[R-sig-ME] Variable transformation and back transformation

[ONKELINX, Thierry]

Dear Christina,

Beform backtransforming the data you should thing about the level you
want to use. Do you need specific data (for the plots and soil depth in
your dataset)? Or rather data at population level: for an average plot
and an average soil depth? In the first case you can use the formula
that you mentioned in your first mail. There is no need to add the
variance of the random effects as you allready take them into account.
In the case you want predictions at the population level, you should
omit the effects from the random effects but add their variances
instead. 

HTH,

Thierry

------------------------------------------------------------------------
----
ir. Thierry Onkelinx
Instituut voor natuur- en bosonderzoek / Research Institute for Nature
and Forest
Cel biometrie, methodologie en kwaliteitszorg / Section biometrics,
methodology and 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: Christina Bogner [mailto:christina.bogner at uni-bayreuth.de] 
Verzonden: maandag 23 maart 2009 11:59
Aan: ONKELINX, Thierry
CC: Juan Pedro Steibel; r-sig-mixed-models at r-project.org
Onderwerp: Re: [R-sig-ME] Variable transformation and back
transformation

ONKELINX, Thierry schrieb:
> Dear all,
>   
Dear Dr. Onkelinx, dear Dr. Steibel, dear list,

thanks a lot for your help!
> Christina's question will be a bit more clear with some extra
background
> information on the topic. When interpolating concentrations in the
soil
> with kriging, a log-transformation is often used. The predicted value
> for a location in the log-scale is a distribution with mean mu(s) and
> standard deviation sigma(s). Mu(s) is a function which yields the mean
> value depending on location s.
> A simple form of backtransformation would be exp(mu(s)). That will no
> longer be the mean of the distribution (in the original scale) at
> location s, but rather its median. The mean of the distribution in the
> original scale is exp(mu(s) + 0.5 * sigma(s) ^ 2). That is the reason
> why Christina includes the variance in the backtransformation.
>
> This is the backtransformation one would use with a linear model. So I
> suppose that Christina's question is how the deal with the variance
from
> the random effect in such a backtransformation.
>   
Indeed, I am unsure how to treat the random-effects. On one side, a 
random-effect is a random variable like the within-group error. On the 
other side, a mixed-effects model provides an estimate of random-effects

for different experimental units. So what should one to do when 
backtransforming: taking 0.5*random-variance plus 0.5*within-group error

or the estimate of the random-effect for the respective experimental 
unit and 0.5*within-group variance?
The latter approach follows the logic of fitted values in nlme: we have 
estimates on population level and to get estimates on the level of 
experimental units we add the estimates of random-effects (realisations 
of random variables). So, for backtransformation, I used the fitted 
values on the level of experimental units and added 0.5*within 
group-variance. So, somehow, I treated the fixed and the random-effects 
equally and it confuses me!.
> Personally I would settle with confidence intervals. The nice thing
> about them is that they are based on the order of values. Since a
> monotone transformations (like exp() and log()) don't change the order
> of values, the backtransformation is straightforward: exp([LCL, UCL]).
> That requires two maps to depict the information.
> If you have some important treshold (e.g. some legal maximum
> concentration) you could create a map with the probability of exeeding
> that treshold.
>
> HTH,
>
> Thierry
>   
Thanks again!

Christina
>
>
------------------------------------------------------------------------
> ----
> ir. Thierry Onkelinx
> Instituut voor natuur- en bosonderzoek / Research Institute for Nature
> and Forest
> Cel biometrie, methodologie en kwaliteitszorg / Section biometrics,
> methodology and 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
>
> Dit bericht en eventuele bijlagen geven enkel de visie van de
schrijver weer 
> en binden het INBO onder geen enkel beding, zolang dit bericht niet
bevestigd is
> door een geldig ondertekend document. The views expressed in  this
message 
> and any annex are purely those of the writer and may not be regarded
as stating 
> an official position of INBO, as long as the message is not confirmed
by a duly 
> signed document.
>
>   


Dit bericht en eventuele bijlagen geven enkel de visie van de schrijver weer 
en binden het INBO onder geen enkel beding, zolang dit bericht niet bevestigd is
door een geldig ondertekend document. The views expressed in  this message 
and any annex are purely those of the writer and may not be regarded as stating 
an official position of INBO, as long as the message is not confirmed by a duly 
signed document.