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 × 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.