Ground Motion Modeling Using the Least Absolute Shrinkage and Selection Operator

Authors: Yildiz Stella Dak, Jale Tezcan

Abstract:

Ground motion models that relate a strong motion parameter of interest to a set of predictive seismological variables describing the earthquake source, the propagation path of the seismic wave, and the local site conditions constitute a critical component of seismic hazard analyses. When a sufficient number of strong motion records are available, ground motion relations are developed using statistical analysis of the recorded ground motion data. In regions lacking a sufficient number of recordings, a synthetic database is developed using stochastic, theoretical or hybrid approaches. Regardless of the manner the database was developed, ground motion relations are developed using regression analysis. Development of a ground motion relation is a challenging process which inevitably requires the modeler to make subjective decisions regarding the inclusion criteria of the recordings, the functional form of the model and the set of seismological variables to be included in the model. Because these decisions are critically important to the validity and the applicability of the model, there is a continuous interest on procedures that will facilitate the development of ground motion models. This paper proposes the use of the Least Absolute Shrinkage and Selection Operator (LASSO) in selecting the set predictive seismological variables to be used in developing a ground motion relation. The LASSO can be described as a penalized regression technique with a built-in capability of variable selection. Similar to the ridge regression, the LASSO is based on the idea of shrinking the regression coefficients to reduce the variance of the model. Unlike ridge regression, where the coefficients are shrunk but never set equal to zero, the LASSO sets some of the coefficients exactly to zero, effectively performing variable selection. Given a set of candidate input variables and the output variable of interest, LASSO allows ranking the input variables in terms of their relative importance, thereby facilitating the selection of the set of variables to be included in the model. Because the risk of overfitting increases as the ratio of the number of predictors to the number of recordings increases, selection of a compact set of variables is important in cases where a small number of recordings are available. In addition, identification of a small set of variables can improve the interpretability of the resulting model, especially when there is a large number of candidate predictors. A practical application of the proposed approach is presented, using more than 600 recordings from the National Geospatial-Intelligence Agency (NGA) database, where the effect of a set of seismological predictors on the 5% damped maximum direction spectral acceleration is investigated. The set of candidate predictors considered are Magnitude, Rrup, Vs30. Using LASSO, the relative importance of the candidate predictors has been ranked. Regression models with increasing levels of complexity were constructed using one, two, three, and four best predictors, and the models’ ability to explain the observed variance in the target variable have been compared. The bias-variance trade-off in the context of model selection is discussed.

Keywords: ground motion modeling, least absolute shrinkage and selection operator, penalized regression, variable selection