![Sample our Engineering & Technology journals, sign in here to start your access, latest two full volumes FREE to you for 14 days]({"type":"image" , "src" : "/sda/5933/TOC-Subject-Sample-2021-Engineering-Tech.jpg"})
Abstract
Partial residual plots have a long history and, judging from their prominence in the literature, are frequently used. In this article, I explore the structure and usefulness of partial residual plots and augmented partial residual plots as basic tools for dealing with curvature as a function of selected covariates x 2 in regression problems in which the covariate vector x is partitioned as x T = (x 1 T , x 2 T ). The usefulness of these plots for obtaining a good impression of curvature can depend on the behavior of the covariates through the conditional expectation E(x 1|x 2). Partial residual plots seem to perform best under linear conditional expectations. Augmented partial residual plots allow E(x 1|x 2) to be a quadratic function of x 2. This development leads to a new class of plots, called CERES plots, that includes partial and augmented partial residual plots as special cases. CERES plots may be useful for obtaining an impression of curvature as a function of x 2 when the conditional expectations E(x 1|x 2) are neither linear nor quadratic. The relationship between these developments and generalized additive models is discussed as well.
