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Generalized Additive Models
, 1990
"... Liklihood 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 covariate effects. We introduce the Local Scotinq procedure which replaces the liner form C Xjpj by a sum of smooth functions C Sj(Xj)a ..."
Abstract

Cited by 1314 (33 self)
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Liklihood 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 covariate effects. We introduce the Local Scotinq procedure which replaces the liner form C Xjpj by a sum of smooth functions C Sj(Xj)a The Sj(.) ‘s are unspecified functions that are estimated using scatterplot smoothers. The technique is applicable to any likelihoodbased regression model: the class of Generalized Linear Models contains many of these. In this class, the Locul Scoring procedure replaces the linear predictor VI = C Xj@j by the additive predictor C ai ( hence, the name Generalized Additive Modeb. Local Scoring can also be applied to nonstandard models like Cox’s proportional hazards model for survival data. In a number of real data examples, the Local Scoring procedure 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. In a further generalization, the technique is modified to estimate the form of the link function for generalized linear models. The Local Scoring procedure is shown to be asymptotically equivalent to Local Likelihood estimation, another technique for estimating smooth covariate functions. They are seen to produce very similar results with real data, with Local Scoring being considerably faster. As a theoretical underpinning, we view Local Scoring and Local Likelihood as empirical maximizers of the ezpected loglikelihood, and this makes clear their connection to standard maximum likelihood estimation. A method for estimating the “degrees of freedom ” of the procedures is also given.
www.samsi.info Analysis of Extreme Drinking in Patients with Alcohol Dependence using Pareto Regression
, 2009
"... findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation. ..."
Abstract
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findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.