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Biometrika 1979 66(3):413-418; doi:10.1093/biomet/66.3.413
© 1979 by Biometrika Trust
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Multiplicative models for square contingency tables with ordered categories

LEO A. GOODMAN

Department of Statistics, Universtiy of Chicago

For the analysis of square contingency tables having ordered categories, this paper introduces the diagonals-parameter symmetry model and other related multiplicative models. When these models are applied to the 4 x 4 table on unaided vision first analysed by Stuart (1953, 1955), a possible explanation is obtained for (i) the ‘strange residual pattern’ noted by McCullagh (1978), both in his recent analysis of the data using the palindromic symmetry model and in the analysis of the data using the quasisymmetry model as fitted by Plackett (1974, p. 61) and others; (ii) the observed asymmetry in the table; (iii) the in-homogeneity observed between the row marginal, i.e. right eye vision, and the column marginal, left eye vision; and (iv) the observed association between right eye and left eye vision. The models introduced in this paper are included within the general class of multiplicative models considered by Goodman (1972), but they are different from the specific kinds of models considered in that article.

Key Words: Association • Marginal homogeneity • Multiplicative model • Ordered categorical data • Quasisymmetry • Square contingency table • Symmetry


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