A Comparison of Linking Methods for Longitudinal Designs with the 2PL Model Under Item Parameter Drift

This study investigates longitudinal linking of dichotomous item responses across three time points, focusing on Haberman, Haebara, Stocking-Lord linking, and concurrent calibration under item parameter drift (IPD). Two general approaches, joint and chain linking, are examined. Three simulation studies compared these methods under conditions of IPD and linking designs. The first simulation study assessed linking methods under sampling error and uniform IPD. Results showed Haberman joint linking minimized bias and root mean square error (RMSE), especially at larger sample sizes, while concurrent calibration was most accurate without IPD. The second simulation study introduced two additional designs: one relying solely on anchor items across all three time points, and the other using only adjacent items between consecutive time points. Under no IPD, concurrent calibration remained most precise, while under uniform IPD, Haberman methods balanced bias and precision. The third simulation study analyzed nonuniform IPD, finding Haberman chain linking achieved the best bias and RMSE performance. Overall, chain linking methods outperformed joint linking in the presence of IPD. Implications for analyzing longitudinal linking designs are discussed.