Sankhya: The Indian Journal of Statistics

1998, Volume 60, Series B, Pt. 2, 293--300

A DECOMPOSITION OF THE MARGINAL HOMOGENEITY MODEL INTO THREE MODELS FOR SQUARE CONTINGENCY TABLES WITH ORDERED CATEGORIES

By

SADAO TOMIZAWA
*Science University of Tokyo, Noda City*

SUMMARY. For square contingency tables with ordered categories, this paper decomposes the marginal homogeneity (MH) model into three models, i.e., (i) a generalized MH model, (ii) the model of equality of expectations of monotonic functions of row and column variables and (iii) the model of equality of variances of them. When the MH model fits the data poorly, this decomposition may be useful to understand why it is so. Such an example is given.

*AMS (1991) subject classification.*62H17

*Key words and phrases. *Extended marginal homogeneity, generalized
marginal homogeneity, marginal means, marginal variances, score.