • Hierarchical data structures often present confounding issues where upper-level factors bias lower-level predictor effects.
  • Unaddressed confounding leads to biased estimation of predictor effects.
  • Linear random intercept models can mitigate bias by separating effects into within- and between-components under specific assumptions.

Purpose of the Study:

  • To address unmeasured upper-level confounding in hierarchical data when lower-level predictor effects are moderated by another lower-level predictor.
  • To investigate methods for decomposing interaction terms into within- and between-components to handle confounding.
  • To compare the precision and robustness of different decomposition approaches.

Main Methods:

  • Decomposition of interaction terms into within- and between-components.
  • Centering product terms of predictors before or after multiplication.
  • Analysis using linear random intercept models.

Main Results:

  • Both decomposition approaches yield similar average estimates for interaction effects in linear models.
  • Decomposing by multiplying predictors first and then centering the product term offers greater precision.
  • This preferred method demonstrates increased robustness against misspecification of cross-level and upper-level effects.

Conclusions:

  • Decomposition of interaction terms into within- and between-components is crucial for addressing unmeasured upper-level confounding in hierarchical data.
  • The order of multiplication and centering significantly impacts the precision and robustness of the estimated interaction effects.
  • Prioritizing the multiplication-then-centering approach enhances the reliability of statistical analyses in complex hierarchical data structures.