Considerations about nonlinear regression

Abstract

Differently from linear regression models, where the quality and validity of a proposed model are checked through regression diagnostic methods, for nonlinear models, we should consider additional diagnostic methods. These special diagnostic methods for nonlinear regression models measure the nonlinearity amount of the proposed model. Nonlinear models with behavior too different from linear models could invalidate the asymptotical results, used to get interest inferences, especially in small-sized samples. In this paper, an overview of the main nonlinearity checking methods is offered. In particular, Bates and Watts curvature measures, Box bias measure, simulation methods use and some nonsymmetry measures are focused.