A note on the application of stochastic approximation to computerized adaptive testing

In the study of item response theory (IRT), the maximum information (item selection) method (or procedure, rule) is prevailing in test constructions, including the computerized adaptive testing (CAT). However, this method may not be suitable if the trial number is small in the CAT. In this note, we advocate the use of the stochastic-approximation-based rule for item difficulty determination for short test lengths in the CAT. We also describe a generalized stochastic-approximation rule to take item discrimination into account. In a simulation study, we considered two cases of the IRT, namely the Rasch model and the 2PL model, and for each case compared the performance of the information-based and stochastic-approximation-based procedures for trials from 10 to 60. The results showed that the accelerated stochastic approximation procedure (and its generalization) was more efficient than the information-based method across the trials. Further, in both procedures, the bias of the estimator started to diminish quickly after the early stages of trials. © 2023, The Behaviormetric Society.