Considering Spatial Correlation in Mixed-Effects Regression and the Impact on Ground-Motion Models

Abstract Ground-motion models are commonly used in earthquake engineering to predict the probability distribution of the ground-motion intensity at a given site due to a particular earthquake event. These models are often built using regression on observed ground-motion intensities and are fitted using either the one-stage mixed-effects regression algorithm proposed by Abrahamson and Youngs (1992) or the two-stage algorithm of Joyner and Boore (1993). In their current forms, these algorithms ignore the spatial correlation between intraevent residuals. This paper emphasizes the theoretical importance of considering spatial correlation while fitting ground-motion models and proposes an extension to the Abrahamson and Youngs (1992) algorithm that allows the consideration of spatial correlation. By refitting the Campbell and Bozorgnia (2008) ground-motion model using the mixed-effects regression algorithm considering spatial correlation, it is apparent that the variance of the total residuals and the ground-motion model coefficients used for predicting the median ground-motion intensity are not significantly different from the published values even after the incorporation of spatial correlation. However, there is an increase in the variance of the intraevent residual and a significant decrease in the variance of the interevent residual. These changes have implications for risk assessments of spatially-distributed systems because a smaller interevent residual variance implies lesser likelihood of observing large ground-motion intensities at all sites in a region.