To expand on John's answer, I would agree that simulation is the way to go.
 With simulation you can see how much your lack of normality affects the
results that you are actually interested in (generally the results of a
test or confidence interval).  This post:
https://stat.ethz.ch/pipermail/r-sig-mixed-models/2009q1/001819.html shows
some examples of using simulation with mixed effects models to determine if
the p-values are behaving properly and also show one method of adjustment
(using simulations) for still doing the tests when the formulas based on
the normal assumption don't work.


On Fri, May 3, 2013 at 12:36 PM, Boulanger, Yan <
Yan.Boulanger@rncan-nrcan.gc.ca> wrote:

> 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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-- 
Gregory (Greg) L. Snow Ph.D.
538280@gmail.com

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