No abstract

Online calibration technique has been widely employed to calibrate new items due to its advantages. Method A is the simplest online calibration method and has attracted many attentions from researchers recently. However, a key assumption of Method A is that it treats personparameter estimatesûs (obtained by maximum likelihood estimation [MLE]) as their true values us, thus the deviation of the estimatedûs from their true values might yield inaccurate item calibration when the deviation is nonignorable. To improve the performance of Method A, a new method, MLE-LBCI-Method A, is proposed. This new method combines a modified Lord's biascorrection method (named as maximum likelihood estimation-Lord's bias-correction with iteration [MLE-LBCI]) with the original Method A in an effort to correct the deviation ofûs which may adversely affect the item calibration precision. Two simulation studies were carried out to explore the performance of both MLE-LBCI and MLE-LBCI-Method A under several scenarios. Simulation results showed that MLE-LBCI could make a significant improvement over the ML ability estimates, and MLE-LBCI-Method A did outperform Method A in almost all experimental conditions.

Previous designs for online calibration have only considered examinees' responses to items. However, the use of response time, a useful metric that can easily be collected by a computer, has not yet been embedded in calibration designs. In this article we utilize response time to optimize the assignment of new items online, and accordingly propose two new adaptive designs. These are the D-optimal per expectation time unit design (D-ET) and the D-optimal per time unit design (D-T). The former method uses the conditional maximum likelihood estimation (CMLE) method to estimate the expected response times, while the latter employs the nonparametric k-nearest-neighbour method to predict the response times. Simulations were conducted to compare the two new designs with the D-optimal online calibration design (D design) in the context of continuous online calibration. In addition, a preliminary study was carried out to evaluate the performance of CMLE prior to its application in D-ET. The results showed that, compared to the D design, the D-ET and D-T designs saved response time and accrued larger calibration information per time unit, without sacrificing item calibration precision.

When calibrating new items online, it is practicable to first compare all new items according to some criterion and then assign the most suitable one to the current examinee who reaches a seeding location. The modified D-optimal design proposed by van der Linden and Ren (denoted as D-VR design) works within this practicable framework with the aim of directly optimizing the estimation of item parameters. However, the optimal design point for a given new item should be obtained by comparing all examinees in a static examinee pool. Thus, D-VR design still has room for improvement in calibration efficiency from the view of traditional optimal design. To this end, this article incorporates the idea of traditional optimal design into D-VR design and proposes a new online calibration design criterion, namely, excellence degree (ED) criterion. Four different schemes are developed to measure the information provided by the current examinee when implementing this new criterion, and four new ED designs equipped with them are put forward accordingly. Simulation studies were conducted under a variety of conditions to compare the D-VR design and the four proposed ED designs in terms of calibration efficiency. Results showed that the four ED designs outperformed D-VR design in almost all simulation conditions.