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Quantifying explained variance in multilevel models: An integrative framework for defining R-squared measures.

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Summary
This summary is machine-generated.

This study introduces a new framework for multilevel model (MLM) R-squared measures, clarifying existing methods and offering new variance partitioning approaches. It aids researchers in selecting and interpreting effect sizes for practical significance.

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Area of Science:

  • Multilevel modeling
  • Statistical methods
  • Psychometrics

Background:

  • Existing R-squared measures for multilevel models (MLMs) lack clear analytic relationships and comprehensive variance partitioning.
  • Researchers face challenges in implementing and interpreting various MLM R-squared measures due to a lack of a unifying framework.

Purpose of the Study:

  • To develop an integrative framework for R-squared measures in MLMs with random intercepts and/or slopes.
  • To analytically relate existing measures and introduce new ones for a complete variance decomposition.
  • To provide tools for easier interpretation and implementation of MLM R-squared measures.

Main Methods:

  • Developed a comprehensive variance decomposition framework for MLM R-squared.
  • Analytically related 10 existing measures to 5 measures within the new framework.
  • Created a graphical representation for interpreting and comparing measures.

Main Results:

  • Established analytic relationships among existing MLM R-squared measures, identifying redundancies.
  • Introduced new total and level-specific measures to address previously unanswerable substantive questions.
  • Demonstrated the utility of the framework and a new R function (r2MLM) for calculating and interpreting measures.

Conclusions:

  • The proposed framework unifies MLM R-squared measures, filling gaps and clarifying relationships.
  • The graphical representation and R function facilitate the interpretation and reporting of effect sizes in MLMs.
  • This work enhances the practical significance and discoverability of research findings using multilevel models.