Back Transformations for Lognormal Data

As we continue to move into the Proc GLIMMIX world, we are using more non-Gaussian data, such as binomial, Poisson, etc…  When we take advantage of the strength of GLIMMIX and designate a non-Gaussian distribution, our LSMeans return to us in a transformed format.  But, GLIMMIX has a great option called ILINK to be added to your LSMeasn statement that provides you with the “raw” mean format in your LSMeans table – essentially back-transforming your data so you can present your results in a format that your readers will relate to.

However, if your data conform to a LOGNORMAL distribution, the ILINK option will not work.  You are then left with the same challenges we were left with before.  What do we do?  DO we back-transform the results?  Do we present our results in a log format?  Will our reader understand that?

I will confess that I have been one of those folks that always struggled with the concept of back-transformations.  They don’t always work the way you think they should.  And there was always THAT question – Can I back-transform my standard errors?  And let;s be brutally honest, most folks used Excel or a calculator to run those back-transformations – right or wrong – didn’t matter.

So, along comes GLIMMIX with all these wonderful options for all of our non-Gaussian distributions except Lognormal.  But, hang on, do not despair, there has been a lot of work conducted in this area and we now have wonderful coding options that are easy to implement and provide you with options for back-transforming the standard errors too.

Two methods are available to you now – the Delta method or the Omega method.

This link contains a SAS program with coding for both methods.


5 thoughts on “Back Transformations for Lognormal Data

  1. Very clear! Thank you very much.
    Is it possible to apply it also for differences (among groups) obtained from the glimmix procedure?

  2. I might question why you want to do this? If you are running the analysis to determine whether there are differences between the means – you should use the log data and use lsmeans to determine the differences – and report those results. Rather than back transforming the differences and using those values to determine differences – this would not be the correct approach. I hope this helps.

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