Application of ordinary least square method in nonlinear models
Irina Arhipova, Arhipovs Sergejs · 2007
using OLS in the nonlinear regression analysis are discussed. Models which are nonlinear in parameters, in sense, that by suitable (log) transformation the models can be made linear in parameters. In this case method of Ordinary Least Square (OLS) has been used for transformed equations. However, it is possible that the stochastic term has different variability related to dependent variable: additive or more random and unpredictable. Depending on the stochastic term variability the nonlinear models can be intrinsically linear (in-parameter) regression models (in the sense that by suitable (log) transformation the models can be made linear in the parameters) and can be intrinsically nonlinear in parameters. If for the linear models and models nonlinear in variables the least-squares criterion of minimization has been applied to initial (original) variables, then for the models nonlinear in parameters the least-squares criterion of minimization it has to be applied to transformed variables, for example LnY. However, the parameters estimation for the transformed models OLS is biased. It means that, although nonlinear models can be transformed into linear regression models and can be estimated by OLS, we have to be careful about the properties of the stochastic residual term that enters these models. As the preceding analysis shows, it is necessary to pay attention to the residual term in transforming a model for regression analysis. Otherwise, a formal application of OLS to the transformed model will not produce a model with correct statistical properties. The examples of the different nonlinear models and the application of OLS are considered, as well the transformed models estimated parameters has been compared.