Diagnostics for Nonparametric Regression Models with Additive Terms

Abstract Recent developments of multivariate smoothing methods provide a rich collection of feasible models for nonparametric multivariate data analysis. Among the most interpretable are models with additive terms. Construction of various models and algorithms for computing the models have been the main concern of the existing literature in this area. Few results are available on the validation of computed fits, and many applications of nonparametric methods unfortunately end up interpreting the noise. This article proposes and illustrates some simple retrospective diagnostics to help data analysts in detecting possible aliasing effects in computed nonparametric fits and in building parsimonious models in an interactive fashion. It also discusses the concepts and rationale behind the proposal, including concurvity, diagnostics versus tests, and so forth. For their ready availability, interaction splines are used in the illustrations.