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Empirical assessment of the performance of four estimation methods used in Generalized linear mixed models with binary outcomes

Bruno E. Lokonon, Romain Glèlè Kakaï


Generalized linear mixed models are advanced statistical tools for modelling binary outcomes with random and fixed factors. However, parameters estimation is difficult since there is no analytical solution to maximize the likelihood function. This results in the development of several estimation methods. This study assessed through simulation the effect of intra-class correlation coefficients (ICC) and sample size at both individual and group level on the performance of four estimation methods in the frame of binary logistic mixed effects models. Increased valued of ICC (0.1, 0.25, 0.5), number of groups (N= 5, 10, 25,
75, 100) and group sizes (n= 25, 30, 50, 75, 100) were considered. For each combination of ICC, n and N, data were generated 500 times and on each dataset, the model is run using Penalized Quasi-Likelihood, Adaptative Gauss-Hermite Quadrature, Hierarchical Likelihood Method and Integrated Nested Laplace Approximation. The estimation methods were compared in terms of mean bias, mean-squared error, computing time and convergence. Results revealed that for all estimation methods considered, the mean bias of the estimates decreases when ICC increases in case of fixed effects while the contrary is noticed for the random effects. At least 5 groups and 25 to 30 observations per group are necessary to reach mean bias close to zero to estimate fixed effects. Meanwhile, at least 30 groups and 30 observations per group are required in case of random effects. Overall, the Bayesian method outperforms the other methods for both random and fixed effects


Binary multilevel models, Monte Carlo simulation, intra-class correlation coefficients, sample size, Bayesian analysis.

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