This study considered the effect of error of the item parameter in CAT. Because we fix the item parameter in CAT, the standard error of ability will be underestimate when we just use Fisher information formula. The Author manipulate the item calibration error by the calibration sample size. Then, examine the effects on test length and test efficiency in CAT.
comment:
1) In practice, we design the several linking items to equate the item parameter.(such as balanced incomplete block design, BIB) The reason is we can't let examinee in pretest responds full items in pool. Therefore the item-person response matrix is not filled the full. It causes the covariance matrix cannot be computed. If we want to combine the error of item parameter in the item selection rule and termination rule, we need the item covariance matrix. I image two approach to get the matrix. One is assuming the source of correlation comes from item parameter. We can simulate the each person's response in each item. However, I think this approach still underestimates the error of item parameter. The other method is for BIB test book design, we can calculate the correlation of each pair items by different sample because BIB design let every items in pool to link each other items by different sample.