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# Parameter estimates in proc glimmix?

My data are hospital cost data and I model them as a function of various cost drivers. I need to specify random effects and a lognormal or gamma distribution for my data, therefore I found proc glimmix convenient.My model converges with a lognormal distribution and link=id. I found it very difficult to interprete the parameter estimates. An OLS regression without any explanatory variables renders an intercept of around 77,000. My Glimmix model renders an intercept of about 10,500 (regardless of covariates and random effects). Clearly exponentiating brings these parameters close to the 'true' figure but firstly I can't find any literature telling me to exponentiate and secondly all parameters turn positive when exponentiating. I've spent some time on the internet trying to find solutions.

I hope you can help. Thanx

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## Parameter estimates in proc glimmix?

Do not exponentiate any single parameter estimate.  The lognormal distribution refers to the distribution of the dependent variable, and so you would exponentiate the linear combination you get after plugging in appropriate values in the X matrix.  The only time I could understand exponentiating the intercept is if all independent variables are zero.  Given that, try centering any covariates and see what happens to the intercept.  It would be good to think of the intercept then as estimating the median.  See some recent posts in this community on GLIMMIX for more info.

Steve Denham

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Posts: 2

## Parameter estimates in proc glimmix?

Thanks Steve, it makes a lot of sense.

I gather from your reply that I basically can't use the individual parameter estimates, the way I normally do in proc reg and proc glm. Which is a pity since glimmix is otherwise quite approriate.

Thanks again

Marie

Posts: 2,655

## Parameter estimates in proc glimmix?

Well you can still use the parameter estimates, just remember that a shift of 1 due to an X variable, holding all other variables constant, leads to a shift of exp(beta) in the y variable--if you use a log link as is standard for a gamma distribution.  I'll have to think about the dist=lognormal, as the link is the identity there.  And by think, I mean go plug in some data and look at the results.

Hope this helps.

Steve Denham

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