Estimating Longitudinal Trends with Differential Item Functioning: A Comparison of Five IRT-Based Approaches

In longitudinal assessments, tests are frequently used to estimate trends over time. When item parameters lack invariance, time point comparisons can be distorted, necessitating the use of appropriate statistical methods for accurate estimation. This study compares trend estimates using the 2PL model under item parameter drift (IPD) across five trend estimation approaches for two time points: concurrent calibration, which jointly estimates all item parameters across time points and assumes full invariance; fixed calibration, which calibrates the first time point (T1), and calibrates subsequently the second time point (T2) with the common item parameters being fixed to the estimates from T1; separate calibration of the two time points is followed by robust Haberman or Haebara linking that down-weights outlying common items via $L_p$ or $L_0$ losses to place parameters on the scale of T1; partial invariance via IPD detection, where non-invariant items are identified using likelihood-ratio tests or root mean square deviation (RMSD) with fixed or data-driven cutoffs and trends are re-estimated on the resulting anchor set; and regularized estimation that simultaneously estimates all parameters while shrinking most IPD effects toward zero using a smooth Bayesian information criterion (SBIC).The simulation study varied sample size, number of items, IPD effect size, IPD item proportion, and whether the IPD was balanced or unbalanced. Bias and relative RMSE were evaluated for the mean and SD at T2. An empirical example using synthetic longitudinal reading data, applying trend estimation approaches, is provided.Results indicate that SBIC regularized estimation generally performed best across conditions, maintaining low bias and RMSE. Among robust linking methods, Haberman linking with the $L_0$ loss function showed superior performance under unbalanced IPD. Detection-based approaches revealed that commonly used RMSD cutoffs may be too lenient; stricter cutoffs (0.03 to 0.05) were necessary to achieve satisfactory parameter recovery, especially under unbalanced IPD conditions.