Robust estimation in generalised linear mixed models

We propose robust methods for estimation of parameters of interest in an extended generalised linear mixed model, in which only the conditional means of the responses given the random effects are specified. A first‐step estimator θ of the vector θ of parameters is obtained by solving a system of estimating equations. It is shown that θ is consistent. If, furthermore, the conditional variances are correctly specified, a second‐step estimator, θ, can be obtained by solving a system of optimal estimating equations whose coefficients are estimated by θ. It is shown that θ maintains the asymptotic optimality. Simulations also indicate solid improvement of θ over θ. Two examples involving real data analysis are considered. The methods are developed under a more general framework so that they may be applied to more general estimation problems.