Appling WLE To Early Stage Of CAT

The early stage of computerized adaptive testing (CAT) refers to the phase of the trait estimation during the administration of only a few items. In order to obtain more precision results, bias and instability of estimation should be considered. On one hand, an unbiased or less biased estimation method is desirable. Warm had proved that weighted likelihood estimate (WLE) not only reduces the bias of maximum likelihood estimate (MLE), but also reduces the standard errors (SEs) for three-parameter logistical model with fixed test length. This study introduces WLE to estimate the ability-parameter using the multidimensional nominal response model and has proved that WLE has good results. Firstly, WLE has less bias than MLE with as many as four times as many items according to the results of simulations. Secondly, WLE has lower SEs and RMSEs (root mean square error) than those of MLE at almost all ability levels according to the results of SE and RMSE of the two ability estimation methods for 30 items. Finally, this study shows the average number of items administered to reach the second stopping rule (i.e. fixed maximum standard error of the ability estimate of 0.5) for the two estimators. At the three values of ability -1, 0 and 1, WLE use the numbers of items as few as half as many items as MLE shown from the simulation results. Thus, WLE is better than MLE. On the other hand, an item selection criterion (ISC) can lessen the instability. This study introduces two ISCs: the FI criterion and the KL criterion. Considering the high precision of WLE, it can be applied to the CAT. The results of WLE combined with two ISCs for the nominal response model are discussd. According to the simulation results, the FI criterion is better than the KL criterion at some ability points but not all pionts. Thus WLE(θ) is a less biaesd and its numbers of items used in tests are less than MLE(θ).