Abstract
Generalized additive models (GAMs) have been popularized by the work of Hastie and Tibshirani ( Generalized Additive Models (1990)) and the availability of user friendly gam software in Splus. However, whilst it is flexible and efficient, the gam framework based on backfitting with linear smoothers presents some difficulties when it comes to model selection and inference. On the other hand, the mathematically elegant work of Wahba ( Spline Models for Observational Data (1990)) and co-workers on Generalized Spline Smoothing (GSS) provides a rigorous framework for model selection (SIAM J. Sci. Statist. Comput. 12 (1991) 383) and inference with GAMs constructed from smoothing splines: but unfortunately these models are computationally very expensive with operations counts that are of cubic order in the number of data. A ‘middle way’ between these approaches is to construct GAMs using penalized regression splines (e.g. Marx and Eilers, Comput. Statist. Data Anal. (1998)). In this paper, we develop this idea further and show how GAMs constructed using penalized regression splines can be used to get most of the practical benefits of GSS models, including well founded model selection and multi-dimensional smooth terms, with the ease of use and low computational cost of backfit GAMs. Inference with the resulting methods also requires slightly fewer approximations than are employed in the GAM modelling software provided in Splus. This paper presents the basic mathematical and numerical approach to GAMs implemented in the R package mgcv, and includes two environmental examples using the methods as implemented in the package.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.