Approximation techniques for maximizing likelihood functions of generalized linear mixed models for binary response data


  • Julius Remi Dare Kings university ode omu osogbo Nigeria
  • Dawud Adebayo Agunbiade Olabisi Onabanjo University
  • Oludolapo Kehinde Famurewa Olabisi Onabanjo University
  • Olumide Sunday Adesina Kings University, Odeomu, Nigeria
  • Dayo Funmi Adedotun Olabisi Onabanjo University
  • Olatunde Iyaniwura Kings University,Odeomu





Generalized Linear Mixed Models, Adaptive Gauss-Hermit Quadrature, Likelihood Function, Binary Response, Medicine.


Evaluating Maximum likelihood estimates in Generalized Linear Mixed Models (GLMMs) has been a serious challenge due to some integral complexities encountered in maximizing its likelihood functions. It is computationally difficult to establish analytical solutions for the integrals. In view of this, approximation techniques would be needed. In this paper, various approximation techniques were examined including Laplace approximation (LA), Penalized Quasi likelihood (PQL) and Adaptive Gauss-Hermite Quadrature (AGQ) techniques. The performances of these methods were evaluated through both simulated and real-life data in medicine. The simulation results showed that the Adaptive Gauss-Hermit Quadrature approach produced better estimates when compared with PQL and LA estimation techniques based on some model selection criteria.





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