Statistical Methods and Applications

, Volume 16, Issue 2, pp 263–278 | Cite as

Two-step PLS regression for L-structured data: an application in the cosmetic industry

  • Vincenzo Esposito Vinzi
  • Christiane Guinot
  • Silvia Squillacciotti
Original Article


The present paper proposes a PLS-based methodology for the study of so called “L” data-structures, where external information on both the rows and the columns of a dependent variable matrix is available. L-structures are frequently encountered in consumer preference analysis. In this domain it may be desirable to study the influence of both product and consumer descriptors on consumer preferences. The proposed methodology has been applied on data from the cosmetic industry. The preference scores from 142 consumers on 9 products were explained with respect to the products’ physico-chemical and sensory descriptors, and the consumers’ socio-demographic and behavioural characteristics.


Partial least squares (PLS) regression Preference data External information L-structures 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Amenta P, D’Ambra L (1997) L’analisi in componenti principali in relazione a un sottospazio di riferimento con informazioni esterne, Quaderni di Statistica, 18, DMQTE, PescaraGoogle Scholar
  2. Chatelin YM, Esposito Vinzi V, Tenenhaus V (2002) State of Art on the PLS Path Modelling through the available software. HEC Research Papers, 764/2002Google Scholar
  3. Esposito Vinzi V, Lauro C, Amato S (2004) PLS typological regression: algorithmic, classification and validation issues. In: Vichi M, Monari P, Mignani S, Montanari A (eds) New developments in classification and data analysis. Springer, Berlin Heidelberg New York, pp 133–140Google Scholar
  4. Giordano G, Scepi G (1999) La progettazione della qualità attraverso l’analisi di strutture informative differenti. In: Proceedings of XV Riunione Scientifica SISGoogle Scholar
  5. Höskuldsson A (1988) PLS regression methods. J Chemometrics 2:211–288CrossRefGoogle Scholar
  6. D’Ambra L, Lauro, NC (1992): “Non Symmertical Exploratory Data Analysis”, Statistica Applicata, 4(4), pp 511–529Google Scholar
  7. Martens H, Anderssen E, Flatberg A, Gidskehaug LH, Høy M, Westad F, Thybo A, Martens M (2005) Regression of a data matrix on descriptors of both its rows and its column descriptors via latent variables: L-PLSR. Comput Stat Data Anal 48(1):103–123CrossRefGoogle Scholar
  8. Rayens W, Andersen A (2004) Oriented Partial Least Squares, Rivista di Statistica Applicata, Italian Journal of Applied Statistics, RCE Edizioni, Napoli, 15(3), pp 367–388Google Scholar
  9. Risvik E, UelandØ, Westad F (2003) In: Segmentation strategy for a generic food product in Proceedings of the 5th Pangborn Sensory Science Symposium, Boston, MA, USAGoogle Scholar
  10. Stone M, Brooks RJ (1990) Continuum regression: cross-validated sequentially constructed prediction embracing ordinary least squares, partial least squares, and principal component regression. J R Stat Soc Ser B 52:237–269MATHGoogle Scholar
  11. Takane Y, Shibayama T (1991) Principal component analysis with external information on both subjects and variables. Psychometrika 1:97–120CrossRefGoogle Scholar
  12. Tenenhaus M (1998) La régression PLS: théorie et pratique, Editions Technip, ParisGoogle Scholar
  13. Tenenhaus M, Esposito Vinzi V, Chatelin YM, Lauro C (2005) PLS path modelling. Comput Stat Data Anal 48(1):159–205CrossRefGoogle Scholar
  14. Trygg J, Wold S (2002) Orthogonal projections to latent structures (O-PLS). J Chemometrics 16:119–128CrossRefGoogle Scholar
  15. Umetrics (2002) SIMCA-P and SIMCA-P+ 10 User Guide, UMETRICS AB, Ume  SwedenGoogle Scholar
  16. Wold H (1975) Modelling in complex situations with soft informations. In: Third World Congress of Econometric Society, Toronto, Canada, 21–26 August 1975Google Scholar
  17. Wold H (1982) Soft modelling: the basic design and some extensions. In: Jöreskog KG, Wold H (eds) Systems under indirect observation, vol 2. Wiley, New York, pp 587–599Google Scholar
  18. Wold H (1985) Partial least squares. In: Kotz S, Johnson NL (eds) Encyclopedia of statistical sciences, vol 8. Wiley, New York, pp 581–591Google Scholar
  19. Wold S, Martens H, Wold H (1983) The multivariate calibration problem in chemistry solved by the PLS method. In: Paper presented at the Matrix Pencils, HeidelbergGoogle Scholar

Copyright information

© Springer-Verlag 2006

Authors and Affiliations

  • Vincenzo Esposito Vinzi
    • 1
    • 2
  • Christiane Guinot
    • 4
  • Silvia Squillacciotti
    • 1
    • 3
    • 4
  1. 1.University of Naples “Federico II”NaplesItaly
  2. 2.ESSEC Business SchoolCergy-PontoiseFrance
  3. 3.EDF R&D – Département ICAMEClamartFrance
  4. 4.CE.R.I.E.S.Biometrics and Epidemiology UnitNeuilly-sur-SeineFrance

Personalised recommendations