Non-linear regression analysis: new approach to traditional implementations - Bystritskaya, E. V.; Pomerantsev, A. L.; Rodionova, O. Ye (Journal of chemometrics, 2000)
Non‐linear regression (NLR) analysis in chemometric applications is the main subject of the paper. The following novel items of NLR procedure are reported. The modification of gradient method is considered. For inversion of the Fisher matrix the recurrence algorithm based on the matrix exponential is used. A new method of sequential Bayesian estimation allows processing of the data successively for every response. Each data set is fitted individually, but taking into account the information about common parameters estimated on previous data sets. A posterior Bayesian distribution is built after every set processing. A new method of confidence estimation is suggested. Unlike bootstrap, not initial data but parameter estimates are simulated. This method has the same accuracy as bootstrap but is about 1000 times faster. A new coefficient of non‐linearity is introduced. It is calculated by the Monte Carlo procedure and accounts for the model structure as well as the experimental design features. All new ideas were implemented in the software FITTER, a new Excel Add‐In. Its main capabilities are reported. The paper is illustrated with a number of practical examples in DSC, TMA and TGA data analysis. Copyright © 2000 John Wiley & Sons, Ltd.