For multi-way tables with ordered
categories, the present paper gives a decomposition of the point-symmetry model
into the ordinal quasi point-symmetry and equality of point-symmetric marginal
moments. The ordinal quasi point-symmetry model indicates asymmetry for cell
probabilities with respect to the center point in the table.
References
[1]
Bhapkar, V.P. and Darroch, J.N. (1990) Marginal Symmetry and Quasi Symmetry of General Order. Journal of Multivariate Analysis, 34, 173-184. http://dx.doi.org/10.1016/0047-259X(90)90034-F
[2]
Agresti, A. (2013) Categorical Data Analysis. 3rd Edition, Wiley, Hoboken.
[3]
Tahata, K., Yamamoto, H. and Tomizawa, S. (2011) Linear Ordinal Quasi-Symmetry Model and Decomposition of Symmetry for Multi-Way Tables. Mathematical Methods of Statistics, 20, 158-164.
http://dx.doi.org/10.3103/S1066530711020050
[4]
Agresti, A. (2010) Analysis of Ordinal Categorical Data. 2nd Edition, Wiley, Hoboken.
http://dx.doi.org/10.1002/9780470594001
[5]
Caussinus, H. (1965) Contribution à l’analyse statistique des tableaux de corrélation. Annales de la Faculté des Sciences de l’Université de Toulouse, 29, 77-182. http://dx.doi.org/10.5802/afst.519
[6]
Bishop, Y.M.M., Fienberg, S.E. and Holland, P.W. (1975) Discrete Multivariate Analysis: Theory and Practice. MIT Press, Cambridge.
[7]
Read, C.B. (1977) Partitioning Chi-Square in Contingency Tables: A Teaching Approach. Communications in Statistics, Theory and Methods, 6, 553-562. http://dx.doi.org/10.1080/03610927708827513
[8]
Kateri, M. and Papaioannou, T. (1997) Asymmetry Models for Contingency Tables. Journal of the American Statistical Association, 92, 1124-1131. http://dx.doi.org/10.1080/01621459.1997.10474068
[9]
Tahata, K. and Tomizawa, S. (2014) Symmetry and Asymmetry Models and Decompositions of Models for Contingency Tables. SUT Journal of Mathematics, 50, 131-165.
[10]
Wall, K. and Lienert, G.A. (1976) A Test for Point-Symmetry in J-Dimensional Contingency-Cubes. Biometrical Journal, 18, 259-264.
[11]
Tomizawa, S. (1985) The Decompositions for Point Symmetry Models in Two-Way Contingency Tables. Biometrical Journal, 27, 895-905. http://dx.doi.org/10.1002/bimj.4710270811
[12]
Tahata, K. and Tomizawa, S. (2008) Orthogonal Decomposition of Point-Symmetry for Multiway Tables. Advances in Statistical Analysis, 92, 255-269. http://dx.doi.org/10.1007/s10182-008-0070-5
[13]
Tahata, K. and Tomizawa, S. (2015) Ordinal Quasi Point-Symmetry and Decomposition of Point-Symmetry for Cross-Classifications. Journal of Statistics: Advances in Theory and Applications, 14, 181-194.
[14]
Darroch, J.N. and Ratcliff, D. (1972) Generalized Iterative Scaling for Log-Linear Models. Annals of Mathematical Statistics, 43, 1470-1480. http://dx.doi.org/10.1214/aoms/1177692379
