Partial Measurement Invariance: Extending and Evaluating the Cluster Approach for Identifying Anchor Items.

When measurement invariance does not hold, researchers aim for partial measurement invariance by identifying anchor items that are assumed to be measurement invariant. In this paper, we build on Bechger and Maris's approach for identification of anchor items. Instead of identifying differential item functioning (DIF)-free items, they propose to identify different sets of items that are invariant in item parameters within the same item set. We extend their approach by an additional step in order to allow for identification of homogeneously functioning item sets. We evaluate the performance of the extended cluster approach under various conditions and compare its performance to that of previous approaches, that are the equal-mean difficulty (EMD) approach and the iterative forward approach. We show that the EMD and the iterative forward approaches perform well in conditions with balanced DIF or when DIF is small. In conditions with large and unbalanced DIF, they fail to recover the true group mean differences. With appropriate threshold settings, the cluster approach identified a cluster that resulted in unbiased mean difference estimates in all conditions. Compared to previous approaches, the cluster approach allows for a variety of different assumptions as well as for depicting the uncertainty in the results that stem from the choice of the assumption. Using a real data set, we illustrate how the assumptions of the previous approaches may be incorporated in the cluster approach and how the chosen assumption impacts the results.