Decomposition of Measure for Marginal Homogeneity in Square Contingency Tables with Ordered Categories
DOI:
https://doi.org/10.17713/ajs.v36i2.325Abstract
For the analysis of square contingency tables with ordered categories, Tomizawa et al. (2003) considered a measure to represent the degree of departure from marginal homogeneity (MH). Tomizawa (1993) considered an extended marginal homogeneity (EMH) model. This paper (i) proposes a measure to represent the degree of departure from EMH, (ii) proposes a measure from equality of marginal means (E), and (iii) gives a theorem that the value of measure for MH is equal to the sum of the value of measure for EMH and that for E.References
Agresti, A. (1990). Categorical Data Analysis. New York: John Wiley.
Bishop, Y. M. M., Fienberg, S. E., and Holland, P. W. (1975). Discrete Multivariate Analysis: Theory and Practice. Cambridge, Massachusetts: The MIT Press.
Breslow, N. E., and Day, N. E. (1980). Statistical Methods in Cancer Research, Vol. I—The Analysis of Case-Control Studies. Lyon, France: International Agency for Research on Cancer.
Stuart, A. (1955). A test for homogeneity of the marginal distributions in a two-way classification. Biometrika, 42, 412-416.
Tallis, G. M. (1962). The maximum likelihood estimation of correlation from contingency tables. Biometrics, 18, 342-353.
Tominaga, K. (1979). Nippon no Kaisou Kouzou (Japanese Hierarchical Structure). Tokyo: University of Tokyo Press. (in Japanese)
Tomizawa, S. (1991). Decomposing the marginal homogeneity model into two models for square contingency tables with ordered categories. Calcutta Statistical Association Bulletin, 41, 201-207.
Tomizawa, S. (1993). Diagonals-parameter symmetry model for cumulative probabilities in square contingency tables with ordered categories. Biometrics, 49, 883-887.
Tomizawa, S. (1995). Measures of departure from marginal homogeneity for contingency tables with nominal categories. Journal of the Royal Statistical Society, Series D, The Statistician, 44, 425-439.
Tomizawa, S., and Makii, T. (2001). Generalized measures of departure from marginal homogeneity for contingency tables with nominal categories. Journal of Statistical Research, 35, 1-24.
Tomizawa, S., Miyamoto, N., and Ashihara, N. (2003). Measure of departure from marginal homogeneity for square contingency tables having ordered categories. Behaviormetrika, 30, 173-193.
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