Fitting Generalized Additive Models: A Comparison of Methods
نویسندگان
چکیده
There are several procedures for fitting generalized additive models, i.e. multivariate 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 is used to compare a smoothing parameter optimization approach for selection of smoothness and covariate, 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, correlation between 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 oversmoothed functions, while the functions are less smooth for the boosting approach and variable selection follows a less strict (implicit) criterion. 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.
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