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A semi-parametric Bayesian approach to generalized linear mixed models

K P Kleinman1, J G Ibrahim

  • 1New England Research Institutes, Watertown, MA 02172, USA.

Statistics in Medicine
|December 5, 1998
PubMed
Summary
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This study introduces a novel generalized linear mixed model (GLMM) approach for correlated, non-normal data. By incorporating non-parametric prior distributions for random effects, it offers more flexible and exact statistical inference in longitudinal data analysis.

Area of Science:

  • Statistics
  • Biostatistics
  • Longitudinal Data Analysis

Background:

  • Linear mixed effects models are standard for repeated measures but assume normal errors.
  • Generalized linear models handle non-normal errors but assume independence.
  • Generalized linear mixed models (GLMMs) combine these but often use approximate frequentist methods.

Purpose of the Study:

  • To extend the generalized linear mixed model (GLMM) by incorporating non-parametric prior distributions for random effects.
  • To provide a computationally feasible Bayesian approach for analyzing correlated data with non-normal errors.
  • To enable more exact inference beyond asymptotic assumptions.

Main Methods:

  • Utilized a Dirichlet process prior for the general distribution of random effects within the GLMM framework.

Related Experiment Videos

  • Employed Markov chain Monte Carlo (MCMC) methods, specifically the Gibbs sampler, for computational implementation.
  • Extended the approach to accommodate more general population models.

    • Main Results:

    • Developed a flexible GLMM framework accommodating non-parametric random effects distributions.
    • Demonstrated the computational feasibility of Bayesian inference using MCMC for these extended models.
    • The proposed method allows for 'exact' inference, overcoming limitations of frequentist approximations.

    Conclusions:

    • The proposed non-parametric Bayesian GLMM offers a powerful alternative for analyzing complex longitudinal and correlated data.
    • This approach enhances statistical modeling flexibility and inference accuracy.
    • Facilitates robust analysis where traditional parametric assumptions for random effects may not hold.