It is our intention to derive a methodology for which to model discrete paired longitudinal data. Through the use of transition matrices and maximum likelihood estimation techniques by means of software, we develop a way to model the progression of such data. We provide an example by applying this method to the Wisconsin Epidemiological Study of Diabetic Retinopathy data set. The data set is comprised of individuals, all diabetics, who have had their eyes examined for diabetic retinopathy. The eyes are treated as paired data, and we have the results of the examination at the four unequally spaced time points spanning over a fourteen year duration.