Methods for regression analysis of strong-motion data

Abstract We introduce a new computational method for implementing Brillinger and Preisler's (1984, 1985) one-stage maximum-likelihood analysis of strong-motion data. We also reexamine two-stage methods and agree with Masuda and Ohtake (1992) that rigorous analysis requires off-diagonal terms in the weighting matrix for the second-stage regression but note that Masuda and Ohtake failed to account for the earthquake-to-earthquake component of variance. Analysis by Monte Carlo methods shows that both one-stage and two-stage methods, properly applied, are unbiased and that they have comparable uncertainties. Both give the same correct results when applied to the data that Fukushima and Tanaka (1990) have shown cannot be satisfactorily analyzed by ordinary least squares. The two-stage method is more efficient computationally, but for typical problems neither method requires enough time to make efficiency important. Of the two methods, only the two-stage method can readily be used with the techniques described by Toro (1981) and McLaughlin (1991) for overcoming the bias due to instruments that do not trigger.