Anchor Point Selection: Scale Alignment Based on an Inequality Criterion

For detecting differential item functioning (DIF) between two or more groups of test takers in the Rasch model, their parameters need to be placed on same scale. Typically this is done by means choosing a set so-called anchor items based statistical tests heuristics. Here authors suggest an alternative strategy: By inequality criterion from economics, Gini Index, are shifted optimal position where parameter estimates best overlap. Several toy examples, extensive simulation studies, and empirical application examples presented illustrate properties Index as point selection compare its those used alignment approach Asparouhov Muthén. In particular, show that—in addition globally for point—the plot contains valuable additional information may help discover unaccounted DIF-inducing multidimensionality. They further provide mathematical results that enable efficient sparse grid optimization make it feasible extend approach, example, multiple group scenarios.