Fig 1. Example IVHs constructed from simulated data.

In (A) and (B), linear regression is used to relate a response variable to a single covariate, x, obtained at locations denoted with an “x”. Using x as a simple linear effect (A), only predictions less than the minimum observed value of x or greater than the maximum value of x are outside the IVH (shaded area), as scaled prediction variance in these areas (solid line) is greater than the maximum scaled prediction variance for observed data (dashed line). Using both linear and quadratic effects (B), some intermediate points are also outside the IVH. When both linear and quadratic effects of two covariates (x ₁ and x ₂) are modeled, the IVH is more nuanced and depends on whether interactions are omitted (C) or included (D).