Skip to main content
SpringerLink
Log in

A Bridge Between PLS Path Modeling and Multi-Block Data Analysis

  • Chapter
  • First Online:
Handbook of Partial Least Squares

Part of the book series: Springer Handbooks of Computational Statistics ((SHCS))

Abstract

A situation where J blocks of variables X 1, …, X J are observed on the same set of individuals is considered in this paper. A factor analysis approach is applied to blocks instead of variables. The latent variables (LV’s) of each block should well explain their own block and at the same time the latent variables of same order should be as highly correlated as possible (positively or in absolute value). Two path models can be used in order to obtain the first order latent variables. The first one is related to confirmatory factor analysis: each LV related to one block is connected to all the LV’s related to the other blocks. Then, PLS path modeling is used with mode A and centroid scheme. Use of mode B with centroid and factorial schemes is also discussed. The second model is related to hierarchical factor analysis. A causal model is built by relating the LV’s of each block X j to the LV of the super-block X J + 1 obtained by concatenation of X 1, …, X J . Using PLS estimation of this model with mode A and path-weighting scheme gives an adequate solution for finding the first order latent variables. The use of mode B with centroid and factorial schemes is also discussed. The higher order latent variables are found by using the same algorithms on the deflated blocks. The first approach is compared with the MAXDIFF/MAXBET Van de Geer’s algorithm (1984) and the second one with the ACOM algorithm (Chessel and Hanafi, 1996). Sensory data describing Loire wines are used to illustrate these methods.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 389.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 499.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 499.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Carroll, J. D. (1968). A generalization of canonical correlation analysis to three or more sets of variables”, Proceedings of the 76th Convenction of American Psychological Association, pp. 227–228.

    Google Scholar 

  • Casin, P. A. (2001). A generalization of principal component analysis to K sets of variables. Computational Statistics & Data Analysis, 35, 417–428.

    Article  MATH  MathSciNet  Google Scholar 

  • Chin, W. W. (2005). PLS-Graph User’s Guide, C.T. Bauer College of Business. USA: University of Houston.

    Google Scholar 

  • Chessel, D. & Hanafi M. (1996). Analyses de la Co-inertie de K nuages de points. Revue de Statistique Appliquée, 44(2), 35–60.

    Google Scholar 

  • Chu, M. T. & Watterson, J. L (1993). On a multivariate eigenvalue problem, Part I : Algebraic theory and a power method. SIAM Journal on Scientific Computing, 14,(5), 1089–1106.

    Article  MATH  MathSciNet  Google Scholar 

  • Escofier, B. & Pagès J. (1988). Analyses factorielles simples et multiples. Paris: Dunod.

    Google Scholar 

  • Escofier, B. & Pagès J. (1994). Multiple factor analysis, (AFMULT package), Computational Statistics & Data Analysis, 18, 121–140.

    Article  MATH  Google Scholar 

  • Hanafi, M. (2007). PLS path modelling: Computation of latent variables with the estimation mode B. Computational Statistics,22(2), 275–292.

    Article  MathSciNet  Google Scholar 

  • Hanafi, M. & Kiers H. A. L (2006). Analysis of K sets of Data with differential emphasis between and within sets. Computational Statistics and Data Analysis, 51(3), 1491–1508.

    Article  MATH  MathSciNet  Google Scholar 

  • Hanafi, M., Mazerolles G., Dufour E. & Qannari E. M. (2006). Common components and specific weight analysis and multiple co-inertia analysis applied to the coupling of several measurement techniques. Journal of Chemometrics, 20, 172–183.

    Article  Google Scholar 

  • Hanafi, M. & Qannari E. M. (2005). An alternative algorithm to PLS B problem. Computational Statistics and Data Analysis, 48, 63–67.

    Article  MATH  MathSciNet  Google Scholar 

  • Hanafi, M. & Ten Berge, J. M. F (2003). Global optimality of the MAXBET Algorithm. Psychometrika, 68(1), 97–103.

    Article  MathSciNet  Google Scholar 

  • Horst, P. (1961). Relations among m sets of variables, Psychometrika, 26, 126–149.

    Article  MathSciNet  Google Scholar 

  • Horst, P. (1965). Factor analysis of data matrices. Holt, Rinehart and Winston: New York.

