Inference and computation with generalized additive models and their extensions

Simon N Wood

doi:10.1007/s11749-020-00711-5

Abstract

Regression models in which a response variable is related to smooth functions of some predictor variables are popular as a result of their appealing balance between flexibility and interpretability. Since the original generalized additive models of Hastie and Tibshirani (Generalized additive models. Chapman & Hall, Boca Raton, 1990) numerous model extensions have been proposed, and a variety of practically useful computational strategies have emerged. This paper provides an overview of some widely applicable frameworks for this type of modelling, emphasizing the similarities between the different approaches, and the equivalence of smoothing, Gaussian latent process models and Gaussian random effects. The focus is particularly on Bayes empirical smoother theory, fully Bayesian inference via stochastic simulation or integrated nested Laplace approximation and boosting.

Highlights

IntroductionSince Hastie and Tibshirani (1986, 1990) combined generalized linear models with the smoothing methods developed in the 1970s and 1980s (see especially Wahba 1990)
Regression models in which a response variable is related to smooth functions of some predictor variables are popular as a result of their appealing balance between flexibility and interpretability
The purpose of this paper is to provide an overview of the theory and computational methods for working with these general smooth regression models, emphasizing that the different computational strategies are using essentially the same modelling framework, based on the correspondence between smoothing and latent Gaussian random field models, and the fact that ‘smoothing’ can be induced by an appropriate choice of Gaussian prior

Summary

Introduction

Since Hastie and Tibshirani (1986, 1990) combined generalized linear models with the smoothing methods developed in the 1970s and 1980s (see especially Wahba 1990). Wood to produce the generalized additive model, there has been a great deal of activity extending these models and developing alternative computational approaches to their use. The original GAM was yi ∼ EF(μi , φ) where g(μi ) = Ai γ + f j (x ji ),

Objectives

Methods

Conclusion