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Selection of Splines Models in the Presence of Multicollinearity and Outliers

Objective: In this paper, the selection of the models evaluated using by three penalized regression splines; cubic splines, p-splines, and thin-plate splines are compared to linear models where the multicollinearity exists among covariates at different parameters and a response variable including outliers. Material and Methods: Generalized additive models (GAM) are extension of additive models as generalized linear models are to ordinary linear regression models. Different approaches of fitting these kinds of models that is the penalized regression techniques for representing generalized additive models are used in this study. Results: To examine the tolerance of the effect of multicollinearity and outliers and for the selection of these models and linear regression models, AIC and deviance are used. In all the situations, cubic splines regression models produced a smaller mean deviance in the presence of multicollinearity. On the other hand, cubic splayn regression models loses its dominance of producing smaller mean deviance when outliers are included to the data. It is remarkable that with the increase of sample size the number of times the psplines method produced a smaller deviance. Conclusion: Results of the simulations showed that the GAMs fitted using these nonparametric regression techniques are less prone to multicollinearity and outliers compared to their parametric counterparts.