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