Bayesian DINA Modeling Incorporating Within-Item Characteristic Dependency:

The within-item characteristic dependency (WICD) means that dependencies exist among different types of item characteristics/parameters within an item. The potential WICD has been ignored by current modeling approaches and estimation algorithms for the deterministic inputs noisy “and” gate (DINA) model. To explicitly model WICD, this study proposed a modified Bayesian DINA modeling approach where a bivariate normal distribution was employed as a joint prior distribution for correlated item parameters. Simulation results indicated that the model parameters were well recovered and that explicitly modeling WICD improved model parameter estimation accuracy, precision, and efficiency. In addition, when potential item blocks existed, the proposed modeling approach still demonstrated good performance and high robustness. Furthermore, the fraction subtraction data were analyzed to illustrate the application and advantage of the proposed modeling approach.