Hello, I am currently using mixed models (lme4) to explain variability in
fungal isotope patterns in 800 fungal SPECIES across 24 SITES in the world.
I have thus decided to nest the species within site as hierarchical *random
effects*.  I am just trying to explain the variability in fungal isotopes
values not necessarily predict values of fungi from other areas of the
world.

My *fixed effects* include mean annual temperature, mean annual
precipitation, and latitude.  Perhaps obviously, all three suffer from
strong multicollinearity problems.

*My question is:*  Should I simply omit using fixed effects additively?  In
other words, is it valid to simply use the fixed effects singly or as
interactions (see code below) or do the random effects take care of the
collinearity issue during adjustment of model error variance allowing me to
compare full-factorial models instead?

Thanks in advance to all those with advice or references.

-- 
Jordan Mayor

My code:

> names(ds)
 [1] "STUDY"    "SPECIES"  "SITE"     "MAT"      "MAP"        "X13C"
"X15N"    "LAT"

> mix.model1=lmer(X13C~ MAT:MAP:LAT + (1|SITE/SPECIES), method ="ML",
data=ds)
> mix.model2=lmer(X13C ~ MAT:MAP + (1|SITE/SPECIES), method ="ML", data=ds)
> mix.model3=lmer(X13C ~ MAP:LAT + (1|SITE/SPECIES), method ="ML", data=ds)
> mix.model4=lmer(X13C ~ MAT:LAT + (1|SITE/SPECIES), method ="ML", data=ds)
> mix.model5=lmer(X13C ~ MAT + (1|SITE/SPECIES), method ="ML", data=ds)
> mix.model6=lmer(X13C ~ MAP + (1|SITE/SPECIES), method ="ML", data=ds)
> mix.model7=lmer(X13C ~ LAT + (1|SITE/SPECIES), method ="ML", data=ds)
> mix.model8=lmer(X13C ~ (1|SITE/SPECIES), data=ds)
>
anova(mix.model1,mix.model2,mix.model3,mix.model4,mix.model5,mix.model6,mix.model7,mix.model8,data=ds)

                        Df     AIC        BIC         logLik    Chisq Chi
Df   Pr(>Chisq)
mix.model8.p  4  1024.53  1039.11  -508.26
mix.model1.p  5  1025.65  1043.87  -507.82  0.8800      1     0.3482
mix.model2.p  5  *1016.43*  1034.66  -503.22  9.2145      0     <2e-16 ***
mix.model3.p  5  1022.63  1040.85  -506.31  0.0000      0     <2e-16 ***
mix.model4.p  5  1023.09  1041.31  -506.54  0.0000      0     <2e-16 ***
mix.model5.p  5  1023.25  1041.48  -506.62  0.0000      0     <2e-16 ***
mix.model6.p  5  1025.80  1044.02  -507.90  0.0000      0     <2e-16 ***
mix.model7.p  5  1025.32  1043.55  -507.66  0.4793      0     <2e-16 ***

	[[alternative HTML version deleted]]


