An assessment of estimation methods for generalized linear mixed models with binary outcomes.

Area of Science:

• Statistics
• Computational Statistics

Background:

• Generalized linear mixed models (GLMMs) present analytical challenges.
• Existing likelihood-based methods can yield biased estimates, particularly for binary clustered data with small cluster sizes.
• Bayesian methods, while possessing good frequentist properties, are computationally intensive and require specialized code.

Purpose of the Study:

• To introduce and evaluate a modified hybrid approach for GLMMs.
• To compare its performance against existing likelihood-based methods for binary outcomes.
• To provide a more practical and accurate estimation strategy for GLMMs.

Main Methods:

• A modified hybrid approach combining Bayesian estimation for variance components and Laplacian estimation for regression coefficients.
• Evaluation of adaptive Gaussian quadrature and Laplacian approximation methods.
• Application to three real-world datasets and simulation studies.

Main Results:

• Adaptive Gaussian quadrature and Laplacian approximation demonstrate high accuracy for moderate to large numbers of observations per random effect.
• Adaptive Gaussian quadrature is preferred as the number of observations per random effect increases.
• The hybrid approach shows performance comparable to the Laplace method, with advantages in cases of very sparse random effects.

Conclusions:

• The proposed hybrid approach offers a viable alternative for GLMM analysis, particularly for binary outcomes.
• It provides accurate estimations and can be superior in scenarios with sparse random effects.
• This method bridges the gap between likelihood and Bayesian techniques, enhancing practical applicability.