Prediction intervals in partial least squares

✍ Scribed by Michael C. Denham

• Publisher: John Wiley and Sons
• Year: 1997
• Tongue: English
• Weight: 266 KB
• Volume: 11
• Category: Article
• ISSN: 0886-9383
• DOI: 10.1002/(sici)1099-128x(199701)11:1<39::aid-cem433>3.0.co;2-s

✦ Synopsis

The need for calibration typically arises when an 'expensive' but accurate measurement method is replaced by a 'cheap' but generally less accurate method. As an example we may be interested in the amount of a particular chemical present in a mixture. Here traditional 'wet' chemistry techniques can lead to very accurate determination but are often both costly and laborious, whilst examination of the mixture's infrared (IR) absorbance spectrum can offer a much faster and more affordable alternative. Using an initial set of calibration samples on which both measurements are available, the relationship between the amount of chemical present and the IR spectrum is estimated. This estimated relationship is then used to predict the composition of future samples of material from their infrared spectra.

In many real applications the number of calibration samples, n, will be considerably smaller than the number of absorbances, p, in the IR spectrum. Under such circumstances traditional least squares estimation breaks down since it does not give a unique estimator. Sundberg and Brown 1 examine this issue in some detail, establishing that least squares methods based on regressing chemical composition on IR spectrum and vice versa both give rise to non-unique predictions. These non-unique predictions can be shown to occupy the same Euclidean subspace. Denham and Brown 2 consider approaches to overcome this indeterminacy which take account of the nature of IR spectra. Other approaches based on ridge regression and principal components analysis have been adopted, but the technique which appears to have gained most popularity amongst the chemometric community is partial least squares (PLS) regression. In fact, PLS