Ground‐motion models for response spectral ordinates commonly partition site‐response effects into linear and nonlinear components. The nonlinear components depend upon the earthquake scenario being considered implicitly through the use of the expected level of excitation at some reference horizon. The linear components are always assumed to be independent of the earthquake scenario. This article presents empirical and numerical evidence as well as a theoretical explanation for why the linear component of site response depends upon the magnitude and distance of the earthquake scenario. Although the impact is most pronounced for small‐magnitude scenarios, the finding has significant implications for a number of applications of more general interest including the development of site‐response terms within ground‐motion models, the estimation of ground‐motion variability components and , the construction of partially nonergodic models for site‐specific hazard assessments, and the validity of the convolution approach for computing surface hazard curves from those at a reference horizon, among others. All of these implications are discussed in the present article.