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Generalized additive models for longitudinal data
Author(s) -
Berhane Kiros,
Tibshirani Robert J.
Publication year - 1998
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.2307/3315715
Subject(s) - pointwise , mathematics , smoothing , consistency (knowledge bases) , inference , exponential family , estimating equations , nonparametric statistics , population , convergence (economics) , generalized estimating equation , mathematical optimization , statistics , computer science , maximum likelihood , discrete mathematics , artificial intelligence , mathematical analysis , demography , sociology , economics , economic growth
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.