Partial residual plots in generalized linear models

In this article we explore the structure and usefulness of partial residual plots as tools for visualizing curvature as a function of selected predictors x₂ in a generalized linear model (GLM), where the vector of predictors x is partitioned as x^T = (x^T₁, x^T₂). The GLM extension of ceres plots is discussed, but to a lesser extent. The usefulness of these plots for obtaining a good visual impression of curvature may be limited by the specified GLM, the link function, and the stochastic behavior of the predictors. Partial residual plots seem to work well when modeling is in a region where the conditional mean of the response given x stays well away from its extremes so that the link is essentially linear, and E(x₁ | x₂) is linear in x₂. ceres plots, however, require only the first condition. The behavior of these plots is contrasted with their behavior in additive-error models.