Q: If PPMC tells us that the model is fit to data but other index not, how do we make a decision?
A: Well, model-data misfit certainly include many kind of violations, multidimensional, or local dependence, or data gen from 3PL but fit with Rasch. Too many situations.
The index in PPMC is just sensitive for certain kind of violation. For example, LR may be sensitive for the local independence but not sensitive for multidimensionality. But Q3 may be sensitive for both kind of violations. Therefore, not any index in PPMC is perfact. We should decide which kind of violation and select proper index in PPMC.
Q: Have any available package or program up to now? I think it may be some hard for us to check the correctness of program if we write it on our own.
A: The most hard part of the program is to compute the index. The replication data could be gen by writing a line of code direclty in WINBUGS.