[R-sig-ME] request for help with glmm

[Πίττα Eύα]

Thank you for your response.
I have built this model:

data.lmer6=glmer(Beta_diversity ~ 
Taxon+Island+log10(Area+1)+log10(Distance+1)+log10(Elevation+1)+(1|Archipelago/Island), 
data=data_mine, family="binomial", weights=c(N))


The problem of non independence is restricted only to data from the 
same archipelago but I used archipelago as a random factor.
If a glmm allows for correlation between the observations of the same 
random factor doesn't it mean that I can use it in this case?

Ι did partial mantel tests to check for correlations between beta 
diveristy and inter-island distance, area and elevation differences 
between islands
in the same archipelago (in my case an archipelago can have oceanic or 
landbridge islands but not both kinds).
But I also wanted to test for the effect of taxon and island type 
(oceanic vs landbridge) on beta diversity and I could not do
that with mantel tests. So I used a mixed model.

The data are to complex for any other kind of analyses.
I understand that if the observations where from only one archipelago I 
could run a regression and due to the lack of independence of 
observations
I would estimate the regression parameters using bootstrap.
But in this case (because I have 11 archipelagos) I do not have a 
complete lack of independence because observations from different 
archipelagos are independent.
And even if a bootstrap was the correct way to go I do not think that 
there is an available procedure for this. Or if it is even possible to 
bootstrap a mixed effects model.

I have enough data (3076 observations) to support a glmm.

The output from the model is the following:

Generalized linear mixed model fit by the Laplace approximation
Formula: Beta_diversity ~ Taxon + Island + log10(Area + 1) + 
log10(Distance +      1) + log10(Elevation + 1) + (1 | 
Archipelago/Island)
    Data: data_mine
   AIC  BIC logLik deviance
  4723 4777  -2353     4705
Random effects:
  Groups             Name        Variance Std.Dev.
  Island:Archipelago (Intercept) 0.22045  0.46952
  Archipelago        (Intercept) 0.22045  0.46952
Number of obs: 3076, groups: Island:Archipelago, 11; Archipelago, 11

Fixed effects:
                      Estimate Std. Error z value Pr(>|z|)
(Intercept)          -1.84347    0.31407  -5.870 4.37e-09 ***
Taxonlizards         -0.27649    0.09055  -3.053  0.00226 **
Taxonsnakes          -0.10781    0.09258  -1.165  0.24420
Islandoceanic         0.84422    0.41087   2.055  0.03991 *
log10(Area + 1)       0.12917    0.02497   5.173 2.31e-07 ***
log10(Distance + 1)   0.41862    0.02587  16.182  < 2e-16 ***
log10(Elevation + 1)  0.16041    0.03128   5.128 2.93e-07 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Correlation of Fixed Effects:
             (Intr) Txnlzr Txnsnk Islndc l10(A+1 l10(D+1
Taxonlizrds -0.221
Taxonsnakes -0.212  0.922
Islandocenc -0.560 -0.061 -0.049
log10(Ar+1) -0.038  0.047  0.031 -0.014
lg10(Dst+1) -0.399  0.014  0.009 -0.017  0.023
lg10(Elv+1) -0.131  0.008  0.001  0.003 -0.608  -0.014


Do you think I could trust this model?

Thnak's
Eva Pitta



Πίττα Eύα <epitta at ...> writes:


     Hi, I am a phd student in Greece. And I have some questions 
regarding the use of glmm if the data include dissimilarity values.


     I do not know if this mailing list is appropriate for my questions 
but I do not know who else to turn to.


   You might be better off with the r-sig-ecology mailing list,
where there will be more expertise on community ecology topics
such as beta diversity ...


     My data include islands in various archipelagos and 
presence-absence of species of 3 taxa on the them. I estimated beta 
diversity as compositional dissimilarity between pairs of islands in the 
same archipelago using the Jaccard coefficient (proportion of common 
species between two islands). For example if I have 5 islands in a given 
archipelago I end up with 10 dissimilarity values. I fitted a glmm model 
(using package lme4) to test for the effect of taxon and also the effect 
of inter-island distance, area and elevation differences between pairs 
of islands on beta diversity using archipelago as a random factor. 
However, dissimilarity values (and the rest) are not independent of each 
other in the same archipelago, because each island contributes to N - 1 
of them. I read that a glmm allows for correlation between the 
observations of the same random factor. Does this mean that a glmm takes 
into account the fact that the dissimilarity values are not independent 
from each other? Or should I somehow take into account the fact that 
dissimilarity values in the same archipelago are not independent of each 
other.


   This is a little bit tricky.  You *might* be able to do this
by using 'island identity' as a random factor as well, but it's
also quite possible that you would just run out of data that way.
People often use Mantel and partial Mantel tests to do inference
on these kinds of pairwise comparisons (i.e. use randomization
to compare the matrix of pairwise area differences with the matrix
of pairwise compositional dissimilarities).  It's certainly
the case that the model you've set up so far does *not* account
for the correlation due to island identity.

   Ben Bolker

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