[R-sig-ME] is multicollinearity of fixed effects resolved by random effects

[John Maindonald]

Don't you want MAT+MAP+LAT, possibly with first order
interactions in also?  If you still find multicollinearity, look
at the relationship between MAT, MAP and LAT, probably
using regression.  If you still find multi-collinearity, you
need to work out which variables or constructed variables
are most meaningful to retain.

Surely you should allow for a fixed effect of species.  So my
guess would be:

mix.model1 <- lmer(X13C~ MAT+MAP+LAT + SPECIES + (1|SITE/SPECIES),  
method ="ML", data=ds)
or maybe
mix.model1 <- lmer(X13C~ (MAT+MAP+LAT + SPECIES)^2 + (1|SITE/SPECIES),  
method ="ML", data=ds)

But before you go too far, consider whether some species may
show very consistent variation across sites, whereas others may
be quite incognisant of sites; they're the tourists who live in
expensive luxury hotels that are the same wherever they go!
Fit fixed effect models for each species, then xyplot() to look at
the pattern of change of parameter estimates across species.

John Maindonald             email: john.maindonald at anu.edu.au
phone : +61 2 (6125)3473    fax  : +61 2(6125)5549
Centre for Mathematics & Its Applications, Room 1194,
John Dedman Mathematical Sciences Building (Building 27)
Australian National University, Canberra ACT 0200.


On 18 May 2008, at 5:21 AM, Jordan Mayor wrote:

> 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  
> ***
>
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