Weighting schemes for updating regression models - a theoretical approach

While multivariate calibration has been successfully employed in the monito ring of chemical processes, difficulties arise in that sensors are inherent ly prone to drift and processes are susceptible to unmodeled upsets. Having detected an unmodeled source of variance within new samples, the usual rem edy is to update the model with additional calibration samples that contain the new chemical interferent or instrumental variation. In the event that relatively few new calibration samples are available, these new samples can be assigned higher weights by incorporating two or more copies of each whe n constructing the updated model. While weighting has been suggested as a m eans of improving prediction estimates for samples containing a new source of variance, no theoretical explanation has been provided as to why weighti ng is advantageous and no criteria have been proposed in selecting weights for the new calibration samples. In this paper, the utility of sample weigh ting is explained theoretically using both model error and leverage argumen ts and a leverage-based criterion for selecting weights for the new calibra tion samples is presented. Employing both simulated and process spectral da ta, a close correspondence is demonstrated between weights selected using p rediction error and leverage-based criteria. Additionally, paired simulatio n experiments show that the reduction in prediction error achieved by sampl e weighting increases as the level of noise in the responses increases, sug gesting that this method will be of particular value when constructing cali bration models using noisy instrumental responses. (C) 1999 Elsevier Scienc e B.V. All rights reserved.