Bifactor model has used to account for subsets of locally dependent items. This model is a special case of multidimensional IRT model. The example of this kind of situations can be showed as testlet. Based on Bifactor model, the author showed joint likelihood to describe the marginal trace line is equivalent to the bifactor model while only a single item involving the secondary dimension. The marginal trace line can be simply obtained by logistic approximations. The purpose of this study is proposing an ECV index for evaluating the weight of general dimension in bifactor model. Using this index can create the unidimensional short form from the multiple contents test.
1) The situation about only a single item used in each specific dimension is hard to find an appropriate example. I don’t think the latent trait which just explains one single item could be useful for scoring because the effect is similar with standardizing.
2) In mathematic aspect, I don’t understand why the function 9, L, can be claimed considering LD but function 11, L*, ignoring LD?