Non-linear Models

Many relationships between factors observed in the natural world are non-linear. A popular statistical approach to the study of these relationships is to transform them so that they are approximately linear and therefore amenable to the well-established numerical methods of linear modelling. Linear transformation works well in many situations but is not possible in others.

A substantial problem with fitting transformed variables is that errors you assumed to be normal in the non-transformed variable become non-normal after transformation. In specific applications, such as probit analysis, the error calculations have been designed for use with data that have a specified error distribution other than normal. It is not advisable to feed transformed variables through linear regression without a sound statistical argument for doing so. If you are confident of a particular model then you may be justified in using a generalised linear model method to fit your data. Examples of this are probit analysis and logistic regression. StatsDirect offers general logistic regression for dichotomous responses. SAS provides logistic regression for dichotomous and ordinal responses. GLIM provides a broad range of generalised linear models. R and S+ provide more general modelling platforms.

Non-linear statistical modelling is a highly complex subject that blends the instincts of experience with art and science. Seek the help of a Statistician if you wish to use non-linear methods.