A Novel Regression Analysis Method for Randomly Truncated Strong-Motion Data

Abstract

Regression analysis is a basic and essential tool for developing the ground motion prediction equation (GMPE). Generally, the probability of intensity measurement for a given ground motion scenario described by several predictors is assumed to be normally distributed. However, because of the triggering threshold of the strong-motion station, ground motion records below the triggering threshold are truncated (i.e., not recorded), and the truncated intensity levels of spectral accelerations at different periods are random variables. Consequently, the sampling of the ground motion data used in GMPE development is biased, and the observed probability of the intensity measurement is no longer normally distributed. Therefore, a novel two-step maximum-likelihood method is proposed in this paper as a regression tool to overcome this problem in GMPE development. The advantage of the proposed method is that the correlation between records from the same events and those from the same sites as well as the biased sampling problem can be considered simultaneously, and more ground motion data can be considered to derive more reliable analysis results.