1. It is odd to me that the authors used IRT to generate data and then use CTT to estimate reliability since they are two different approach.
2. It was stated that under direct range restriction, equation 3 had two assumptions which may be failed and consequently lead to biased resutls. However, why equation 3 were still used for a and w under direct condition? I did not find the reasons.
3. a and w were not found to perform well. Did the results related to the violations of assumptions in Equation 3?
4. Equation 5 seemed to a desirable correction, however, it is not applicable for a and w since it requires a second administration.