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

Christina Bogner christina.bogner at uni-bayreuth.de
Thu Mar 12 08:49:27 CET 2009

Dear all,
I have fitted a couple of mixed-effects models to environmental data 
(chemical and physical soil parameters) with log-transformed dependent 
variables. I tried generalized mixed-models, but the results were not 
satisfactory (probably because I am a soil scientist and not a 
statistician ;-)) Now, as log of concentrations are ecologically not 
very informative, I would like to back-transform my model parameters. 
Taking a Gaussian linear mixed-model:

where Mg2 is the concentration of magnesium, betas are fixed-effects and 
bs random ones. All independent variables except Silt are factors; Silt 
is continuous.
I would write:
Mg2=exp(intercept+beta1*mean(Silt in respective 
Soil.Depth)+beta3*Flow.region+estimate of b1*Plot + estimate of 
to back-transform to the original scale on the Soil.Depth-level.
To back-transform the fixed-effects only, I would drop the estimates of 
the random-effects:
Mg2=exp(intercept+beta1*mean(Silt in respective 
Soil.Depth)+beta3*Flow.region+ 0.5*var)
This approach treats the estimated random effects as dummies, not as an 
additional variance. Is this right?

Thanks a lot for your help

Christina Bogner

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