ABSTRACT
In Item Response Theory, the most important assumptions to be evaluated are the ones of subpopulation invariance—a violation often labeled as differential item functioning—the shape of the item response functions, and local stochastic independence. Maydue-Olivares and Joe and also see, Maydue-Olivares and Montag introduced a family of goodness-of-fit statistics for testing hypotheses in multidimensional contingency tables that can also be applied to Item Response Theory models. A plethora of residuals can be defined, including residuals that target potential violations of specific well-known model assumptions. The column labeled “Res” gives the residuals indicating whether the observed associations were too high or too low.
