PROC GENMOD: How to interpret the beta estimates of a model with a square root power link

[MigMaster12]

Greetings!

I'm running a generalized linear model (GLM) in SAS via PROC GENMOD.

I've specified a gamma distribution since my Y response variable is skewed to the right & is non-negative. I've specified a square root power link (since I found that transforming my Y via the square root improves the skewed distribution). I have 2 X predictor variables, X1 and X2.

My code looks something like:

PROC GENMOD DATA=SAMPLE;

MODEL Y = X1 X2 / DIST=GAMMA LINK=POWER(0.5);

RUN;

SAS gives me an output of the 2 regression estimates for X1 & X2. For example:

X1:  0.64

X2:  -0.08

How would I go about interpreting these estimates in terms of my Y variable? Can I just say that 1 unit change in X1 results in a increase of 0.64 in Y (assuming that my specific link function has already taken care of the transformation)? Or do I have to take the square of the estimates to obtain the original un-transformed Y?

Thank you in advance for your help!

[unison]

Add the output option:

Output pred=Pred;

So that you can view the prediction table. Take a look at the table and try a few observations with how you’ve hypothesized the link function to work. Report back with what you find!

here are some helpful docs: https://support.sas.com/documentation/cdl/en/statug/63962/HTML/default/viewer.htm#statug_genmod_sect...

-unison