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Summary
This summary is machine-generated.

For complex generalized linear mixed models, SAS GLIMMIX (Laplace) and SuperMix (Gaussian quadrature) show superior performance. These methods offer better accuracy, precision, convergence, and speed for analyzing correlated random effects in logistic regression.

Keywords:
Adaptive Gauss-Hermite integrationAntismoking advertisingLaplace approximationMixed-effects logistic regressionPenalized quasi-likelihood

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Area of Science:

  • Statistics
  • Biostatistics
  • Computational Statistics

Background:

  • Generalized linear mixed models (GLMMs) are estimated using penalized quasi-likelihood, Laplace, or Gauss-Hermite methods.
  • Previous studies on mixed-effects logistic regression focused on simpler models with fewer random effects.
  • Complex models with multiple correlated random effects often face computational challenges and convergence issues.

Purpose of the Study:

  • To comprehensively review the pros and cons of different GLMM estimation methods.
  • To compare the performance of penalized quasi-likelihood, Laplace, and Gauss-Hermite methods across statistical packages using simulations.
  • To evaluate these methods in the context of two- and three-level logistic regression models with multiple correlated random effects.

Main Methods:

  • Simulation study comparing penalized quasi-likelihood, Laplace, and Gauss-Hermite estimation methods.
  • Analysis of two- and three-level logistic regression models with at least three correlated random effects.
  • Application of findings to a real-world dataset on smoking status and anti-tobacco advertisement exposure.

Main Results:

  • Parameter estimates for models with multiple random effects can vary significantly between statistical packages, even with the same estimation method.
  • SAS GLIMMIX using the Laplace method and SuperMix using Gaussian quadrature demonstrated strong performance.
  • These two packages excelled in accuracy, precision, convergence rates, and computational speed.

Conclusions:

  • SAS GLIMMIX (Laplace) and SuperMix (Gaussian quadrature) are recommended for complex GLMMs with multiple correlated random effects.
  • The choice between these packages may depend on specific considerations related to sample size.
  • Accurate and efficient estimation of complex GLMMs is crucial for reliable statistical inference.