Model Selection and Variable Transformations in Nonlinear Regression

The results of analyzing experimental data using a parametric model may heavily depend on the chosen model. In this paper we propose procedures for the adequate selection of nonlinear regression models if the intended use of the model is among the following: prediction of future values of the response variable, estimation of the unknown regression function, calibration or estimation of some parameter with a certain meaning in the corresponding field of application. The performance of the selected model is discussed, and several examples illustrate the behaviour of the procedures. Programs written in Splus for handling such problems are described as well. Moreover, we propose a procedure for selecting an appropriate nonlinear transformation of the observations which may lead to an improved accuracy.