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Misreporting is a problem that plagues researchers who use survey data. In this article, we develop a parametric model that corrects for misclassified binary responses using information on the misreporting patterns obtained from auxiliary data sources. The model is implemented within the Bayesian framework via Markov Chain Monte Carlo (MCMC) methods and can be easily extended to address other problems exhibited by survey data, such as missing response and/or covariate values. While the model is fully general, we illustrate its application in the context of estimating models of turnout using data from the American National Elections Studies.