I'm responsible for challenging a gamma model with log link. The developer claims that an assumption of the gamma-log generalized linear model is that the response variable, in this case average balances is distributed gamma. He then uses distributional tests (like Anderson-Darling) to test the empirical distribution and support his claim.
I'm a little unsure whether this is actually the assumption for generalized linear model and whether this method is appropriate to support his claim. Most of the assumptions I've been able to find about the GLM are around the error term and the selection of the link function. Other generalized linear models, like a logistic regression have an empirical binomial distribution, but use the logit because it theoretically maps the probabilities between 0 and 1.
Furthermore, the Anderson-Darling test seems inappropriate as a method to select distributions for the generalized linear model.