A hybrid estimator in nonlinear and generalised linear mixed effects models

A hybrid method that combines Laplace's approximation and Monte Carlo simulations to evaluate integrals in the likelihood function is proposed for estimation of the parameters in nonlinear mixed effects models that assume a normal parametric family for the random effects. Simulations show that these parametric estimates of fixed effects are close to the nonparametric estimates even though the mixing distribution is far from the assumed normal parametric family. An asymptotic theory of this hybrid method for parametric estimation without requiring the true mixing distribution to belong to the assumed parametric family is developed to explain these results. This hybrid method and its asymptotic theory are also extended to generalised linear mixed effects models.