For square contingency tables with ordered categories, this paper introduces polynomial diagonal marginal symmetry (PDMS) models. Tomizawa's (1990b) polynomial diagonals-parameter symmetry (PDPS) models are decomposed into the PDMS model and Goodman's (1979) diagonals-parameter symmetry model. It is noted that the likelihood ratio statistic for testing the PDPS model is equal to the sum of those for testing the decomposed models.
