Scholars of legislative studies typically use ideal point estimates from scaling procedures to test theories of legislative politics. We contend that theory and methods may be better integrated by directly incorporating maintained and to be tested hypotheses in the statistical model used to estimate legislator preferences. In this view of theory and estimation, formal modeling (1) provides auxiliary assumptions that serve as constraints in the estimation process, and (2) generates testable predictions. The estimation and hypothesis testing procedure uses roll call data to evaluate the validity of theoretically derived to be tested hypotheses in a world where maintained hypotheses are presumed true. We articulate the approach using the language of statistical inference (both frequentist and Bayesian). The approach is demonstrated in analyses of the well-studied Powell amendment to the federal aid-to-education bill in the 84th House and the Compromise of 1790 in the 1st House.
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