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Journal article

Inference in Generalized Additive Mixed Models by Using Smoothing Splines

Lin X, Zhang D ...see all

Source Journal of the Royal Statistical Society. Series B (Statistical Methodology) J. R. Statist. Soc. B, vol. 61, issue 2 (1999) pp. 381-400

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Abstract

JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org. Summary. 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 flexible functional dependence of an outcome variable on covariates by using nonparametric regression, while accounting for correlation between observations by using random effects. We estimate nonparametric functions by using smoothing splines and jointly estimate smoothing parameters and variance components by using marginal quasi-likelihood. Because numerical integration is 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 method proposed 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 by 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 we evaluate its performance through simulation.

Author-supplied keywords

  • Correlated data
  • Generalized linear mixed models
  • Laplace approximation
  • Marginal quasi-likelihood
  • Nonparametric regression
  • Penalized quasi-likelihood
  • Smoothing parameters
  • Variance components

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Authors

  • Xihong Lin

  • Daowen Zhang

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