Measure of departure from marginal homogeneity using marginal odds for multi-way tables with ordered categories

For square contingency tables with ordered categories, this paper proposes a measure to represent the degree of departure from the marginal homogeneity model. It is expressed as the weighted sum of the power-divergence or Patil–Taillie diversity index, and is a function of marginal log odds ratios. The measure represents the degree of departure from the equality of the log odds that the row variable is i or below instead of i+1 or above and the log odds that the column variable is i or below instead of i+1 or above for every i. The measure is also extended to multi-way tables. Examples are given.