This paper proposed a model for answer changes on test items based on an interesting testing phenomenon. That is, school teachers would change the item response in order to get high score for their students, or students would cheat on test items after wrote down their initial responses. The proposed model is fixing the theta (student ability), c = 0 and setting the a and b as free to be estimate. Then introduce statistical test for find out the irregular answer change behavior. After the model is formulated and procedures are described, an empirical example was conducted for demonstration. Further, a simulation study based on empirical data set was conducted to investigate the robustness of the proposed model in the situation that students do not have enough time to review all test items.
The author also stated that the “enough time to review items” assumption of the model and cautioned that when we are making decisions about cheating, more qualitative evidence should be involved rather than just based on the statistical evidence.
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First of all, the authors did not mention an important assumption of the student ability equivalence between two stages of the proposed model. The procedure is some kind like Known item parameters -> Estimate ability parameters -> Reestimate item parameters. By doing so, the ability parameter estimates might shift based on the two data set (One is initial response and the other is response changed) and confounded with the change of item parameters. Consequently, this will affect the probability of WR erasures estimation.
Second, in practices, it is hard to claim whether or how much do the students review their responses. But the degree of review would affect the critical value which is an important information while conduct the cheating analysis.
Third, I was curious that how about this model and similar procedures in Rasch measurement. Remembering the Andersen’s theorem was used for guessing behavior in a sample and subsample situation. The situation of this answer changed is not the same with that one. But the similar procedure could be imagined.