1.1 IRT-based DIF methods.
The basic idea of LRT is that item parameters should be invariant across different subgroups. In order to test item parameter invariance, likelihood of a compact model in which the parameters are constrained to be the same and an augmented model in which all variables of interest are allowed to vary between the subgroups are compared. The significance of this comparison is tested by means of the usual likelihood ratio test. Based on the selected IRT model, not only the item difficulties (1PL model), but also discriminations (2PL model), and pseudo-guessing parameters (3PL model) are allowed vary between the groups. The main idea is to compare the likelihood of two models and choose the model which has the largest likelihood. The LRT test statistic is defined as