On Multicollinearity in Nonlinear Regression Models

Regression analysis includes many techniques for modeling and analyzing the relationship between a dependent variable and one or more independent variables. Linear and nonlinear regression models has widely used in many fields of applied science. One of the frequency problems in regression analysis is multicollinearity problem between the explanatory variables. If there is no linear (approximately linear) relationship between the regressors, they are said to be orthogonal. In the case of orthogonal variables, statistical inference on the model is quite reliable. But in real life, fully unbound variables which are explaining the dependent variable are likely to be very low. When the explanatory variables are not orthogonal, then least squares parameter estimation method will not provide a suitable convergence, and deviations from reality will ocur. For the linear model, many techniques were developed for the multicollinearity problem (Hoerl, AE (1962), Hoerl AE and Kennard RW (1968.1970)), but for nonlinear models there has not been any conclusive work yet. In this study, multicollinearity in nonlinear models will be analyzed and a remedy for the problem will be given.