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

Abstract 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 er-godic 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 demon-strates that the multistage procedures that have been adopted by previous researchers can be replaced by the use of more elaborate mixed-effects regression analyses. Addi-tionally, 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.