I can recommend the book "A Beginner's Guide to GLM and GLMM with R" by Zuur et al. It is just recently published and I find it very helpful. There is a section about gamma models in it. http://www.highstat.com/books.htm

EDIT: The section is quite short though. The book is great so I still recommend it. Regarding choice of link function they recommend looking at AIC for choosing the best one, alternatively looking at Pearson residual plots. Choosing wrong link-function seems to produce some potentially serious problems.

The inververse or log-link function are conventionally used, but I prefere log-link as it typically runs more stable.

Hi Joacim, thanks for your suggestion! This could work well for me, as I actually use R. I checked out the table of contents; do you know which chapter the link function references are in?

The gamma-model link functions are discussed shortly in chapter 6. "GLMM for strictly positive data: biomass of rainforest trees", specificly on page 178-179. Link functions in general are discussed in several parts of the book.

What it says in chapter 6 is:

"The choice among these three link functions depends on the functional relationship between the expected values [of biomass] and the covariates. Choosing wrong link function may result in non-convergence of the mathematical algorithm, negative fitted values, patterns in the residuals, and further modelling misery."

Inverse is default in R while log-link is default in SPSS.

Google "goodness of link"; you'll find lots of ideas, including often cited old paper by Daryl Pregibon in Appl. Statist. (1980),. 29, No. 1, pp. 15-24. Goodness of Link Tests for Generalized. Linear Models and book on determining a goodness of link test by bootstrapping by Cole and McDonald.