Advertisement

Residual Analysis of Statistical Dependence in Multiway Contingency Tables

  • Shusaku Tsumoto
  • Shoji Hirano
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6401)

Abstract

A Pearson residual is defined as the residual between actual values and expected ones of each cell in a contingency table. This paper shows that this residual is represented as linear sum of determinants of 2 ×2, which suggests that the geometrical nature of the residuals can be viewed from grasmmanian algebra.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Everitt, B.: The Analysis of Contingency Tables, 2nd edn. Chapman & Hall/CRC, Boca Raton (1992)Google Scholar
  2. 2.
    Tsumoto, S.: Contingency matrix theory: Statistical dependence in a contingency table. Inf. Sci. 179(11), 1615–1627 (2009)zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Tsumoto, S., Hirano, S.: Meaning of pearson residuals - linear algebra view. In: Proceedings of IEEE GrC 2007. IEEE press, Los Alamitos (2007)Google Scholar
  4. 4.
    Tsumoto, S., Hirano, S.: Contingency matrix theory ii: Degree of dependence as granularity. Fundam. Inform. 90(4), 427–442 (2009)zbMATHMathSciNetGoogle Scholar
  5. 5.
    Tsumoto, S., Hirano, S.: Dependency and granularity indata. In: Meyers, R.A. (ed.) Encyclopedia of Complexity and Systems Science, pp. 1864–1872. Springer, Heidelberg (2009)Google Scholar
  6. 6.
    Tsumoto, S., Hirano, S.: Statistical independence and determinants in a contingency table - interpretation of pearson residuals based on linear algebra. Fundam. Inform. 90(3), 251–267 (2009)zbMATHMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Shusaku Tsumoto
    • 1
  • Shoji Hirano
    • 1
  1. 1.Department of Medical Informatics, Faculty of MedicineShimane UniversityJapan

Personalised recommendations