07-11-2017 11:28 PM
I have a lognormal response variable (depressive score - heavily right skewed), and I run GLIMMIX to assess the assocation between the transformed (DIST=lognormal) score and distance to roadway. I read from a couple previous posts from Mr. Steve Denham that we can get the estimates on the original scale using the forumlas (see image) from the GLIMMIX MODEL statement, DIST options. I have tried it but the back-transformed "original scae" estimates, and the confidence intervals don't make sense to me. If they are back in the original scale, the CI for row 2 that is not statistically signficiant should contain 0, but it is not the case. It looks more like a ratio than mean change. If my math is wrong, please let me know where is the problem. if it is correct, how can I interpret the back-transformed values? I am looking for the interpretation similar to something like "Xx change in the depressive score per 50 meter closer to the main road".
For example, I have the estimate, StdErr, and p-value as the following:
1) -0.0085 0.002541 0.0008
2) -0.00307 0.002115 0.1463
The corresponding back-transformed estimate (Ey) variance (VarY), lower and upper CI should be:
1) 0.99154 6.35E-06 0.98661 0.99648
2) 0.99693 4.45E-0.6 0.99280 1.00107
Thank you very much.