Within the rich literature on generalized linear models, substantial efforts have been devoted to models for categorical responses that are either completely ordered or completely unordered. Few studies have focused on the analysis of partially ordered outcomes, which arise in practically every area of study, including medicine, the social sciences, and education. To fill this gap, we propose a new class of generalized linear models—the partitioned conditional model—that includes models for both ordinal and unordered categorical data as special cases. We discuss the specification of the partitioned conditional model and its estimation. We use an application of the method to a sample of the National Longitudinal Study of Youth to illustrate how the new method is able to extract from partially ordered data useful information about smoking youths that is not possible using traditional methods. Copyright © 2011 John Wiley & Sons, Ltd.