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

[ONKELINX, Thierry]

Dear all,

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.

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


------------------------------------------------------------------------
----
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 

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