1. When the discussion took place, the cut scores were found decrease across round. In other words, the local dependence may occure even conditional on theta, difficulty, round effent and the thresholds. Should it be ignored and Equation 1 still be used anyway?
2. It was assumed that the rating scale structure is the same across the entire set of items (ie, there is no i subscription in taujk). The assumpition may be too stringent. Instead, we may assume different items have different rating scale structure and a random effect approach can be adopted.