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

In longitudinal assessments, tests are frequently used to estimate trends over time. However, when item parameters lack invariance, time-point comparisons can be distorted, necessitating appropriate statistical methods to achieve accurate estimation. This study compares trend estimates using the two-parameter logistic (2PL) model under item parameter drift (IPD) across five trend-estimation approaches for two time points: First, concurrent calibration, which jointly estimates item parameters across multiple time points. Second, fixed calibration, which estimates item parameters at a single time point and fixes them at the other time point. Third, robust linking with Haberman and Haebara as linking methods with <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub><mml:mrow><mml:mi>L</mml:mi></mml:mrow> <mml:mrow><mml:mi>p</mml:mi></mml:mrow> </mml:msub> </mml:mrow> </mml:math> or <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub><mml:mrow><mml:mi>L</mml:mi></mml:mrow> <mml:mrow><mml:mn>0</mml:mn></mml:mrow> </mml:msub> </mml:mrow> </mml:math> losses. Fourth, non-invariant items are detected using likelihood-ratio tests or the root mean square deviation statistic with fixed or data-driven cutoffs, and trend estimates are then recomputed using only the detected invariant items under partial invariance. Fifth, regularized estimation under a smooth Bayesian information criterion (SBIC) is applied, shrinking small or null IPD effects toward zero while estimating all others as nonzero. Bias and relative root mean square error (RMSE) were evaluated for the mean and <i>SD</i> at T2. An empirical example using synthetic longitudinal reading data, applying the trend-estimation approaches, is provided. The results indicate that the regularized estimation with SBIC performed best across conditions, maintaining low bias and RMSE, followed by robust linking methods. Specifically, Haberman linking with the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub><mml:mrow><mml:mi>L</mml:mi></mml:mrow> <mml:mrow><mml:mn>0</mml:mn></mml:mrow> </mml:msub> </mml:mrow> </mml:math> loss function showed superior performance under unbalanced IPD, outperforming the partial invariance approaches. Concurrent and fixed calibration showed the poorest trend recovery under unbalanced IPD conditions.