Compound Optimal Design for Online Item Calibration Under the Two-Parameter Logistic Model

Under the theory of sequential design, compound optimal design with two optimality criteria can be used to solve the problem of efficient calibration of item parameters of item response theory model. In order to efficiently calibrate item parameters in computerized testing, a compound optimal design is proposed for the simultaneous estimation of item difficulty and discrimination parameters under the two-parameter logistic model, which adaptively focuses on optimizing the parameter which is difficult to estimate. The compound optimal design using the acceptance probability can provide ability design points to optimize the item difficulty and discrimination parameters, respectively. Simulation and real data analysis studies showed that the compound optimal design outperformed than the D-optimal and random design in terms of the recovery of both discrimination and difficulty parameters.