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# Generalized Additive Models,10.1214/ss/1177013604,Statistical Science,Trevor Hastie,Robert Tibshirani

Likelihood-based regression models such as the normal linear regression model and the linear logistic model, assume a linear (or some other parametric) form for the covariates $X_1, X_2, \cdots, X_p$. We introduce the class of generalized additive models which replaces the linear form $\sum \beta_jX_j$ by a sum of smooth functions $\sum s_j(X_j)$. The $s_j(\cdot)$'s are unspecified functions that are estimated using a scatterplot smoother, in an iterative procedure we call the local scoring algorithm. The technique is applicable to any likelihood-based regression model: the class of generalized linear models contains many of these. In this class the linear predictor $\eta = \Sigma \beta_jX_j$ is replaced by the additive predictor $\Sigma s_j(X_j)$; hence, the name generalized additive models. We illustrate the technique with binary response and survival data. In both cases, the method proves to be useful in uncovering nonlinear covariate effects. It has the advantage of being completely automatic, i.e., no "detective work" is needed on the part of the statistician. As a theoretical underpinning, the technique is viewed as an empirical method of maximizing the expected log likelihood, or equivalently, of minimizing the Kullback-Leibler distance to the true model.
Journal: Statistical Science - STAT SCI , vol. 1, no. 1986, pp. 297-310, 1986
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## Citation Context (1336)

• ...smoothing splines (Wahba, 1990) and generalized additive models (Hastie and Tibshirani, 1990)), and extension to regression with non-normal error distributions, namely, generalized linear models (McCullagh and Nelder, 1989)...

### Yoonkyung Lee, et al. Regularization of Case-Specific Parameters for Robustness and Efficien...

• ...” (Hastie and Tibshirani 1990; Wood 2006)...

### Raquel De Boni, et al. Traffic crashes and alcohol outlets in a Brazilian state capital

• ...2007), and generalized additive regression (Hastie and Tibshirani 1986, 1990)...

### Marco A. Reyna, et al. Relative risk of death from exposure to air pollutants: a short-term (...

• ...Generalised additive models 11 27 advanced the concept by incorporating smooth functions of explanatory variables and, more recently, the simultaneous modelling of up to four distribution parameters (e...

### Vlasios Voudouris, et al. Modelling skewness and kurtosis with the BCPE density in GAMLSS

• ...We analyzed internode lengths from number two to 13 using Generalized Additive Models ...

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