Many applications of the Fellegi-Sunter model use simplifying assumptions and ad hoc modifications to improve matching efficacy. Because of model misspecification, distinctive approaches developed in one application typically cannot be used in other applications and do not always make use of advances in statistical and computational theory. An Expectation-Maximization (EMH) algorithm that constrains the estimates to a convex subregion of the parameter space is given. The EMH algorithm provides probability estimates that yield better decision rules than unconstrained estimates. The algorithm is related to results of Meng and Rubin (1993) on Multi-Cycle Expectation-Conditional Maximization algorithms and make use of results of Haberman (1977) that hold for large classes of loglinear models.

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