Generalized additive models for longitudinal data

We introduce a class of models for longitudinal data by extending the generalized estimating equations approach of Liang and Zeger (1986) to incorporate the flexibility of nonparametric smoothing. The algorithm provides a unified estimation procedure for marginal distributions from the exponential family. We propose pointwise standard-error bands and approximate likelihood-ratio and score tests for inference. The algorithm is formally derived by using the penalized quasilikelihood framework. Convergence of the estimating equations and consistency of the resulting solutions are discussed. We illustrate the algorithm with data on the population dynamics of Colorado potato beetles on potato plants. Nous introduisons une classe de modeles pour les donnees longitudinales en etendant l'approche des equations d'estimation generalisees de Liang et Zeger (1986) afin d'incorporer la flexibility du lissage non-parametrique. L'algorithme fournit une procedure d'estimation unifiee pour les distributions marginales de la famille exponentielle. Nous proposons des bandes d'erreur standard par point et des tests de taux de vraisemblance approximative et de score pour l'inference. L'algorithme est formellement derive en utilisant le cadre de reference de la quasi-vraisemblance penalisee. La convergence des equations d'estimation et des solutions resultantes est discutee. Nous illustrons l'algorithme a l'aide de donnees concernant la dynamique des populations d'insectes des pommes de terre du Colorado sur les plants de pommes de terre.

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