A moment method is proposed for regression analysis of bivariate ordered categorical data using the global odds ratio as the measure of association. For modeling the margins, this method utilizes the stochastic ordering implicit in the data. This method allows for covariate effects in modeling the association between responses. An application of the proposed model is illustrated using the ophthalmological data from the Wisconsin Epidemiologic Study of Diabetic Retinopathy for identifying risk factors among younger onset diabetics. This model is also extended to a longitudinal data setting with more than two repeated measures.