1. I suspect there is a typo in Equation 8.
2. In the marginal trace line approach, nuisance dimension is integrated so that only the general dimension remains. Apparently, the information of specific dimensions cannot be recovered from the marginal trace line. It is probable we will regret someday that important data information (specific dimensions) is covered with the marginal trace line approach.
3. Since the true model (Equation 1) has been recognized, why don’t we fit the true model directly?
4. As illustrated, ignoring local item dependence results in biased joint marginal likelihood. To correct the effect, it was proposed that only a single item is used per specific dimension. It suggests that, for a test with 50 items, there are 1 (general) + 50 (specific) dimensions. The high dimensionality sounds crazy.