Detecting differential item functioning with unknown subgroups and anchor items in cognitive diagnostic assessment

Differential item functioning (DIF) analysis is essential for evaluating measurement invariance in educational and psychological assessments. In cognitive diagnostic assessment, however, most existing methods require prespecified comparison subgroups and anchor items. When subgroup membership and anchor items are unavailable or mis-specified, DIF detection and parameter estimation may be biased. To overcome these limitations, this study puts forward a DIF detection method that incorporates an extended modelling framework and a two-stage estimation algorithm. The proposed modelling framework directly integrates DIF parameters into the measurement model and uses a structural model to characterize subgroup differences in attribute mastery distributions. A two-stage expectation maximization algorithm with an adaptive lasso penalty is developed to identify anchor items, classify respondents into latent subgroups and estimate model parameters. The performance of the proposed method was evaluated through a simulation study and an empirical data analysis. Simulation results indicated generally satisfactory DIF detection and parameter recovery, although subgroup-classification accuracy varied across conditions. When applied to the empirical data, the proposed method identified 10 of the 28 items as exhibiting DIF.