Solving the measurement invariance anchor item problem in item response theory.

The efficacy of tests of differential item functioning (measurement invariance) has been well established. It is clear that when properly implemented, these tests can successfully identify differentially functioning (DF) items when they exist. However, an assumption of these analyses is that the metric for different groups is linked using anchor items that are invariant. In practice, however, it is impossible to be certain which items are DF and which are invariant. This problem of anchor items, or referent indicators, has long plagued invariance research, and a multitude of suggested approaches have been put forth. Unfortunately, the relative efficacy of these approaches has not been tested. This study compares 11 variations on 5 qualitatively different approaches from recent literature for selecting optimal anchor items. A large-scale simulation study indicates that for nearly all conditions, an easily implemented 2-stage procedure recently put forth by Lopez Rivas, Stark, and Chernyshenko (2009) provided optimal power while maintaining nominal Type I error. With this approach, appropriate anchor items can be easily and quickly located, resulting in more efficacious invariance tests. Recommendations for invariance testing are illustrated using a pedagogical example of employee responses to an organizational culture measure.