Question (actually a trick question) - how do you know that the distribution for residuals is not normal? Did you do some sort of test? There are well-known issues with almost every hypothesis test for normality (overpowered with N greater than about 40, underpowered for N less than about 15), and the linear mixed model is remarkably robust to the assumption of normality of the residuals, so long as the empirical distribution is mono-modal, not truncated, and lacks extremely large absolute values. The mono-modal basically boils down to sex differences.
So here are some ways to attack the issue, from simple to complex:
bin your responses to four or five categories and consider using Cochran-Mantel-Haenszel methods where you stratify by sex.
Plot your data and see what the shape looks like. From that, use a generalized linear model, assuming the distribution you have a picture of. If you have what might be considered random effects, use a generalized linear mixed model.
Bootstrap your data. Simulate a lot of datasets that could possibly occur based on your current data.
Use a Bayesian analysis with noninformative priors. This does a lot better job of simulating the data needed to construct credible intervals as you can include correlations over time or clusters. I don't think you have any random effects, so a good start on this can be found by looking through the documentation for PROC BGLIMM.
Given what you have done so far, I would recommend #4. You can use most of your PROC MIXED code, and you can examine each distribution/link to see which best fits your data.
SteveDenham
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