I have posted this thread in the "SAS procedures" forum which I believe is not the right place for this topic. I am sorry for the confusion. I am posting it here again.
I am learning to use proc genmod. I am running an analysis of quality of life data: around 400 subjects, continuous outcome and scores range from -0.24 to 1.00. The distribution of scores is strongly left skewed. My model include 1 continuous predictor and 5 indicator variables. For this reason OLS assumptions are not met. Raising the 3rd power of the scores would allow meeting regression assumptions. I also linearly transformed the distribution of scores to have only positive values with the following:
Following is the Genmod code used for the analysis.
Proc genmod data=[data-set]
class v1 v2 v3 v4 v5
model y= cov1 v1 v2 v3 v4 v5\ dist=norm link=power(3);
the model did not converge. I got the following error messages:
Warning: the specified model did not converge
Error: error in computing the inverse link function
It's odd because if I use fractional powers....the model converge: too bad that fractional powers don't do in my case.
Double odd is the fact that I ran a similar one for another QOL index (range, 0.34 to 1.00), same distributional issues, same power link but with no convergence issues.
Your GENMOD code probably is not doing what you expect. When you specify a link and DIST=NORMAL, GENMOD still assumes that the response itself (not transformed) is normal and then models g(y) where g(.) is the link function. If you want to transform the response to be normal and then model that
normalized response, do the transformation in a DATA step and then use a procedure (GLM, MIXED, or GENMOD with DIST=NORMAL) that models the transformed response assuming it is normally distributed. An alternative in your case would be to try a nonnormal distribution (maybe gamma) in GENMOD for your QOL1 response.
I am relieved as the first approach I used was transforming the response and use Proc GLM. Though adjusted means estimates are of concern here and one internal reviewer raised the issue of back-transformation bias even though I used Duan's smearing estimate to correct it. With transformed responses there is also the issue of interpretation of beta coefficient in the original scale. He suggested to use generalized linear models to avoid back-transformation bias. Generalized Linear Models and Proc Genmod are completely new for me.
Anyway, I implemented your suggestion to try with a gamma distribution and identity link but the model did not converge. If you have any other suggestion, it is very welcome.