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This study introduces new R-squared measures for multilevel models (MLMs) with three or more levels, clarifying their relationships and computation across different predictor centering strategies.

Keywords:
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Area of Science:

  • Statistics
  • Quantitative Psychology

Background:

  • Multilevel models (MLMs) with three or more levels are increasingly used.
  • Existing R-squared measures for these complex models are limited.
  • Understanding explained variance and predictor centering effects is crucial.

Purpose of the Study:

  • To extend existing R-squared frameworks for MLMs to handle three or more levels.
  • To clarify analytic relationships between total and level-specific R-squared measures.
  • To explicate the impact of predictor centering on R-squared computation and interpretation.

Main Methods:

  • Extension of the Rights and Sterba two-level MLM R-squared framework to higher levels.
  • Mathematical and pedagogical clarification of total and level-specific R-squared relationships.
  • Demonstration of R-squared computation under various predictor centering strategies.

Main Results:

  • A general set of R-squared measures for MLMs with three or more levels is proposed.
  • Preexisting three-level measures are shown to be special cases of the new framework.
  • The framework accommodates all predictor centering strategies for R-squared calculation.

Conclusions:

  • The developed R-squared measures provide a comprehensive approach to quantifying explained variance in complex MLMs.
  • The study offers clarity on the interplay between R-squared, model levels, and centering strategies.
  • Associated software (r2mlm R package) is provided for practical application and visualization.