Roll call data are widely used to assess legislators’ preferences and ideology, as well as to test theories of legislative behavior. In particular, roll call data is often used to determine whether the revealed preferences of legislators are affected by outside forces such as party pressure, minority status or procedural rules. This talk will describe Bayesian hierarchical models that extend existing spatial voting models to test sharp hypotheses about differences in preferences. We consider two main applications. In the first one, we study the impact of party switching in evenly divided legislatures on representative’ preferences (as was the case, for example, during the 107th U.S. Senate). In the second one, we estimate how legislators’ preferences have varied across various policy domains in the U.S. House of Representatives over the last 30 years. In the last part of the talk we discuss some of our work in progress where we extend these models to identify variables that can explain observed differences in preferences across domains. This is joint work with Scott Moser (Nottingham) and Chelsea Lofland.