GLM Family = Gamma Link = Identity

[Doug DeMoulin]

gamma distributions yield different forms based on two parameters: shape parameter and scale parameter. When running a GLM family=gamma link=identity in stata, the output gives the scale parameter. Does stata automatically assume the shape parameter based on the underlying distribution of my dependent variable?

[Nick Cox]

With gamma distribution and identity link, and no predictors glm reports the mean and implicitly treats any second parameter as ancillary. To fit a gamma distribution directly gammafit from SSC is one possibility. I don't know how far that answers your question.

[Doug DeMoulin]

Thank you for your reply Nick Cox. I apologize, this is the first time using this site and did not know where general posts were.

I forgot to include in my question the crude and adjusted model with respective covariates. For example, assessing the relationship between the dependent variable and explanatory variable for crude model, and full model while adjusting for potential confounders. I am doing a stratified analysis but the distributions between strata differ, and seem to follow a gamma distribution but am not sure if stata assumes the distribution when running the GLM gamma with identity link, or if the data needs to be transformed using rgamma

[Nick Cox]

There is no need to transform anything unless for quite different reasons it is a good idea to transform any predictors.

[Jeff Wooldridge]

I think using the gamma quasi-likelihood is the same as the exponential distribution — which is fine provided you’re interested only in the mean and you use robust standard errors. I assume y > 0, correct? You should use the log link so that E(y|x) = exp(x*b).