Applying the Liu-Agresti estimator of the cumulative common odds ratio to DIF detection in polytomous items

Liu and Agresti (1996) proposed a Mantel and Haenszel-type (1959) estimator of a common odds ratio for several 2 x J tables, where the J columns are ordinal levels of a response variable. This article applies the Liu-Agresti estimator to the case of assessing differential item functioning (DIF) in items having an ordinal response variable. A simulation study was conducted to investigate the accuracy of the Liu-Agresti estimator in relation to other statistical DIF detection procedures. The results of the simulation study indicate that the Liu-Agresti estimator is a viable alternative to other DIF detection statistics.