On the structure of partial least squares regression

Communications in Statistics - Simulation and Computation

Volumn 17, Issue 2, 1988, Pages 581-607

  Helland, Inge S ^a  

^a NORWEGIAN UNIVERSITY OF LIFE SCIENCES   (Norway)

Author keywords

biased regression; partial least squares regression; PLS algorithms; prediction equation; relevant factors

Indexed keywords

EID: 84946280337     PISSN: 03610918     EISSN: 15324141     Source Type: Journal    
DOI: 10.1080/03610918808812681     Document Type: Article

References (34)

1. Aastveit, A.H. and Martens, H. (1986). ANOVA interactions interpreted by Partial Least Squares regression. 829-844. Biometrics. 42 829-844.
2. Brown, P.J. (1982). Multivariate calibration. J.R. Statist. Soc. B. 44 287–321.
3. Copas, J.B. (1983). Regression, prediction and shrinkage. J-R-Statist. Soc. B. 45 311–354.
4. Fearn, T. (1983). Misuse of ridge regression in the calibration of near infrared reflectance instrument. Applied Statistics. 32 73–79.
5. Geladi, P. and Kowalski, B.R. (1986). Partial least-squares regression: A tutorial. Analytica Chimica Acta. 185 1–17.
6. Gunst, R.F. and Mason, R.L. (1979). Some considerations in the evaluation of alternate prediction equations. Technometrics. 21 55–63.
7. Hoerl, A.E., Kennard, R.W. and Hoerl, R.W. (1985). Practical use of ridge regression: A challenge met. Applied Statistics. 34 114–120.
8. Hoskuldson, A. (1987). PLS methods. Submitted to J. Chemometrics.
9. Joliffe, I.T. (1982). A note on the use of principal components in regression. Applied Statistics. 31. 300–303.
10. Kruskal, J.B. (1978). Factor analysis and principal components I. Bilinear methods. In: International Encyclopedia of Statistics. Collier Macmillan Publishers, London.
11. Krutchkoff, R.G. (1967). Classical and inverse regression methods of calibration. Technometrics. 9 425–439.
12. Lorber, A., Wangen, L.E.: and Kowalski, B.R. (1987). A theoretical foundation for the PLS algorithm. J. Chemometrics, 1 19–31.
13. Manne, R. (1987). Analysis of two partial-least-squares algorithms for multivariate calibration. Chemometr.&Int. Lab. Syst. 2 187–197.
14. Marquardt, D.W. (1980). Comment to Smith and Campbell (1980).
15. Martens, H. (1985). Multivariate Calibration. Dr. techn. Thesis. Technical University of Norway, Trondheim.
16. Martens, H. (1987). Multivariate calibration: Combining harmonies from an orchestra of instruments into reliable predictors of chemical compositions. 46th Session of the ISI, Invited paper.
17. Martens, H. and Jensen, S.A. (1983). Partial least squares regression: A new two-stage NIR calibration method. In: Progress in Cereal Chemistry and Technology 5a (Proceedings, 7th world Cereal and Bread Congress, Prague, June 1982, J. Holas, J. Kratochvit, eds.) Elsevier Publ., Amsterdam, 607–647.
18. Martens, M., Lea, P. and Martens, H. (1983a). Predicting human response to food quality by analytical measurements: the PLS regression method. Proc. Nordic Symposium on Applied Statistics (O.H.J. Christie, ed.), June 1983. Stokkand Forlag Publ., Stavanger, Norway.
19. Martens, H. and Naes, T.(1987). Multivariate calibration by data compression. In: Near-Infraread Technology for the Agricultural and Food Industries. (P. Williams and K. Norris, eds.) Amer. Ass. of Cereal Chemists. St. Paul.
20. Martens, H., Vangen, O. and Sandberg, E. (1983b). Multivariate calibration of an X-ray computer tomograph by smoothed PLS regression. Proc. Nordic Symposium on Applied Statistics (O.H.J. Christie, ed.), June 1983, Stokkand Forlag Publ., Stavanger, Norway.
21. Mason, R.L. and Gunst, R.F. (1985). Selecting principal components in regression. Statistics & Probability Letters, 3 299–301.
22. Naes, T. and Martens, H. (1985). Comparison of prediction methods for multicollinear data. Commun. Statist. - Simula. Computa. 14 545–576.
23. Nass, T. (1985). Multivariate calibration when the error covariance matrix is structed. Technometrics. 27 301–311.
24. Nses, T., Irgens, C. and Martens, H. (1986). Comparison of linear statistical methods for calibration of NIR instruments. Applied Statistics, 35 195–206.
25. Schweder, T. (1987). Canonical regression. Report no 804. Norwegian Computing Center, Oslo.
26. Smith, G. and Campbell, F. (1980). A critique of some ridge regression methods. J. Amer. Statist. Ass. 75 74–103.
27. Stone, M. (1974). Cross-validatory choice and assessment of statistical predictions. J.Roy. Statist. Soc. 36 111–133.
28. Sundberg, R. (1985). When is the inverse regression estimator MSE-superior to the standard regression estimator in multivariate controlled calibration situations? Statistics & Probability Letters. 3 75–79.
29. Sundberg, R. and Brown, P. (1985). Multivariate calibration with more variables than observations. Research report no. 139. Institute of Actuarial Mathematics and Mathematical Statistics, University of Stockholm.
30. Wold, H. and Jöreskog, K.G., eds. (1982). Systems under indirect observation, Causality - structure - prediction. Contributions to Economic Analysis, 139, parts I and II. North-Holland Publ. Co. Amsterdam.
31. Wold, S., Martens, H. and Wold, H. (1983). The multivariate calibration problem in chemistry solved by the PLS method. Proc. Conf. Matrix Pencils (A. Ruhe, B. Kågstrϕm, eds.), March 1982, Lecture Notes in Mathematics, Springer Verlag, Heidelberg, 286–293.
32. Wold, S. (1974). A theoretical foundation of extra thermodynamic relationships (linear free energy relationships). Chimica Scripta. 5 97–106.
33. Wold, S. (1978). Cross validatory estimation of the number of components in factor and principal component models. Technometrics, 20 397–405.
34. Wold, S., Wold, H., Dunn, W.J. and Ruhe A., (1984) The collinearity problem in linear regression. The partial least squares (PLS) approach to generalized inverses. Siam J. Sci. Stat. Comput. 5 735–743.