Insights into multivariate calibration using errors-in-variables modeling
A {ital q}-vector of responses, y, is related to a {ital p}-vector of explanatory variables, x, through a causal linear model. In analytical chemistry, y and x might represent the spectrum and associated set of constituent concentrations of a multicomponent sample which are related through Beer`s law. The model parameters are estimated during a calibration process in which both x and y are available for a number of observations (samples/specimens) which are collectively referred to as the calibration set. For new observations, the fitted calibration model is then used as the basis for predicting the unknown values of the new x`s (concentrations) form the associated new y`s (spectra) in the prediction set. This prediction procedure can be viewed as parameter estimation in an errors-in-variables (EIV) framework. In addition to providing a basis for simultaneous inference about the new x`s, consideration of the EIV framework yields a number of insights relating to the design and execution of calibration studies. A particularly interesting result is that predictions of the new x`s for individual samples can be improved by using seemingly unrelated information contained in the y`s from the other members of the prediction set. Furthermore, motivated by this EIV analysis, this result can be extended beyond the causal modeling context to a broader range of applications of multivariate calibration which involve the use of principal components regression.
- Research Organization:
- Sandia National Labs., Albuquerque, NM (United States)
- Sponsoring Organization:
- USDOE, Washington, DC (United States)
- DOE Contract Number:
- AC04-94AL85000
- OSTI ID:
- 286116
- Report Number(s):
- SAND--96-1973C; CONF-9608115--1; ON: DE96013406
- Country of Publication:
- United States
- Language:
- English
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