Marginal asymmetry model for square contingency tables with ordered categories

For the analysis of square contingency tables with ordered categories, this paper proposes a model which indicates the structure of marginal asymmetry. The model states that the absolute values of logarithm of ratio of the cumulative probability that an observation will fall in row category <italic>i</italic> or below and column category <italic>i</italic>+1 or above to the corresponding cumulative probability that the observation falls in column category <italic>i</italic> or below and row category <italic>i</italic>+1 or above are constant for every <italic>i</italic>. We deal with the estimation problem for the model parameter and goodness-of-fit tests. Also we discuss the relationships between the model and a measure which represents the degree of departure from marginal homogeneity. Examples are given.