First post in this magnificent forum!

In my master thesis I'm estimating health care expenses to patients, who has experienced a occupational injure on administrative data.

The depended variable is total health care expenses for a given individual a year after the injure.

Due to typical right skewness in the depended variable I have estimated two models; the first is GLM model using log-link function and a gamma distribution for the depended variable. The mean expenses are estimated to around DKK16,000 (approximately $2200) for the treatment group (people who has experienced a occupational injurie) and around DKK5,000 for the control group.

As an alternative to the GLM model, I have also estimated the expenses using a OLS-regression with logarithm transformed depended variable. After using a Duan-smearing factor and "retransforming" the estimate, I obtain an estimate for the predicted expenses of DKK15,000 and DKK4,000 for the treated and the control group.

My question is; how can I compare for the fit of the models and choose the "best" one or at least the better one? Both with regard to a graphically and/or test.

Steinberg