Performance of spline-based GAM in the presence of outliers and multicollinearity

Generalized additive models (GAMs) are an extension of additive models as generalized linear models (GLMs) are to ordinary linear regression model. There are different approaches of approaching these kinds of models one of which is the smoothing bases approach, where variety alternatives of smoothing functions are used to define the bases of the model matrix. Penalized regression spline which is estimated by penalized regression techniques is one alternative method for representing GAM models. In this thesis, three penalized regression splines; cubic spline, p-spline, and thin-plate spline are proposed to fit GAM for a simulated data. The performance of these smoothers is evaluated and compared for tolerance of the effect of outliers, multicollinearity and both when they exist together. Results of the experiments showed that the GAMs fitted using these nonparametric regression techniques are less prone to multicollinearity and outliers compared to their parametric counterparts. Keywords: Generalized additive models, Smoothing, Penalized regression spline, Outlier, Multicollinearity.