The Adaptation of Curvature Measures to Assess Nonlinearity in 'Functionless' Models

Abstract

Bates and Watts (1980) presented curvature measures for assessing the effects of nonlinearity in regression models. The practical and routine methods for assessing this nonlinearity during data analysis employ the methodology of profile plots and traces. (Bates and Watts, 1988). In their book on Nonlinear Regression these profiling methods were clearly demonstrated with the fitting of nonlinear regression models, compartmental models and multiresponse models to data. This paper demonstrates that these profile methods can be extended to models similar to the above. This new class of models does not require that an analytical function or mathematical form of solution be specified. Such 'functionless' models generally require numerical schemes for their solution.