Dear list members,
I have just a quick question:
I fitted a non-linear model y=a/x+b to describe my data (x=temperature and
y=damage in %) and it works really nicely (see example below). I have 7
different species and 8 individuals per species. I measured damage for each
individual per species at 4 different temperatures (e.g. -5, -10, -20, -40).
Using the individuals per species, I fitted one model per species. Now I'd like
to use the fitted model to go back and predict the temperature that causes 50%
damage (and it's error). Basically, it pretty easy by just rearranging the
formula to x=a/(y-b). But that way I don't get a measure of that temperature's
error, do I? Can I use the residual standard error that R gave me for the
non-linear model fit? Or do I have to fit 8 lines (each individual) per
species, calculate x based on the 8 individuals and then take the mean?
Unfortunately, dose.p from the MASS package doesn't work for non-linear models.
When I take the log(abs(x)) the relationship becomes not satisfactory linear
either.
Any suggestions are highly appreciated!
Thank you!
Stefan
EXAMPLE for species #1:
y.damage<-c(5.7388985,1.7813519,3.7321461,2.9671031,
0.3223196,0.3207941,-1.4197658,-5.3472160,
41.1826677,29.3115243,31.3208841,35.3934115,
58.5848778,31.1541049,42.2983479,27.0615648,
64.1037728,54.7003353,66.7317044,65.4725881,
72.5755056,67.2683495,64.8717942,65.9603073,
75.0762273,56.7041960,60.0049429,70.0286506,
73.2801947,72.7015642,75.0944694,81.0361280)
x.temp<-c(-5,-5,-5,-5,-5,-5,-5,-5,-10,-10,-10,-10,-10,-10,-10,
-10,-20,-20,-20,-20,-20,-20,-20,-20,-40,-40,-40,-40,-40,
-40,-40,-40)
nls(y.damage~a/x.temp+b,start=list(a=400,b=80))
plot(y.damage~x.temp,xlab='Temperature',ylab='Damage [%]')
curve(409.61/x+81.84,from=min(x.temp),to=max(x.temp),add=T)
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