1) The model for Data generation seems similar with Restrictd factor analysis (RFA) no matter with LMS or RSP Method. For Example, we know the effect of moderator variable is equal to interaction statistically. Thus LMS should be true model which with the best performance can be expected . The model of RSP method is a little ambiguous in the article. In RSP, the interaction term in function 2 was replaced with a violator variable with random slop. When the random slop is the function of treat variable (it means c'= u'+ a't at the last paragraph in page 656), this function will be equal to function 2. Whereas in MGFA, this model could be written as the function 2 without interaction term and the v variable is dichotomous data. Thus It is sensible RFA/LMS and RFA/RSP performs better than MGFA.
2) In page 654, the second sentence described parameter v from a normal distribution with mean -0.4. However, see Table 1, I think parameter t in this sentence should be correct.
3) In my opinion, RFA/LMS is the model corresponding to the model for generation (true model). But why RFA/LMS encountered the convergence problem? On the other hand, even RFA/LMS cannot converge well, why the author can claim it's result is almost the same with RFA/RSP in the iterative precudure?