DETECTION OF INTERACTION AND OUTLIERS WITH ADDITIVE NONPARAMETRIC REGRESSION MODELS

Abstract

The paper proposes a new procedure to detect interaction and outliers with nonparametric regression model that cannot directly express interaction by itself. In other words, based on the residuals from fitting Generalized Additive Model (GAM) to the data with interaction, systematic inadequacy is regarded as interaction. Along with the idea mentioned above, the procedure to detect interaction and outliers graphically and numerically is proposed. The outline of the procedure is as follows. Fit GAM to the data, and then stratify the observations with respect to the value(s) of the explanatory variable(s). And when the tendency of the residual plots differs between the strata, it's concerned that the data contain interaction. Furthermore, with respect to the statistics evaluating the difference of tendency between the strata, the hypothesis of "no interaction" or "no local data structure" can be examined. From the simulation study, when the tendency of the residual plots differs between the strata, it was confirmed that the data contain interaction. And, when the clear-cut difference cannot be seen in the residual plots between strata, it was confirmed that the data don't contain interaction. Finally, it was shown that the test could judge the existence of interaction adequately. Besides, it's confirmed that local interactions, outliers and global interactions can be detected essentially in the same manner.