Programming the statistical procedures from SAS

Back-transformation where dependent variable is lognormal (GLIMMIX)

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Back-transformation where dependent variable is lognormal (GLIMMIX)

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. 


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