On likelihood inference in binary mixed model with an application to COPD data

In the cluster regression set up, it is common to collect binary responses from the individuals in a large number of clusters, where the responses of the individuals of a given cluster are structurally correlated through a common random effect shared by the individuals. Obtaining consistent as well as efficient estimates of the parameters of the binary mixed model has, however, proven to be difficult. In this paper, we apply a simulation based likelihood estimation method that provides consistent as well as efficient estimates of the parameters of the model. The performance of the simulated likelihood estimators is compared with that of the simulated moment estimators (J. Amer. Statist. Assoc. 93 (1998) 720) through a Monte Carlo study. Also, the likelihood estimation methodology is illustrated by using chronic obstructive pulmonary disease data from Cohen (Amer. J. Epidemiol. 112 (1980) 274).