Evaluation of Model Discrimination, Parameter Estimation and Goodness of Fit in Nonlinear Regression Problems By Test Statistics Distributions

There are many programs for fitting nonlinear models to experimental data, and the use of this type of software is now widespread. After fitting a model or sequence of models, these programs usually calculate x2, run, sign, F and I statistics as an aid to model discrimination and parameter estimation. The distribution of such statistics from linear regression is well known, but these random variables do not have the stated named distribution after fitting nonlinear models. First we describe a set of programs that can be used to study the distribution of these well known test statistics from nonlinear regression. Then we present the results from a study of two models that are frequently employed in the life-sciences, and summarize our results from more extensive simulations. Finally, we explain how these programs can be used to create the appropriate cumulative distribution functions, so that exact probability levels can be calculated, given the models of interest, the design points and error structure of a data set.