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Test administrators often face the challenge of detecting differential item functioning (DIF) with samples of size smaller than that recommended by experts. A Bayesian approach can incorporate, in the form of a prior distribution, existing information on the inference problem at hand, which yields more stable estimation, especially for small samples. A large volume of past data is available for many operational tests and such data could be used to establish prior distributions for a Bayesian DIF analysis. This article discusses how to perform such an analysis. The suggested approach is found to be more conservative and preferable with respect to several overall criteria than the existing DIF detection methods in a realistic simulation study.
Sinharay et al. (Mon,) studied this question.