where xi is the binary response of subject n to item i; is the ability of subject n; and ai, bi, and ci are, respectively, the discrimination, difficulty, and pseudo-guessing parameters of item i. The 2PL model can be obtained from Equation 1 by fixing ci to 0; the 1PL model can be obtained by additionally fixing ai to 1. In this study, results of IRT-based DIF detection methods were compared and the 2PL IRT method was used to estimate ability and item parameters.