Inference in Generalized Additive Mixed Models

Abstract


Generalized additive mixed models are proposed for overdispersed and correlated data, which arise frequently in studies involving clustered, hierarchical and spatial designs. This class of models allows for flexible functional dependence of an outcome variable on covariates using nonparametric regression, while accounting for correlation among observations using random effects. We estimate nonparametric functions using smoothing splines, and jointly estimate smoothing parameters and variance components using marginal quasi-likelihood. In view of numerical integration often required by maximizing the objective functions, double penalized quasi-likelihood is proposed to make approximate inference. Frequentist and Bayesian inferences are compared. A key feature of the proposed method is that it allows us to make systematic inference on all model components within a unified parametric mixed model framework and can be easily implemented by fitting a working generalized linear mixed model using existing statistical software. A bias correction procedure is also proposed to improve the performance of double penalized quasi-likelihood for sparse data. We illustrate the method with an application to infectious disease data and evaluate its performance through simulation.

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