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

[Christina Bogner]

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:
 
log(Mg2)=intercept+beta1*Silt+beta2*Soil.depth+beta3*Flow.region+b1*Plot+b2*/Soil.Depth%in%Plot+var 

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 
b2*/Soil.Depth%in%Plot+0.5*var)
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