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.
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References
Everitt, B.: The Analysis of Contingency Tables, 2nd edn. Chapman & Hall/CRC, Boca Raton (1992)
Tsumoto, S.: Contingency matrix theory: Statistical dependence in a contingency table. Inf. Sci. 179(11), 1615–1627 (2009)
Tsumoto, S., Hirano, S.: Meaning of pearson residuals - linear algebra view. In: Proceedings of IEEE GrC 2007. IEEE press, Los Alamitos (2007)
Tsumoto, S., Hirano, S.: Contingency matrix theory ii: Degree of dependence as granularity. Fundam. Inform. 90(4), 427–442 (2009)
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)
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)
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Tsumoto, S., Hirano, S. (2010). Residual Analysis of Statistical Dependence in Multiway Contingency Tables. In: Yu, J., Greco, S., Lingras, P., Wang, G., Skowron, A. (eds) Rough Set and Knowledge Technology. RSKT 2010. Lecture Notes in Computer Science(), vol 6401. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-16248-0_41
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DOI: https://doi.org/10.1007/978-3-642-16248-0_41
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-16247-3
Online ISBN: 978-3-642-16248-0
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