1. I can't understand these three methods, and what differences between them would bring the different performances?
2. What is the effect of different ability estimation methods, like CML and JML?
3. In practical condition, the true model is unknown. What the users do is to find out the best model among a list of alternatives. Thus, it is possible that all alternative models are rejected based on the R1, R2, and M2, in this case, what can the researcher do next?
4. If the statistics are based on or can approximate to some distribution, what is the effect of sample size? For example, as sample size getting large, the chi-squared statistic tends to always reject the model. What about the other statistics?