Please Note: This seminar will be held online.
Approximate Marginal Likelihood Inference for Cluster-Dependent Data
Cluster-dependent data arise when repeated measurements are taken on subjects. Generalized non-linear regression models, including the popular generalized linear mixed model, for these data are used extensively in ecology, medicine, pharmacology, psychology, and really pretty much any field you can think of. Inferences in these models are based on a marginal likelihood which involves an intractable integral. The marginal likelihood must be approximated in order to make inferences. In this talk I discuss how quadrature is, should be, and should not be used to approximate the marginal likelihood, in terms of the convergence properties of the resulting maximum likelihood estimators. The Laplace approximation is often appropriate, and when it isn’t, adaptive Gaussian quadrature works incredibly well. In contrast, any non-adaptive quadrature yields inconsistent estimators in any statistical model satisfying weak concentration conditions (local asymptotic normality), and is not merely less efficient than its adaptive version.