NDLI: A comparison of methods for the fitting of generalized additive models

Content Provider	Springer Nature Link
Author	Binder, Harald Tutz, Gerhard
Copyright Year	2007
Abstract	There are several procedures for fitting generalized additive models, i.e. regression models for an exponential family response where the influence of each single covariates is assumed to have unknown, potentially non-linear shape. Simulated data are used to compare a smoothing parameter optimization approach for selection of smoothness and of covariates, a stepwise approach, a mixed model approach, and a procedure based on boosting techniques. In particular it is investigated how the performance of procedures is linked to amount of information, type of response, total number of covariates, number of influential covariates, and extent of non-linearity. Measures for comparison are prediction performance, identification of influential covariates, and smoothness of fitted functions. One result is that the mixed model approach returns sparse fits with frequently over-smoothed functions, while the functions are less smooth for the boosting approach and variable selection is less strict. The other approaches are in between with respect to these measures. The boosting procedure is seen to perform very well when little information is available and/or when a large number of covariates is to be investigated. It is somewhat surprising that in scenarios with low information the fitting of a linear model, even with stepwise variable selection, has not much advantage over the fitting of an additive model when the true underlying structure is linear. In cases with more information the prediction performance of all procedures is very similar. So, in difficult data situations the boosting approach can be recommended, in others the procedures can be chosen conditional on the aim of the analysis.
Starting Page	87
Ending Page	99
Page Count	13
File Format	PDF
ISSN	09603174
Journal	Statistics and Computing
Volume Number	18
Issue Number	1
e-ISSN	15731375
Language	English
Publisher	Springer US
Publisher Date	2007-10-20
Publisher Place	Boston
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Generalized additive models Selection of smoothness Variable selection Boosting Mixed model approach Artificial Intelligence (incl. Robotics) Mathematics Numeric Computing Statistics Statistics and Computing/Statistics Programs
Content Type	Text
Resource Type	Article
Subject	Statistics and Probability Theoretical Computer Science Computational Theory and Mathematics Statistics, Probability and Uncertainty

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