A Comparison of Estimation Methods for Multilevel Logistic Models

In this paper a comparison between Penalized Quasi Likelihood (PQL) and estimation by numerical integration is made for the analysis of two-level experimental binary data with two treatment conditions. The comparison between the estimation methods is made for three situations: randomization to treatment conditions at the cluster level, randomization at the person level with treatment by cluster interaction, and without such interaction. Criteria for comparison are convergence of the estimation process and improper estimates (i.e. unrealistic high point estimates), criteria concerning the point estimation (bias, variance, and mean squared error) and testing (bias of the point estimates and of the variances as reported by the software) of the treatment effect. The results show that non-convergence occurs more often when estimation is done by numerical integration. This method may also lead to improper estimates. First order PQL performs best in terms of point estimation of the treatment effect, but should not be used for testing. For the latter purpose second order PQL is more applicable.