Analysis of Nonlinear Models — the Nonlinear Response Surface

Abstract

The role of the likelihood function in statistical inference is discussed, with particular reference to problems where exact probability (structural or fiducial) distributions for the parameters are unknown. The methods and uses of response surface methodology are briefly discussed, especially the usefulness of nonlinear models, and the difficulties in inferences about these models. Likelihood inference is suggested as a method of overcoming these problems, and the procedures for this are developed. Three examples using biological data demonstrate the procedures.