Performance of likelihood-based estimation methods for multilevel binary regression models

By means of a fractional factorial simulation experiment, we compare the performance of penalised quasi-likelihood (PQL), non-adaptive Gaussian quadrature and adaptive Gaussian quadrature in estimating parameters for multilevel logistic regression models. The comparison is done in terms of bias, mean-squared error (MSE), numerical convergence and computational efficiency. It turns out that in terms of MSE, standard versions of the quadrature methods perform relatively poorly in comparison with PQL.