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A note on permutation tests for variance components in multilevel generalized linear mixed models.

Garrett M Fitzmaurice1, Stuart R Lipsitz, Joseph G Ibrahim

  • 1Harvard Medical School, Boston, MA, USA. fitzmaur@hsph.harvard.edu

Biometrics
|April 4, 2007
PubMed
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A new permutation test accurately controls Type I error rates for testing random effects variance components in generalized linear mixed models. This method is more powerful than existing chi-square mixture tests for multilevel data analysis.

Area of Science:

  • Statistics
  • Biostatistics
  • Multilevel Modeling

Background:

  • Generalized linear mixed models (GLMMs) are widely used for analyzing multilevel data.
  • Testing for the presence of random effects (variance components) is crucial in GLMM applications.
  • Standard asymptotic tests for zero variance components often violate assumptions, leading to incorrect Type I error rates.

Purpose of the Study:

  • To propose a novel permutation test for accurately assessing the significance of random effects variance components in GLMMs.
  • To address the limitations of traditional chi-square based tests under the null hypothesis.

Main Methods:

  • Development of a permutation test by randomly permuting indices at a specific model level.
  • Evaluation of the proposed test's Type I error rate and power through simulation studies.

Related Experiment Videos

  • Comparison with tests utilizing mixtures of chi-square distributions.

    • Main Results:

    • The proposed permutation test maintains the correct Type I error rate under the null hypothesis.
    • Simulation results indicate superior power compared to tests based on chi-square distributions.
    • The test is effective in practical applications, as demonstrated with sleep disturbance data.

    Conclusions:

    • The permutation test offers a reliable and more powerful alternative for testing random effects variance components in GLMMs.
    • This method provides accurate statistical inference for multilevel data analysis.
    • The approach is applicable to various fields dealing with hierarchical data structures.