Testing for interactions in generalized additive models: Application to SO2 pollution data

Authors:
J. Roca-Pardiñas;C. Cadarso-Suárez;W. González-Manteiga
Affiliations:
Department of Statistics and Operations Research, University of Vigo, Spain;Department of Statistics and Operations Research, University of Santiago de Compostela, Spain;Department of Statistics and Operations Research, University of Vigo, Spain
Venue:
Statistics and Computing
Year:
2005

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Abstract

In this paper we considered a generalized additive model with second-order interaction terms. A local scoring algorithm (with backfitting) based on local linear kernel smoothers was used to estimate the model. Our main aim was to obtain procedures for testing second-order interaction terms. Backfitting theory is difficult in this context, and a bootstrap procedure is therefore provided for estimating the distribution of the test statistics. Given the high computational cost involved, binning techniques were used to speed up the computation in the estimation and testing process. A simulation study was carried out in order to assess the validity of the bootstrap-based tests. Lastly, our method was applied to real data drawn from an SO2 binary time series.