Misreporting is a problem that plagues researchers that use survey data. In this paper, we give conditions under which misreporting will lead to incorrect inferences. We then develop a model that corrects for misreporting using some auxiliary information, usually from an earlier or pilot validation study. This correction is implemented via Markov Chain Monte Carlo (MCMC) methods, which allows us to correct for other problems in surveys, such as non-response. This correction will allow researchers to continue to use the non-validated data to make inferences. The model, while fully general, is developed in the context of estimating models of turnout from the American National Elections Studies (ANES) data.