Non-linear regression analysis: new approach to traditional implementations

Non-linear regression (NLR) analysis in chemometric applications is the mai n subject of the paper. The following novel items of NLR procedure are repo rted. The modification of gradient method is considered. For inversion of t he Fisher matrix the recurrence algorithm based on the matrix exponential i s used. A new method of sequential Bayesian estimation allows processing of the data successively for every response. Each data set is fitted individu ally, but taking into account the information about common parameters estim ated on previous data sets. A posterior Bayesian distribution is built afte r 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 fast er. A new coefficient of non-linearity is introduced. It is calculated by t he Monte Carlo procedure and accounts for the model structure as well as th e experimental design features. All new ideas were implemented in the softw are FlTTER, a new Excel Add-in. Its main capabilities are reported. The pap er is illustrated with a number of practical examples in DSC, TMA and TGA d ata analysis. Copyright (C) 2000 John Wiley & Sons, Ltd.