This paper described an interesting issue about the test taker change their answer after reviewing the initial response. The previous studies just used response pattern to detect the irregular changing answers. This study suggested a stronger evidence that is the directly observed erasure by the optical scanners. Then, the cheating motive of the erasure listed in this article, such as the teacher changes his student's response and the discussion between the two adjacent classmates. The purpose of this study is modeling the probability of correctly erasure and detecting such cheating erasures. The ability parameter is decided by the initial response, then the second correctly response probability which condition on the incorrect initial response would be used to estimate the second item parameters. This comparison of the initial and second estimates of item parameters can be used to explain whether the erasure behavior can improve the final correctly response. Then, the number of Wrong-to-Right (WR) erasures, which fallows binomial distribution, mainly was tested to detect the cheating behavior, and the residual for the test taker can be observed for interpreting suspicious pattern of WR erasures.
1) in the function 9, z is a dummy variable. If z is the item response, I think the function should be more reasonable to write as #[Q*(1-z)+P*z]. However, this paper didn't describe z clearly.
2) Why the figure 4 shows the e-star increases by less review time? It express the critical value of number of WR need to rise for achieving the alpha level?