AbstractFor an accurate regional seismic loss assessment, it is essential to quantify the uncertainties and correlations of the engineering demand parameters (EDP) of the building structures. Previous studies predicted the mean EDP of each structure by a regression function of the selected intensity measure (IM), while its variability is described by the “EDP residual.” The authors recently proposed a new formulation and Incremental Dynamic Analysis (IDA)‐based methods to evaluate the correlation between EDP residuals. This paper proposes an IM‐invariant method for estimating the variances and correlations of the EDP residuals of building structures. Based on the EDP residuals of various buildings estimated using the proposed method, primary structural characteristics affecting EDP residuals are identified. In addition, this study develops EDP estimation regression equations using predictive variables defined based on the identified structural characteristics to facilitate consideration of the EDP residual correlation in regional seismic loss assessment. Numerical examples verify the regression models and demonstrate that the proposed method can improve the accuracy of a regional loss assessment by considering the building types in the inventory.