Nonlinear least squares fitting applied to copolymerization modeling

The choice of the statistical method to determine the reactivity ratios in copolymerization modeling is shown to be very important. Problems in literature, as well as possible pitfalls when using available statistical programs that are in itself correct are pointed out. These problems mainly involve (knowledge of) the error structure, as the error structure determines the weighting scheme of the data points in fitting procedures. A simple, robust, statistically correct non-linear least squares (NLLS) method is reintroduced which is based on the visualization of the sum of squares of residuals in the so-called sum of squares space (SSS). The advantages of this method include the fact that the method is easy to understand and can be implemented in simple computer programs, as well as the fact that the method allows important aspects of the error structure to be incorporated. Furthermore, in the SSS the joint confidence interval (JCI) with exact shape can be constructed. The exact shape of the JCI is not always ellipsoidal and following a normal distribution, depending on the linearity of the fitted equations. This can sometimes lead to wrong conclusions.