Calculation of PLS prediction intervals using efficient recursive relations for the Jacobian matrix

• Published in: Journal of chemometrics Vol. 18; no. 2; pp. 76 - 80
• Main Authors: Serneels, Sven, Lemberge, Pascal, Van Espen, Pierre J.
• Format: Journal Article
• Language: English
• Published: Chichester, UK John Wiley & Sons, Ltd 01.02.2004; Wiley; Wiley Subscription Services, Inc
• Subjects: Algorithms; Chemistry; Exact sciences and technology; General and physical chemistry; Jacobian matrices; latent variable structure; Matrix; partial least squares regression; PLS algorithms; prediction equation; prediction intervals; Recursive algorithms; Jacobian matrices; partial least squares regression; PLS algorithms; latent variable structure; Prediction; Equation; Calculation; prediction intervals; Structure; prediction equation; Algorithm; Chemometrics
• ISSN: 0886-9383; 1099-128X
• DOI: 10.1002/cem.849

Several algorithms to calculate the vector of regression coefficients and the Jacobian matrix for partial least squares regression have been published. Whereas many efficient algorithms to calculate the regression coefficients exist, algorithms to calculate the Jacobian matrix are inefficient. Here we introduce a new, efficient algorithm for the Jacobian matrix, thus making the calculation of prediction intervals via a local linearization of the PLS estimator more practicable. Copyright © 2004 John Wiley & Sons, Ltd.