    MATH  Google Scholar 

  • Kettenring, J. R. (1971). Canonical analysis of several sets of variables. Biometrika, 58, 433–451.

    Article  MATH  MathSciNet  Google Scholar 

  • Lafosse, R. (1989). Proposal for a generalized canonical analysis. In R. Coppi & S. Bolasco (Eds.), Multiway data analysis (pp. 269–276). Amsterdam: Elsevier Science.

    Google Scholar 

  • Lohmöller, J. B. (1989). Latent Variables Path Modeling with Partial Least Squares, Physica-Verlag, Heildelberg.

    Google Scholar 

  • Long, J. S. (1983). Confirmatory Factor Analysis, Series: Quantitative Applications in the Social Sciences, Thousand Oaks, CA: Sage.

    Google Scholar 

  • Mathes, H. (1993). Global optimisation criteria of the PLS-algorithm in recursive path models with latent variables. In K. Haagen, D. J. Bartholomew, M. Deister (Eds), Statistical modelling and latent variables. Amsterdam: Elsevier.

    Google Scholar 

  • Morrison, D. F. (1990). Multivariate statistical methods, New York: McGrawHill.

    Google Scholar 

  • Ten Berge, J. M. F (1988). Generalized approaches to the MAXBET and the MAXDIFF problem with applications to canonical correlations. Psychometrika, 42, 1, 593–600.

    Google Scholar 

  • Tenenhaus, M. & Esposito Vinzi V. (2005). PLS regression, PLS path modeling and generalized Procustean analysis: a combined approach for multiblock analysis. Journal of Chemometrics, 19, 145–153.

    Article  Google Scholar 

  • Tenenhaus, M., Esposito Vinzi V., Chatelin Y.-M., Lauro C. (2005). PLS path modeling. Computational Statistics & Data Analysis, 48, 159–205.

    Article  MATH  MathSciNet  Google Scholar 

  • Van de Geer, J.P. (1984). Linear relations among K sets of variables, Psychometrika, 49, 1, 79–94.

    Article  MathSciNet  Google Scholar 

  • Wold, H. (1982). Soft modeling: The basic design and some extensions, in Systems under indirect observation, Part 2, K.G. Jöreskog & H. Wold (Eds), North-Holland, Amsterdam, 1–54.

    Google Scholar 

  • Wold, H. (1985). Partial Least Squares. In Encyclopedia of Statistical Sciences, vol. 6, S. Kotz and N.L. Johnson (Eds), John Wiley & Sons, New York, 581–591.

    Google Scholar 

  • Wold, S., Kettaneh N. & Tjessem K. (1996). Hierarchical multiblock PLS and PC models for easier model interpretation and as an alternative to variable selection. Journal of Chemometrics, 10, 463–482.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department SIAD, HEC School of Management, 1 rue de la Libération, 78351, Jouy-en-Josas, France

    Michel Tenenhaus

  2. Unité Mixte de Recherche (ENITIAA-INRA) en Sensométrie et Chimiométrie, ENITIAA, Rue de la Géraudière – BP 82225, 44322, Nantes Cedex 3, France

    Mohamed Hanafi

Authors
  1. Michel Tenenhaus
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Mohamed Hanafi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Michel Tenenhaus .

Editor information

Editors and Affiliations

  1. Dept. Inf. Systems & Decision Sciences, ESSEC Business School of Paris, av. Bernard Hirsch, Cergy Pontoise CX, 95021, France

    Vincenzo Esposito Vinzi

  2. Bauer College of Business, University of Houston, Houston, 77204-6282, U.S.A.

    Wynne W. Chin

  3. Nijmegen School of Management, Radboud University, Nijmegen, Netherlands

    Jörg Henseler

  4. School of Economics & Management, BeiHang University, XueYuan Road 37, Beijing, 100083, China, People's Republic

    Huiwen Wang

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Tenenhaus, M., Hanafi, M. (2010). A Bridge Between PLS Path Modeling and Multi-Block Data Analysis. In: Esposito Vinzi, V., Chin, W., Henseler, J., Wang, H. (eds) Handbook of Partial Least Squares. Springer Handbooks of Computational Statistics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-32827-8_5

Download citation

Publish with us

Policies and ethics

Search

Navigation