[R-sig-ME] comparing treatment with different skewness

[Maarten de Groot]

Dear Thierry,

The response variable y is a continuous variable without any zero's. 
Regarding the design, there are 15 animals which are repeatedly used for 
5 signal treatments. When you look at the distributions of residuals of 
y per treatment they are skewed and there are different skew parameters 
per treatment (see below).

skewness of every treatment is as following:
tr A: 2.364193
tr B: -0.5022666
tr C:  -0.4669217
tr D: -0.0790484
tr E: 0.7737216

When you plot all the residuals than they seem to be normally 
distributed. However it was always told to me that response variable 
should be normally distributed per treatment in order to compare them 
with an anova or lm.
In a previous email Ben Bolker already mentioned that if the skew 
parameters per treatment are different and can not be transformed, which 
I tried with several transformations, this is outside the scope of mixed 
models and should turn to WinBUGS or AD model builder. If any one thinks 
that there is no problem with the skewness or knows a way how to 
transform data so that treatments with opposite skewness parameters get 
a similar distribution, please let me know.

Kind regards,

Maarten

On 3/4/2011 11:18 AM, ONKELINX, Thierry wrote:
> Dear Maarten,
>
> The assumption of normality does not apply to the response (y) but to the residuals of the model.
> Some more information on what y is (maybe counts?) and the design might help us to formulate a better solution for your problem.
>
> Best regards,
>
> Thierry
>
> ----------------------------------------------------------------------------
> ir. Thierry Onkelinx
> Instituut voor natuur- en bosonderzoek
> team Biometrie&  Kwaliteitszorg
> Gaverstraat 4
> 9500 Geraardsbergen
> Belgium
>
> Research Institute for Nature and Forest
> team Biometrics&  Quality Assurance
> Gaverstraat 4
> 9500 Geraardsbergen
> Belgium
>
> tel. + 32 54/436 185
> Thierry.Onkelinx at inbo.be
> www.inbo.be
>
> To call in the statistician after the experiment is done may be no more than asking him to perform a post-mortem examination: he may be able to say what the experiment died of.
> ~ Sir Ronald Aylmer Fisher
>
> The plural of anecdote is not data.
> ~ Roger Brinner
>
> The combination of some data and an aching desire for an answer does not ensure that a reasonable answer can be extracted from a given body of data.
> ~ John Tukey
>
>
>> -----Oorspronkelijk bericht-----
>> Van: r-sig-mixed-models-bounces at r-project.org
>> [mailto:r-sig-mixed-models-bounces at r-project.org] Namens
>> Maarten de Groot
>> Verzonden: vrijdag 4 maart 2011 10:35
>> Aan: Nicholas Lewin-Koh
>> CC: r-sig-mixed-models at r-project.org
>> Onderwerp: Re: [R-sig-ME] comparing treatment with different skewness
>>
>> Hi Nicholas and list,
>>
>> Sorry to be so short in explanation about my problem. I am
>> working on the effect of five different acoustic signals
>> (=treatments) on the response of one insect species. The
>> animals I used I presented with the signals on different
>> days. When I plotted the response variable y with the
>> treatments I realized that within the treatments y was not
>> normally distributed, and even worse y was not distributed
>> equally for every treatment. With other words, for treatment
>> 1 the response variable was more skewed to the lower region
>> of the boxplot and in treatment 2 to the higher region, etc.
>> I tried to incorporate the variance into the model as
>> suggested by Nicholas:
>>
>> mod1<-lme(y~treatment,
>> weights=varPower(form=~1|treatment),random=~1|animal,data=mydata)
>>
>> However this did not work. There is one question I have.
>> Nicholas, you are talking about "group" and I do not really
>> understand what you mean with this.
>>
>> Hopefully this gives you a better insight and will help me to
>> solve the problem.
>>
>> Kind regards,
>>
>> Maarten
>>
>> On 3/3/2011 10:40 PM, Nicholas Lewin-Koh wrote:
>>> Hi Maarten,
>>> Without the random effects, you are basically asking can you fit a
>>> model where the variance is a function of the group.
>>> So I would think you could do this using nlme, ie somehthing like
>>> library(nlme)
>>> lme(y~T + X1, data=mydat,
>>> weights=varPower(form=~1|group),random=~1|whatever)
>>>
>>> However, without more information it is hard to say more than that.
>>>
>>> Nicholas
>>>
>>>
>>>> Message: 2
>>>> Date: Thu, 3 Mar 2011 11:11:51 +0100
>>>> From: Maarten de Groot<Maarten.deGroot at nib.si>
>>>> To:<r-sig-mixed-models at r-project.org>
>>>> Subject: [R-sig-ME] comparing treatment with different skewness
>>>> Message-ID:<4D6F6967.8010303 at nib.si>
>>>> Content-Type: text/plain; charset="ISO-8859-1"; format=flowed
>>>>
>>>> Dear list,
>>>>
>>>> I have a problem regarding choosing the distribution family for a
>>>> mixed model. I want to compare my response variable y with
>> treatment
>>>> A,B,C and D. In each of the treatments the distribution of y is
>>>> differently. Is there a way to implement this in a mixed model?
>>>>
>>>> Kind regards,
>>>>
>>>> Maarten
>>>>
>>>>
>>>>
>>> .
>>>
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