John,
You have specified a model with
E(y) = 1/eta where eta = X beta is the linear predictor
and
E(y) must be >0, since the family is Gamma
and
you have a lot of covariates in the model.
glm now has to try to find a best linear predictor, but under the constraint
that eta>0 for every single one of the observations (the log-likelihood
involves
a log(eta) term). The internal computational engine of glm is not designed to
solve the general constrained problem. The message you are getting can be
rephrased as "I tried my best, but I'm lost".
If a. the actual MLE is not on the boundary and b. you give it starting
estimates that are close enough to the final solution so that the interation
path never steps over the boundary on its way to the solution; then all will be
well. Sometimes you can use the estimates from a model with fewer terms as the
starting point.
If the MLE lies on the boundary, which is not unlikely when there are a
large
number of significant variables, then life is much harder.
I have encountered the same issues with additive risk models.
Terry Therneau
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