Multivariate Calibration: Quantification of Harmonies and Disharmonies in Analytical Data

  • Tormod Næs
  • Harald Martens
Part of the Modern Analytical Chemistry book series (MOAC)


The simplest string instruments have only one string. It is possible to play nicely on such primitive instruments, because our memory can recognize a series of successive sounds in terms of melody and rhythm.


Partial Little Square Partial Little Square Regression Principal Component Regression Stepwise Multiple Linear Regression Multivariate Calibration 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    H. Martens, S. Å. Jensen, P. Geladi, “Multivariate Linearity Transformation for Near-Infrared Reflectance Spectrometry,” Proc. Nordic Symp. on Applied Statistics (O. H. J. Christie, ed.), June 12–14, 1983, Stokkand Forlag Publ., Stavanger, Norway, 1983, pp. 208–234.Google Scholar
  2. 2.
    P. Geladi, D. MacDougall, and H. Martens, “Linearization and Scatter-Correction for Near-Infrared Reflectance Spectra of Meat, Appl. Spectrosc. 39(3), 491–500 (1985).CrossRefGoogle Scholar
  3. 3.
    H. Martens, and T. Næs, “Multivariate Calibration. I. Concepts and Distinctions,” Trends Analyt. Chem. 3, 204–210 (1984).CrossRefGoogle Scholar
  4. 4.
    D. L. Wetzel, “Near-Infrared Reflectance Analysis: Sleeper among Spectroscopic Techniques,” Analyt. Chem. 55(12), 1165A–1176A (1983).CrossRefGoogle Scholar
  5. 5.
    H. Martens and T. Næs, “Multivariate Calibration by Data Compression,” in Near Infrared Reflection Spectroscopy (P. Williams, ed.), Am. Assoc. Cereal Chem., St. Paul, Minnesota, 1984, in press.Google Scholar
  6. 6.
    T. Fearn, “Misuse of Ridge Regression in the Calibration of a Near Infrared Reflectance Instrument,” Appl. Stat. 32, 73–79 (1983).CrossRefGoogle Scholar
  7. 7.
    K. Norris and P. C. Williams “Optimization of Mathematical Treatment of Reflectance Data for the Estimation of Protein in Wheat,” Cereal Foods World 22, 461 (1977).Google Scholar
  8. 8.
    T. Næs, “Comparison of Approaches to Multivariate Linear Calibration,” Biom. J. 27, 265–275 (1985).CrossRefGoogle Scholar
  9. 9.
    T. Næs, “Multivariate Calibration when the Error Covariance Matrix is Structured,” Technometrics 27, 301–311 (1985).CrossRefGoogle Scholar
  10. 10.
    T. Næs, “Multivariate Calibration by Covariance Adjustment,” Biom. J. 28, 99–107 (1986).CrossRefGoogle Scholar
  11. 11.
    T. Næs, and H. Martens, “Multivariate Calibration. II. Chemometric Methods,” Trends Analyt. Chem. 3, 266–271 (1984).CrossRefGoogle Scholar
  12. 12.
    M. Stone, “Cross-Validatory Choice and Assessment of Statistical Prediction,” J. R. Stat. Soc. B 36, 111–133 (1974).Google Scholar
  13. 13.
    H. Martens, “Multivariate Calibration,” thesis for the Dr. techn. degree at Technical University of Norway, Trondheim, 1985.Google Scholar
  14. 14.
    R. F. Gunst and R. L. Mason, “Some Considerations in the Evaluation of Alternate Prediction Equations,” Technometrics 21, 55–63 (1979).CrossRefGoogle Scholar
  15. 15.
    J. Mandel, “Use of the Singular Value Decomposition in Regression Analysis,” Am. Stat. 36, 15–24 (1982).CrossRefGoogle Scholar
  16. 16.
    H. Wold, “Estimation of Principal Components and Related Models by Iterative Least Squares,” in Multivariate Analysis (P. R. Krishnaiah, ed.), Academic, New York, 1966.Google Scholar
  17. 17.
    T. Næs and H. Martens, “Comparison of Prediction Methods for Multicollinear Data,” Commun. Stat. Simulation Computation 14(3), 545–576 (1985).CrossRefGoogle Scholar
  18. 18.
    S. Wold et al. “The Collinearity Problem in Linear Regression. The Partial Least Squares (PLS) Approach to Generalized Inverses,” SIAM J. Sci. Stat. Comput. 735–743 (1984).Google Scholar
  19. 19.
    I. S. Heiland, “The Structure of Partial Least Squares,” Report from Agricultural University of Norway, Ås, 1986.Google Scholar
  20. 20.
    S. Wold, H. Martens, and H. Wold, “The Multivariate Calibration Problem in Chemistry Solved by the PLS Method,” Proc. Conf. Matrix Pencils (A. Ruhe, B. Kågström, eds.), March 1982, Lecture Notes in Mathematics, Springer Verlag, Heidelberg, 1983, pp. 286–293.Google Scholar
  21. 21.
    H. Martens and S. Å. Jensen, “Partial Least Squares regression: A New Two-Stage NIR Calibration method,” Proc. 7th World Cereal and Bread Congress, Prague, June 1982 (Holas and Kratochvil, eds.), Elsevier, Amsterdam, 1983, pp. 607–647 (pp. 613 and 614 are mistakenly interchanged).Google Scholar
  22. 22.
    S. Å. Jensen, L. Munck, and H. Martens, “The Botanical Constituents of Wheat and Wheat Milling Fractions. I. Quantification by Autofluorescence,” Cereal Chem. 59(6), 477–484 (1982).Google Scholar
  23. 23.
    H. Martens, O. Vangen and E. Sandberg, “Multivariate Calibration of an X-Ray Computer Tomograph by Smoothed PLS Regression,” Proc. Nordic Symp. on Applied Statistics (O. H. J. Christie, ed.), June 12–14, 1983, Stokkand Forlag Publ., Stavanger, Norway, 1983, pp. 235–268.Google Scholar
  24. 24.
    K. I. Hildrum, M. Martens, and H. Martens, “Research on Analysis of Food Quality,” Proc. International Symp. “Control of food quality and food analysis” at Reading University, England, March 22–24, 1983.Google Scholar
  25. 25.
    T. Næs, “Leverage and Influence Measures Related to Principal Component Regression,” Report from Agricultural University of Norway, Ås, 1986, submitted.Google Scholar
  26. 26.
    H. Martens, “UNSCRAMBLER,” Program package for multivariate calibration on IBM micro- and VAX computers. Marketed by Computer-Aided Modelling (CAMO), Lademoen, N-7000 Trondheim, Norway, 1986.Google Scholar

Copyright information

© Plenum Press, New York 1987

Authors and Affiliations

  • Tormod Næs
    • 1
  • Harald Martens
    • 2
  1. 1.Norwegian Food Research InstituteAs-NLHNorway
  2. 2.Norwegian Computing CenterOslo 3Norway

Personalised recommendations