RE: $OMEGA blocks and log-likelihood profiling

From: "Kowalski, Ken" Ken.Kowalski@pfizer.com Subject: RE:[NMusers] $OMEGA blocks and log-likelihood profiling Date: Wed, June 9, 2004 8:55 am Leonid, I don't think Nick has provided sufficient detail to know how insufficient the accuracy might be. Moreover, even for the 28% which did achieve sufficient sigdigit accuracy, only one quarter (7%) of these had a successful COV step so I still think the problem could be due to a very flat likelihood response surface where difficulty in achieving sufficient accuracy can be problematic (i.e., the problem of over-parameterization where there is an infinite number of solutions for the parameters that result in essentially the same OFV). In any event, if indeed the majority of runs are failing with rounding error messages where the minimum sigdigits for the run is 2.9 then I would expect the bootstrap distribution for these failed runs would be no different from the successful runs. The whole point to doing the bootstrapping is to construct these distributions. So regardless of the reason for the failure, the proof is in the estimates obtained to generate these empirical distributions. I'm just concerned that there is the potential for many of them to fail near a local minima or perhaps not move very much from the starting values. In this setting, the bootstrap distribution for the failed runs could be very ugly (e.g., bimodal). That might not be the case for Nick's example but in general the potential is there...which is why we have to be cautious when we have such a high convergence failure rate. Ken