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Related Experiment Videos

Testing random effects in the linear mixed model using approximate bayes factors.

Benjamin R Saville1, Amy H Herring

  • 1Department of Biostatistics, Vanderbilt University School of Medicine, S-2323 Medical Center North, Nashville, Tennessee 37232-2158, USA. benjamin.r.saville@vanderbilt.edu

Biometrics
|September 2, 2008
PubMed
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This study introduces a novel Bayes factor approach for testing random effects in linear mixed models. The method simplifies model selection by efficiently approximating complex integrals, offering a robust solution for statistical analysis.

Area of Science:

  • Statistics
  • Biostatistics
  • Statistical Modeling

Background:

  • Comparing linear mixed models with varying random effects presents challenges.
  • Standard model selection criteria are often inadequate for these complex models.
  • Boundary testing issues complicate asymptotic distributions and Bayes factor approximations.

Purpose of the Study:

  • To develop a straightforward method for testing random effects in linear mixed models.
  • To address limitations of existing model selection criteria for models with different random effects.
  • To provide a robust approach for statistical model comparison.

Main Methods:

  • Proposing a Bayes factor approach for testing random effects.
  • Scaling random effects to residual variance and introducing a relative contribution parameter.

Related Experiment Videos

  • Utilizing closed-form solutions for integration and Laplace's method for approximation.
  • Developing a default prior distribution for the contribution parameter.

    • Main Results:

    • The proposed method simplifies the calculation of Bayes factors.
    • Integrals become low-dimensional and efficient to approximate.
    • Simulations demonstrate good properties for model selection.
    • The approach is illustrated on clinical trial and environmental study data.

    Conclusions:

    • The Bayes factor method offers a practical solution for testing random effects.
    • It overcomes limitations of standard methods when comparing models with different random effects.
    • The approach is applicable to real-world data, including clinical and environmental studies.