A test of three fitting criteria for multiresponse non‐linear modeling

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Abstract
This work evaluates objective functions for multiresponse non‐linear modeling using computer simulations. Tests are performed under a variety of signal‐to‐noise ratios and noise variance–covariance structures. The standard error of prediction for the model parameters, computed from 50 trials, is used for performance comparisons. The full rank and rank‐deficient problems are considered. For the full rank problem one model was investigated, a first‐order two‐step consecutive reaction model, and two objective functions were considered, the total sum of squares and the determinant criterion. No distinction could be made between the two objective functions for this model.For the rank‐deficient case two models were investigated, a first‐order two‐step consecutive reaction as in the full rank case, and a pH titration model described by the Henderson–Hasselbalch equation. Three objective functions were investigated for the rank‐deficient case, the total sum of squares, a weighted total sum of squares and the determinant criterion. The total sum of squares was found to perform poorly under all conditions tested compared to the weighted total sum of squares and the determinant criterion. The determinant criterion was found to perform much better than the other two criteria when the data have a combination of a low signal‐to‐noise ratio and high variance–covariance noise structure.