[R-sig-ME] Ok with a "small amount" of non-normality?

[John Maindonald]

One recourse I'd temporarily forgotten is to examine the sampling 
distributions of the parameter estimates that are given by mcmcsamp().  
You can check these for approximate normality, and you can derive 
credible intervals that do not depend on normality assumptions (but 
they will depend somewhat on the mcmcsamp() choice of prior).

Also, long-tailedness or kurtosis at a crucial level in the design may
I think lead to inefficient estimates, even though the sampling
distributions of parameter estimates appear close to normal.

John Maindonald             email: john.maindonald at anu.edu.au
phone : +61 2 (6125)3473    fax  : +61 2(6125)5549
Centre for Mathematics & Its Applications, Room 1194,
John Dedman Mathematical Sciences Building (Building 27)
Australian National University, Canberra ACT 0200.
http://www.maths.anu.edu.au/~johnm

On 05/05/2013, at 2:32 AM, Greg Snow <538280 at gmail.com> wrote:

> 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 at 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 at gmail.com
> 
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