Crossed and Nested Mixed-Effects Approaches for Enhanced Model Development and Removal of the Ergodic Assumption in Empirical Ground-Motion Models

Limitations in the size of strong-motion databases that are used for the development of empirical ground-motion models has necessitated the use of the ergodic assumption. Several recent efforts, using different databases from around the world, have been made to estimate the single-station standard deviation of spectral accelerations. The computed estimates have been found to be very stable globally, despite the various researchers using quite different approaches. This paper demonstrates that the multistage procedures that have been adopted by previous researchers can be replaced by the use of more elaborate mixed-effects regression analyses. Additionally, the traditional use of additive random effects to capture source, path, and site effects is shown to have conceptual shortcomings that are addressed through the use of a more complex treatment of mixed-effects models. A model for the residual variance (within-event single-station variance) is presented using these advanced approaches.