Introduction

Abstract

Many scientific problems reduce to modeling the relationship between two sets of variables. Regression methodology is designed to quantify these relationships. Due to their mathematical simplicity, linear regression for continuous data, logistic regression for binary data, proportional hazard regression for censored survival data, and mixed-effect regression for longitudinal data are among the most commonly used statistical methods. These parametric (or semiparametric) regression methods, however, may not lead to faithful data descriptions when the underlying assumptions are not satisfied. As remedies, extensive literature exists to perform diagnosis of parametric or semiparametric regression models, but the practice of the model diagnosis is uneven at best. A common practice is the visualization of the residual plots, which is a straightforward task for a simple regression model, but can be highly sophisticated as the model complexity grows. Furthermore, model interpretation can be problematic in the presence of higher-order interactions among potent predictors. Nonparametric regression has evolved to relax or remove the restrictive assumptions.