Issue definitions, the way policy issues are understood, are an important component for understanding the policymaking process. Research on issue definitions has been divided between a macro level that examines collective issue definitions and a micro level focusing on the ways in which policy actors frame policy issues. This article develops a model of issue definitions that assumes issues are multidimensional, competition exists among policy actors in defining issues, and that collective issue definitions can be understood as the aggregation of individual issue definitions. This model is then estimated using quantitative text analysis. While various approaches to text analysis and categorization have been used by scholars, latent Dirichlet allocation (LDA), a specific type of topic modeling, is used to estimate issue definitions. Using LDA, witness testimony taken from Congressional hearings that occurred from 1975 to 2012 about the issue of used nuclear fuel (UNF) is examined and seven distinct dimensions of the UNF debate are estimated. The construct validity of these dimensions is checked by testing them against two major policy changes that occurred in the UNF domain. I conclude with a discussion of the strengths and weakness of topic modeling, and how this approach could be used to test hypotheses drawn from several of the major policymaking theories.