Dually Adaptive Online IRT Testing System


H. Hirose


Bulletin of Informatics and Cybernetics Research Association of Statistical Sciences, Vol.48, pp.1-17, December 2016.

The item response theory (IRT) provides us not only the abilities of examinees but also the difficulties of items (problems), and it is believed that the estimated abilities are fairer and more accurate than those obtained by the classical test methods.
Using the estimated difficulties, we can construct an adaptive online testing system such that the system sequentially selects the most appropriate items to examinees automatically, resulting more accurate ability estimation and more efficient test procedures, where the term ``adaptive'' means the adequate item selection at each item selection step.
However, as the number of examinees is growing in online testing, the difficulty values measured previously will possibly differ from those assessed by the new examinees.
Then, calibration of the difficulty values may be required.
For such conditions, we propose to use the dually adaptive online IRT testing system, where ``dually adaptive'' means that one is targeted to the adequate item selection and the other is targeted to the adjustment of the difficulty values for items.
The key idea of this is to use the incomplete matrix completion.
Using the proposed method, new items can be added and their difficulties are optimally adjusted without equating.
We applied this method to mathematics testing cases, and we found that the system worked well.

Key Words

item response theory; online adaptive testing; matrix completion; dually adaptive online IRT; item registration function.



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