Many social processes studied by demographers can be viewed as two-sided matching markets. For example, heterosexual marriages, job searching, and residency assignments for medical school graduates all require members of two disjoint groups to mutually consent to form a relationship, or “match.'' Yet the underlying mechanisms dictating such processes are often opaque. Demographers require statistical models for partnership formation that separate the underlying preferences individuals have for various types of partners from the availability of such partners.