To see the differences in a reasonable manner, simulate some right skewed data. Compare the following analyses: untransformed, log transformed outside of GLIMMIX fit with a normal distribution, untransformed with a log link, untransformed with a lognormal distribution, untransformed with a gamma distribution. All of the above may fit the data, some better than others, and there may be a variety of problems/opportunities arising during the fit. In this case, any of the methods may seem like a reasonable choice--and it is very difficult to select one over the others based on objective measures arising from the likelihood function. The key is that the expected values of the estimate are different in each of the cases (although 2 and 3 look the same to me). Specifying a distribution and/or using a specific link function should also consider the process by which the dependent variable is generated. If it is waiting times being modeled, a gamma link is justifiable on theoretical grounds--and that should satisfy folks. Except it seldom does, especially if there is a history in the field of using untransformed data. (Yes, I am looking at the clinical pathologists now.) Steve Denham
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