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Related Experiment Videos

Measuring explained variation in linear mixed effects models.

Ronghui Xu1

  • 1Department of Biostatistics, Harvard School of Public Health and Dana-Farber Cancer Institute, 44 Binney Street, Boston, MA 02115, USA. rxu@jimmy.harvard.edu

Statistics in Medicine
|November 6, 2003
PubMed
Summary
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Researchers generalized the R(2) measure for linear regression to linear mixed effects models. This helps quantify explained variance in complex studies, offering new tools for statistical analysis.

Area of Science:

  • Statistics
  • Biostatistics
  • Clinical Trials

Background:

  • The R(2) measure is widely used in linear regression to assess model fit.
  • Linear mixed effects models are increasingly employed in complex study designs, such as cluster-randomized trials.
  • Quantifying explained variance in linear mixed models is crucial for accurate interpretation of study results.

Purpose of the Study:

  • To generalize the R(2) measure for linear regression to linear mixed effects models.
  • To develop and evaluate methods for quantifying covariate-explained variation in linear mixed models.
  • To provide easily implementable measures for assessing model fit in complex statistical analyses.

Main Methods:

  • Generalization of the R(2) measure for linear regression to linear mixed effects models.

Related Experiment Videos

  • Development of three types of measures: variance-based, residual sum of squares-based, and Kullback-Leibler information gain-based.
  • Monte Carlo simulations to evaluate the performance of the proposed measures.

    • Main Results:

    • The proposed generalized R(2) measures effectively quantify explained variation in linear mixed models.
    • All three types of measures demonstrated good performance in simulations.
    • The measures are readily obtainable from standard statistical software.

    Conclusions:

    • The generalized R(2) measures provide valuable tools for assessing model fit in linear mixed effects models.
    • These measures are applicable to various complex study designs, including cluster-randomized trials.
    • The study offers practical methods for researchers to better understand and report the explanatory power of their models.