Skip to main content
SpringerLink
Log in
Book cover

Classification and Multivariate Analysis for Complex Data Structures pp 237–244Cite as

Partitioning the Geometric Variability in Multivariate Analysis and Contingency Tables

  • Conference paper
  • First Online:

  • 2881 Accesses

Abstract

Most methods of multivariate analysis obtain and interpret an appropriate decomposition of the variability. In canonical variate analysis, multidimensional scaling and correspondence analysis, the variability of the data is measured in terms of distances. Then the geometric variability (inertia) plays an important role. We present a unified approach for describing four methods for representing categorical data in a contingency table. We define the generalized Pearson contingency coefficient and show situations where this measure can be different from the geometric variability.

This is a preview of subscription content, 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   84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   109.99
Price excludes VAT (USA)
  • Compact, lightweight 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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Aitchison, J., Greenacre, M.J.: Biplots of compositional data. Appl. Stat. 51, 375–392 (2002)

    MathSciNet  MATH  Google Scholar 

  2. Cuadras, C.M.: Correspondence analysis and diagonal expansions in terms of distribution functions. J. Stat. Plan. Inference 103, 137–150 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  3. Cuadras, C.M.: Distance-based multisample tests for multivariate data. In: Arnold, B.C. et al. (eds.) Advances in Mathematical and Statistical Modeling, pp. 61–71. Birkhauser, Boston, MA (2008)

    Chapter  Google Scholar 

  4. Cuadras, C.M., Atkinson, R.A., Fortiana, J.: Probability densities from distances and discriminant analysis. Stat. Probab. Lett. 33, 405–411 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  5. Cuadras, C.M., Cuadras, D.: A parametric approach to correspondence analysis. Linear Algebra Appl. 417, 64–74 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  6. Cuadras, C.M., Cuadras, D., Greenacre, M.J.: A comparison of different methods for representing categorical data. Commun. Stat. Simul. Comp. 35, 447–459 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  7. Cuadras, C.M., Fortiana, J., Oliva, F.: The proximity of an individual to a population with applications in discriminant analysis. J. Classification 14, 117–136 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  8. Fichet, B., Gbegan, A.: Analyse factorielle des correspondances sur signes de présence-absence. In: Diday, E. et al. (eds.) Data Analysis and Informatics IV, pp. 209–219. Elsevier, Amsterdam (1985)

    Google Scholar 

  9. Goodman, L.A.: Correspondence analysis, association analysis, and generalized nonindependence analysis of contingency tables: saturated and unsaturated models, and appropriate graphical displays. In: Cuadras, C.M., Rao, C.R. (eds.) Multivariate Analysis: Future Directions 2, pp. 265–294. Elsevier, Amsterdam (1993)

    Google Scholar 

  10. Greenacre, M.J.: Theory and Applications of Correspondence Analysis. Academic Press, London (1984)

    MATH  Google Scholar 

  11. Greenacre, M.J.: Power transformations in correspondence analysis. Comput. Stat. Data Anal. 53, 3107–3116 (2008)

    Article  MathSciNet  Google Scholar 

  12. Kroonenberg, P.M., Lombardo, R.: Nonsymmetric correspondence analysis: a tool for analysing contingency tables with a dependence structure. Multivariate Behav. Res. 34, 367–396 (1999)

    Article  Google Scholar 

  13. Lauro, N., D’Ambra, L.: L’analyse non symetrique des correspondances. In: Diday, E. et al. (eds.) Data Analysis and Informatics III, pp. 433–446. North Holland, Amsterdam (1984)

    Google Scholar 

  14. Lewi P.J.: Spectral mapping, a technique for classifying biological activity profiles of chemical compounds. Arzneim. Forsch. (Drug Res.) 26, 1295–1300 (1976)

    Google Scholar 

  15. Light, R.J., Margolin, B.H.: An analysis of variance for categorical data. J. Am. Stat. Assoc. 66, 534–544 (1971)

    Article  MathSciNet  MATH  Google Scholar 

  16. Rao, C.R.: Diversity: Its measurement, decomposition, apportionment and analysis. Sankhya A 44, 1–21 (1982)

    MATH  Google Scholar 

  17. Rao, C.R.: A review of canonical coordinates and an alternative to correspondence analysis using Hellinger distance. Qüestiió 19, 23–63 (1995)

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Statistics, University of Barcelona, Barcelona, Spain

    Carles M. Cuadras

  2. IDIBELL, Barcelona, Spain

    Daniel Cuadras

Authors
  1. Carles M. Cuadras
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Daniel Cuadras
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Carles M. Cuadras .

Editor information

Editors and Affiliations

  1. , Laboratoire d' Informatique, Université d' Aix-Marseille II, Avenue de Luminy 163case 901, Marseille cedex 9, 13288, France

    Bernard Fichet

  2. , Dipartimento di Scienze Statistiche, Università di Napoli "Federico II", Via Leopoldo Rodinò 22, Naples, 80138, Italy

    Domenico Piccolo

  3. , Facoltà di Studi Politici "Jean Monnet", Seconda Università di Napoli, Via del Setificio 15, Caserta, 81100, Italy

    Rosanna Verde

  4. , Facoltà di Scienze Statistiche, Università di Roma "La Sapienza", P.le Aldo Moro 5, Rome, 00185, Italy

    Maurizio Vichi

Rights and permissions

Reprints and permissions

Copyright information

© 2011 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Cuadras, C.M., Cuadras, D. (2011). Partitioning the Geometric Variability in Multivariate Analysis and Contingency Tables. In: Fichet, B., Piccolo, D., Verde, R., Vichi, M. (eds) Classification and Multivariate Analysis for Complex Data Structures. Studies in Classification, Data Analysis, and Knowledge Organization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13312-1_24

Download citation

Publish with us

Policies and ethics

Search

Navigation