Abstract
For square contingency tables with ordered categories, the present paper considers two kinds of weak marginal homogeneity and gives measures to represent the degree of departure from weak marginal homogeneity. The proposed measures lie between –1 to 1. When the marginal cumulative logistic model or the extended marginal homogeneity model holds, the proposed measures represent the degree of departure from marginal homogeneity. Using these measures, three kinds of unaided distance vision data are analyzed.
Highlights
Consider an R R square contingency table with ordered categories
For square contingency tables with ordered categories, the present paper considers two kinds of weak marginal homogeneity and gives measures to represent the degree of departure from weak marginal homogeneity
When the marginal cumulative logistic model or the extended marginal homogeneity model holds, the proposed measures represent the degree of departure from marginal homogeneity
Summary
Let pij denote the probability that an observation will fall in the ith row and jth column of the table ( i 1, , R ; j 1, , R ). When the MH model does not hold, we are interested in applying the model that has weaker restriction than the MH model As such a model, for example, there are the marginal cumulative logistic (ML) model ([2]) and the extended marginal homogeneity (EMH) model ([3,4,5]). When the structure of weak MH does not hold, we are interested in measuring what degree the departure from weak MH is.
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