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In this paper, a review is given of various goodness-of-fit measures that have been proposed for the binary choice model in the last two decades. The relative behaviour of several pseudo-R2 measures is analysed in a series of misspecified binary choice models, the misspecification being omitted variables or an included irrelevant variable. A comparison is made with the OLS-R2 of the underlying latent variable model and with the squared sample correlation coefficient of the true and predicted probabilities. Further, it is investigated how the values of the measures change with a changing frequency rate of successes.
Frank Windmeijer (Sun,) studied this question.