| The
item response theory (IRT) gives us the valuable information about
the difficulties of problems as well as the abilities of students,
whereas the classical test method provides only the abilities of
students with pre-determined scores to each problem. To enhance
the use of the IRT, we have developed a concise IRT evaluation
Web system via the drag-and-drop EXCEL file in which 0/1 scores
of the test result are stored. In addition, we have introduced
an online adaptive IRT system to assess the students' abilities
more accurately with fewer problems. In such a system, the item
bank is pre-stored and the problem difficulties are determined
in advance. However, as the number of online adaptive examinees
becomes large, the calibration for parameters to problems, incorporating
the new examinees' results for problem difficulties, may be needed.
For the calibration, parameter estimation methods of problem difficulties
and students' abilities for incomplete response matrices are required.
In this paper, we propose a new method to estimate the problem
difficulties and students' abilities for incomplete item response
matrices via the LIRT, which is based on the item response theory
and the EM-algorithm. Then, we show a calibration procedure expressing
the problem difficulties and students' abilities to some online
adaptive system. We have found
the estimates for discrimination parameters vary to some extent from
the beginning to the end. However, the estimates for the difficulty
parameters do not vary much, which corresponds to that the estimates
for the ability parameters do not vary much. |
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response theory, online adaptive system, limiting IRT, calibration,
EM-type algorithm.
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