Introduction to Nonlinear Models

There are many problems where the response variable and the predictors are related through a known nonlinear function, which involves the fitting of a nonlinear regression model by least squares.

The resulting normal equations are not linear and, in general, difficult to solve. The nonlinear estimation usually requires heavy iterative calculations. Therefore, a good computer software offers a way of measuring accuracy, reliability and robustness of nonlinear models.

Nonlinear models are useful in many fields, such as chemistry, biology, politics and other sciences. Perhaps the best known category of nonlinear models are growth models. In these cases nonlinear growth curves that follow a specific nonlinear function over time enable to model complex developmental patterns. The type of model that may best fit to the data can be determined by viewing a plot of the data over time.