Published studies using the regression discontinuity design have been limited to cases in which linear regression is applied to a categorical treatment indicator and an equal interval outcome. This is unnecessarily narrow. We show here how a generalization the usual regression discontinuity design can be applied in a wider range of situations. We focus on the use of categorical treatment and response variables, but we also consider the more general case of any regression relationship. We also show how a resampling sensitivity analysis may be used to address the credibility of the assumed assignment process. The broader formulation is applied to an evaluation of California's inmate classification system, which is used to allocate prisoners to different kinds of confinement.