RE: $OMEGA blocks and log-likelihood profiling

From: jeffrey.a.wald@gsk.com Subject: RE:[NMusers] $OMEGA blocks and log-likelihood profiling Date: Thu, June 3, 2004 7:59 am Nick My point referenced what might have been seen in the distributions of parameter estimates if the runs that failed to converge had actually provided some information...assuming that the full model was not identifiable in this set of runs. What you have seen in the parameters defining the covariate effects is not surprising as the runs that potentially show the over-parameterization are the ones that are censored out of the distribution. The 'correct' bootstrap distribution statement refers to the distribution of parameter estimates that makes an appropriate statement about the uncertainty that we have in the joint distribution of parameter values. By potentially ignoring a large fraction of the plausible parameter values - that is assuming a simpler model would have given a plausible answer - we risk assuming that we know more than we really do. Most of this string has been based on the premise that the model is over parameterized. I think that proposing technical solutions detracts from the philosophical point at hand. Even if the model is not over parameterized, the fact that so many runs fail to converge tells me something about the uncertainty in the model, its parameter estimates, or the tools we have to evaluate the model. I do not necessarily know how to quantify that uncertainty, but I have a hard time dismissing it. Jeff