Generalized Asymptotic Regression and Non-Linear Path Analysis

It is a fundamental fact of statistical inference that the information contained in an analysis of experimental data is the sum of the a priori information built into the statistical model employed and the a posteriori information contained in the data itself. For this reason the biometrician must be concerned not only with the efficiency of his estimation procedures but also with the adequacy of his descriptive model. Much care must be taken to ensure that all relevant a priori information is utilized in the construction of the model. In some cases it is possible to derive rather sophisticated theoretical models on the basis of acquired knowledge and intelligent hypothesizing. These models are often conveniently found as solutions of differential equations. In other cases little more may be known than that the biological process in question is continuous. In this latter case one may resort to polynomial models where the degree of the polynomial is either found empirically or by prior consideration of the number of bends which one can reasonably assume to take place in the process being studied. In certain other cases it may be known that the process approaches some asymptotic value. This is especially true in those cases known as growth processes. The general ineptness of polynomial models for purposes of describing such asymptotic situations has been repeatedly pointed out, although polynomials in the reciprocals may sometimes be used conveniently. Stevens 1951 and Pimentel-Gomes 1953, writing in this journal, have discussed inferential methods related to one form of transcendental asymptotic model, the so-called exponential model,