This paper describes the graded response model. The graded response model represents a family of mathematical models that deal with ordered polytomous categories, such as: (1) letter grading; (2) an attitude survey with "strongly disagree, disagree, agree, and strongly agree" choices; (3) partial credit given in accord with an individual's degree of attainment; and (4) computerized cognitive diagnosis. Equations are given for the general model and for homogeneous and heterogeneous cases. Conditions are outlined for model selection, and estimation of the operating characteristics is described. (Contains 1 table, 10 figures, and 18 references.) (SLD)