Summary This paper introduces the concept of bivariate structural regression analysis, a new technique which offers some advantages compared to the well-known structural relationship approach. The concept is not restricted to multivariate normal distribution, and without additional constraints the model remains identifiable in the bivariate case. A bivariate calibration line is developed first by the maximum likelihood method and then also distribution-free by applying rank statistics. Both estimation procedures coincide, if the distribution assumption is satisfied. Hence, the distribution-free approach has an efficiency of 100%. Our concept of analysis is applied to the comparison of analytical methods in clinical chemistry. Appropriate statistical tests concerning accuracy and precision as well as the model fit are offered.
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Feldmann et al. (1987) studied this question.