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In this paper, the performance and advantages and disadvantages of various regression methods to derive coefficients of an attenuation relationship have been investigated. A database containing 350 records out of 85 earthquakes with moment magnitudes of 5–7.6 and Joyner–Boore distances up to 100 km in Europe and the Middle East has been considered. The functional form proposed by Ambraseys et al (2005 Bull. Earthq. Eng. 3 1–53) is selected to compare chosen regression methods. Statistical tests reveal that although the estimated parameters are different for each method, the overall results are very similar. In essence, the weighted least squares method and one-stage maximum likelihood perform better than the other considered regression methods. Moreover, using a blind weighting matrix or a weighting matrix related to the number of records would not yield in improving the performance of the results. Further, to obtain the true standard deviation, the pure error analysis is necessary. Assuming that the correlation between different records of a specific earthquake exists, the one-stage maximum likelihood considering the true variance acquired by the pure error analysis is the most preferred method to compute the coefficients of a ground motion predication equation.

Comparative study on parameter estimation methods for attenuation relationships