[R-sig-ME] Testing for collinearity / variance inflation # glmmTMB

[Hein van Lieverloo]

Dear Members,

I'm trying new variables in my glmmTMB genpois model (details below).
Adding one possibly collinear variable led to a much lower AIC (from 8031.7
to 7899.3) although the coefficient is not different from 0  (p(H1) = 0.66).

I'd like to test for variance inflation / collinearity between variables in
glmmTMB models.
For lm and lmer models, I can use VIF (I tested the same model in lmer (with
log(counts, -1 <- 0) and found no correlation, this model is given below in
the details).
Could someone help me with this (should I test for collinearity and how to
do that in glmmTMB models?)

I read about spatial and temporal autocorrelation in the GLMM FAQ on GitHub:
https://bbolker.github.io/mixedmodels-misc/glmmFAQ.html but if I understand
that correctly, that is about independency of sampling locations and
repeated measures, which I can test using the DHARMa package Mollie Brooks
pointed me to (great). I can't find any collinearity test there either. 

Background

The model and the results are below, the new variable is logbR2A25 (log of
'plate count' bacteria on R2A medium 25 C, 10 days in water flushed from
hydrants).
The Asellidae (b4Wapit, counts filtered (100 um mesh) from 4 m3 water
flushed from hydrants) are significantly related with the concentration
dissolved organic carbon in water from treatment plants.
The bacteria (R2A plate count as index) may be an intermediary / collinear
variable though    DOC -> bacteria -> Asellidae  or  DOC -> bacteria  and
DOC -> x -> Asellidae (x are other or more trophic levels).

Thanks in advance

Kind regards,

Hein van Lieverloo



Details of the models


Family: genpois  ( log )
Formula:          b4Wapit ~ pTDOC + tCa + logtFe + lnOType + logbS500 +
bTemp +  
    logbR2A25 + blWavlo + blRoeiNaup + blMoskr + (1 | vNr/lNr)
Data: AllData

     AIC      BIC   logLik deviance df.resid 
  7899.6   7976.9  -3934.8   7869.6     1264 

Random effects:

Conditional model:
 Groups  Name        Variance Std.Dev.
 lNr:vNr (Intercept) 1.727    1.314   
 vNr     (Intercept) 2.130    1.459   
Number of obs: 1279, groups:  lNr:vNr, 175; vNr, 34

Overdispersion parameter for genpois family ():  593 

Conditional model:
             Estimate Std. Error z value Pr(>|z|)    
(Intercept) -0.712907   1.192110  -0.598 0.549826    
pTDOC        0.596179   0.162938   3.659 0.000253 ***
tCa          0.038302   0.010659   3.593 0.000326 ***
logtFe       1.084413   0.391032   2.773 0.005551 ** 
lnOTypeland  0.848745   0.341383   2.486 0.012912 *  
lnOTypestad -0.557032   0.579695  -0.961 0.336600       This is one factor
level that was and is not significantly different from the reference 
logbS500     0.413405   0.079401   5.207 1.92e-07 ***
bTemp        0.030599   0.009214   3.321 0.000897 ***

logbR2A25    0.033845   0.076619   0.442 0.658688       Coefficient mean not
significantly different from 0

blWavlo      0.044184   0.029413   1.502 0.133050          Now this one is
also not significant anymore
blRoeiNaup   0.115044   0.038998   2.950 0.003178 ** 
blMoskr     -0.116707   0.073944  -1.578 0.114493         Now this one is
also not significant anymore
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Linear mixed model fit by REML ['lmerMod']
Formula: blWapit ~ pTDOC + tCa + logtFe + lnOType + logbS500 + bTemp +  
    logbR2A25 + blWavlo + blRoeiNaup + blMoskr + (1 | vNr/lNr)
   Data: AllData

REML criterion at convergence: 2066.4

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-4.8586 -0.4306 -0.0618  0.3586  6.2652 

Random effects:
 Groups   Name        Variance Std.Dev.
 lNr:vNr  (Intercept) 0.4806   0.6933  
 vNr      (Intercept) 0.3921   0.6262  
 Residual             0.1810   0.4254  
Number of obs: 1279, groups:  lNr:vNr, 175; vNr, 34

Fixed effects:
             Estimate Std. Error t value
(Intercept) -1.314870   0.511630  -2.570
pTDOC        0.272967   0.069991   3.900
tCa          0.013413   0.004527   2.963
logtFe       0.543973   0.175699   3.096
lnOTypeland  0.378729   0.152018   2.491
lnOTypestad  0.058470   0.228750   0.256
logbS500     0.132559   0.030340   4.369
bTemp        0.007874   0.003296   2.389
logbR2A25    0.073598   0.032762   2.246
blWavlo      0.031790   0.011911   2.669
blRoeiNaup   0.043181   0.015952   2.707
blMoskr     -0.061650   0.030685  -2.009

Correlation of Fixed Effects:
            (Intr) pTDOC  tCa    logtFe lnOTypl lnOTyps lgS500 bTemp  lR2A25
blWavl
pTDOC       -0.326

tCa         -0.538 -0.132

logtFe       0.671 -0.047 -0.050

lnOTypeland -0.300 -0.035  0.074 -0.071

lnOTypestad -0.183  0.069 -0.096 -0.115  0.440

logbS500     0.020  0.019 -0.014 -0.001  0.036   0.001

bTemp       -0.058  0.008 -0.010  0.002  0.004  -0.001   0.078

logbR2A25   -0.219 -0.024  0.002 -0.027  0.029  -0.004  -0.080 -0.013

blWavlo      0.012 -0.015  0.013 -0.011 -0.002  -0.003   0.008 -0.257 -0.082

blRoeiNaup  -0.024 -0.012 -0.029  0.007  0.020   0.023  -0.013  0.015 -0.015
-0.185
blMoskr      0.061  0.007 -0.011  0.009  0.001   0.021  -0.046  0.026 -0.026
-0.066
            blRoNp
pTDOC             
tCa               
logtFe            
lnOTypeland       
lnOTypestad       
logbS500          
bTemp             
logbR2A25         
blWavlo           
blRoeiNaup        
blMoskr     -0.036

> vif(Mx)
               GVIF Df GVIF^(1/(2*Df))
pTDOC      1.028332  1        1.014067
tCa        1.047301  1        1.023377
logtFe     1.021198  1        1.010544
lnOType    1.052972  2        1.012988
logbS500   1.018038  1        1.008979
bTemp      1.080318  1        1.039384
logbR2A25  1.019387  1        1.009647
blWavlo    1.125894  1        1.061081
blRoeiNaup 1.042468  1        1.021013
blMoskr    1.011175  1        1.005572