I noticed a post on this topic to the list a few months ago but there weren't any workable suggestions at that time.
I am trying to do GOF with median c-hat. I am comparing different within-season parameterizations of a 4-state multi-state dataset (using the simple MS, robust design, and open robust design). GOF is a bit of a mess - I've been using Pearson's from MSSURVIVRD but there isn't anything very satisfying for the ORDMS and it would be nice to try the new comprehensive method for all 3 data types.
The problem is that I can't do median c-hat simulations with the m-logit link. I tried to get the global model for the simple MS case to converge with a logit link and simulated annealing. I also tried back-transforming the real estimates from the converged model (using the m-logit) back to a logit link and using these as starting values. Both of these approaches gave me "estimates" but the likelihoods were vastly different than using the m-logit (which I also got with simulated annealing and then used these estimates as starting values in the default optimization routine).
Just wondering if anyone has any other thoughts.