Hi folks,
This may be more of a "philosophical"- student question. In Zuur et al. (2009). "Mixed effects models and extensions in ecology with R", it is mentioned on page 20 that "[...] we can get away with a small amount of non-normality"
I'm little bit puzzled when I face this kind of affirmation in a textbook. What is really "a small amount"?  Of course, it depends on your "judgement"...  In my case, I have level0 and level1 residuals that are unskewed and that show a relatively modest kurtosis (unbiased) of about 2.5 - 3.0. My models are based on several tens of thousands of individuals and normality tests (e.g., shapiro.test) always fail for residuals. QQ-plot show these rather long tails which correspond to "some" outliers (considering my data, there are several hundreds of "outliers" in this case). Homoscedaticity, when considering or not random effects, is not violated so I wondered if I could rely on these model's estimates considering the non-normality of the residuals. My judgement in this case would be that the departure from normality is not that high and this might not be a problem. But, as an ecologist, not a statistician, I have hard time to convince myself on this...  Any thoughts?

Thanks

Yan




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