Fit is inferred from the consistency between examinee responses and item difficulties. Improbable responses signal inconsistent activity. Computer assisted testing (CAT) usually tailors item difficulties to match examinee ability, but when examinees are administered items selected to give them a 50% chance of success, both right and wrong answers become equally probable, precluding a basis for the usual fit analysis.
There are, however, two statistics which, in combination, can help detect misfit in CAT. The first is the observed percent correct on the test. If CAT targeting is set for 50% success, then instead of reviewing a person's response pattern item by item, we can compare the obtained percent correct with the intended 50%. A significant difference implies a fit problem.
The second statistic is the mean of the differences, (B-D), across all items administered to a person, between the person measure, B, estimated at each step, and the item difficulty, D, of that step. This mean (B-D) difference indicates how well the item bank has provided on-target items. When targeting has been set at 50%, its expected value is zero. When, however, the items provided have been too easy, the difference will be greater than zero, and vice-versa.
The mean (B-D) difference can be converted to an "expected" percent correct, e.g. when the mean difference is +.4 logits, the expected percent correct is 60%. If the expected percent correct deviates from 50%, the item bank is not providing correctly targeted items, and the examinee's expected success rate is no longer 50% but the expected percent correct. Failure of the item bank to provide correctly targeted items usually occurs for very high or very low ability examinees.
Person misfit is implied when the expected percent correct is near 50%, but the examinees observed success rate deviates from 50%. The item pool has provided correctly targeted items but the behavior of the examinee has been inconsistent.
In summary, comparison of observed percent correct with expected percent correct provides a useful check on item bank depth and permits the identification of some types of examinee inconsistency.
Computer-Adaptive Testing: CAT Fit Analysis, B Bergstrom Rasch Measurement Transactions, 1990, 4:3 p. 112
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