Distribution-Free Methods of Approximating Nonlinear Marketing Relationships

Abstract

Many, if not most, of the important functional relationships in marketing are inherently nonlinear. Fitting a nonlinear function to data involves first the specification of a model, and then the estimation of the model's parameters. Where theory gives insufficient guidance for the specification of a model, specification based on observation of the scatterplot may be required. In many instances it is difficult to specify a model accurately solely on the basis of scatterplot observation. In those instances the researcher's power of observation can be enhanced by use of a distribution-free method of approximating the underlying function. The authors discuss alternative distribution-free methods, and demonstrate how the implicit model specification process of exhaustive trial and error curve-fitting can be replaced by an explicit model specification process based on observing an approximation of the underlying function.