1. The idea of considering the estimation error of item parameters used in CAT had been mentioned by Prof. Wang before. However, none of us tried to do it.
2. The author only manipulated the sample size to generate the errors of item estimation. But even in large sample size, other impacts on estimation exist like DIF or slippy error by person.
3. The method of corrected SEs is not used in pratical CAT due to the unstable estimation of covariance matrix of items. In MCMC, we can obtain the distribution of each item in final stage. Would it be possible to use them to correct the conventional SEs? Maybe we can approximate the entropy of each item. As for how to implement it, But let me take time to think about it.