Dear R community,

A quick sketch of my situation:

I have two continuous explanatory variables ("concentration" and "time") 
and a continuous response variable, "biomass".

I've fitted a gamm model to these data using the package mgcv and want 
to predict at what concentration the biomass is significantly different 
from the control treatment (i.e. a concentration of 0) for a given point 
in time.

I've done this by predicting the biomass for a series of 1000 
concentrations at a given point in time (using "predict"), constructing 
95% confidence intervals for these predictions by adding and subtracting 
1.96*SE and then selecting the lowest concentration where the two CI 
show no overlap.

However I've realized that this technique is not adequate because two 
points can also be significantly different at the 5% significance level 
when the 95% CI do overlap and I want to calculate the lowest possible 
concentration. I've read some literature about this and am considering 
the following method:

* Calculate the difference between the control (C0) and a predicted 
point (e.g. C1), thus C0-C1.
* Construct a 95% CI for this difference by adding and subtracting 
1.96*sqrt(SE0^2 + SE1^2).
* Do this for all predictions.
* Select the lowest concentration where the 95% CI does not include 0.

Could you give me some feedback about this as I'm unsure if this method 
can be used for gamms. Any comments or suggestions are much appreciated.

Many thanks in advance & kind regards

Karel

-- 
Karel Viaene
PhD Student
Ghent University
Laboratory of Environmental Toxicology and Aquatic Ecology
Plateaustraat 22
9000 Ghent, Belgium
tel: +32 (0) 9 264 3779


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