# [R] help_transformation

Indermaur Lukas Lukas.Indermaur at eawag.ch
Thu Jun 26 10:16:23 CEST 2008

```Thanks for getting back to me.

i meant that i am seeking for a transformation of an s-shaped response (continuous data)  to assure normally distributed residuals of the response.

however, i am unsure if the "Let F be the distribution..." is now the correct thing for me to do. if this is the right thing to do, could you give me a hint how to code this that i can run the following model with the transformated response?

my model:
lme(fixed=Y~x1+ x2 + x3 , random=~ 1|Pond/Occasion, method="ML")

thanks for your help.
regards,
lukas

________________________________

Von: Prof Brian Ripley [mailto:ripley at stats.ox.ac.uk]
Gesendet: Do 26.06.2008 08:45
An: Moshe Olshansky
Cc: R-help at stat.math.ethz.ch; Indermaur Lukas
Betreff: Re: [R] help_transformation

On Wed, 25 Jun 2008, Moshe Olshansky wrote:

> Let F be the distribution function of Y, PSI the standard normal
> distribution anf IPSI it's inverse. Let f(x) = IPSI(F(x)). It is not
> difficult to see that f(Y) has standard normal distribution. So you can
> replace F with the empirical distribution and IPSI is the qnorm function
> of R.

Only if F is continuous, and 'some zero values' suggests that in this case
that is not a reasonable model.

I think there is a basic misunderstanding here: the response of a linear
regression (including a mixed effects model) is not normally distributed:
it is the Y[i] which are normally distributed under the usual model
assumptions, but with different distributions.

>
>
> --- On Wed, 25/6/08, Indermaur Lukas <Lukas.Indermaur at eawag.ch> wrote:
>
>> From: Indermaur Lukas <Lukas.Indermaur at eawag.ch>
>> Subject: [R] help_transformation
>> To: R-help at stat.math.ethz.ch
>> Received: Wednesday, 25 June, 2008, 9:56 PM
>> heya,
>> i am fitting linear mixed effect model to a response Y. Y
>> shows an s-shaped distribution when using QQ-plots (some
>> zero values and some very high values). hence, which
>> transformation should i apply that Y follows a normal
>> distribution? any r-function/package available to do this?
>>
>> thanks for any hint,
>> regards,
>> lukas
>>
>>
>>
>> °°°
>> Lukas Indermaur, PhD student
>> eawag / Swiss Federal Institute of Aquatic Science and
>> Technology
>> ECO - Department of Aquatic Ecology
>> Überlandstrasse 133
>> CH-8600 Dübendorf
>> Switzerland
>>
>> Phone: +41 (0) 71 220 38 25
>> Fax    : +41 (0) 44 823 53 15
>> Email: lukas.indermaur at eawag.ch
>> www.lukasindermaur.ch <http://www.lukasindermaur.ch/>
>>
>>
>>
>>
>>
>> ______________________________________________
>> R-help at r-project.org mailing list
>> https://stat.ethz.ch/mailman/listinfo/r-help
>> PLEASE do read the posting guide
>> http://www.R-project.org/posting-guide.html
>> and provide commented, minimal, self-contained,
>> reproducible code.
>
> ______________________________________________
> R-help at r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
>

--
Brian D. Ripley,                  ripley at stats.ox.ac.uk
Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
University of Oxford,             Tel:  +44 1865 272861 (self)
1 South Parks Road,                     +44 1865 272866 (PA)
Oxford OX1 3TG, UK                Fax:  +44 1865 272595

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