Model building in chemistry using profile t and trace plots

Abstract

The aim of model building is to determine the ‘correct’ model, which means that the equation describing the phenomenon under study includes all the important factors, in the correct form, and excludes unimportant factors. Practically, of course, we can only use the data at hand to fit a model which is ‘adequate’. In linear and nonlinear regression, a model which is inadequate because an important factor is not included, or because a factor is incorporated in a wrong form, can often be detected by examining plots of the residuals. And in linear regression, models which include too many factors or too many parameters can often be detected by examining the parameter correlation matrix, or the parameter estimates and their standard errors. For nonlinear models, however, such linear approximation summaries are not reliable. To aid in the development of nonlinear models, we recommend using profile likelihood plots. The plots are simple to generate and appear to be especially useful in detecting models which could be simplified by removing factors or by equating parameters. In this paper we use data sets from chemical engineering to illustrate the value of profile t and profile trace plots in model building.