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

Area of Science:

• Psychometrics
• Statistical modeling
• Educational measurement

Background:

• Partial measurement invariance is crucial when overall invariance fails, requiring identification of invariant anchor items.
• Existing methods like Bechger and Maris's focus on identifying differential item functioning (DIF)-free items or invariant item sets.

Purpose of the Study:

• To extend Bechger and Maris's approach for identifying homogeneously functioning item sets.
• To evaluate the performance of the extended cluster approach against existing methods (EMD, iterative forward) under various DIF conditions.

Main Methods:

• Developed an extended cluster approach incorporating an additional step for identifying homogeneously functioning item sets.
• Evaluated performance across conditions with balanced, small, large, and unbalanced differential item functioning (DIF).
• Compared the cluster approach to the equal-mean difficulty (EMD) and iterative forward approaches.

Main Results:

• EMD and iterative forward approaches performed well with balanced or small DIF but failed with large, unbalanced DIF.
• The extended cluster approach, with appropriate thresholds, consistently identified item sets yielding unbiased group mean difference estimates.
• The cluster approach offers flexibility in assumptions and visualizes result uncertainty stemming from assumption choices.

Conclusions:

• The extended cluster approach provides a robust method for partial measurement invariance, outperforming previous methods under challenging DIF conditions.
• This approach enhances the accuracy of estimating group mean differences in psychometric and educational measurement.
• The method's flexibility allows for incorporating various assumptions and understanding their impact on results.