Interpretation of GLMM output in R

Hi

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Dear Ben Bolker and list members,

I?am a PhD-student working on tropical plant-pollinator
interactions (the fig-fig wasp mutualism).

I have some difficulties with my analyses of my data
using lmer (family = Poisson). I have read a lot of threads and searched for
solutions in Zuur 2009, though it was not completely satisfying. I looked at
other papers using GLMM (espeacially for the fig-fig wasp mutualism), but there
were so many different ways in reporting and interpreting p-values, AICs etc.
Therefore, I would be very grateful, if you could go through my output and
answer my questions to hopefully fully understand GLMM. Thank you so much in
advance.

One of my questions is:

Have parasitoids (offspring) and the volume size an
effect on the number of pollinator offspring?

As pollinators are parasitized by parasitoids, I would
expect a negative impact on pollinator offspring. As the size of the fig fruits
might be an additionally factor (due to limited oviposition sites inside the fruit
or due to the ovipositor length of a parasitoid is to short to reach inner most
ovules galled by pollinators), I included it in the model.

I have poisson data (counts):

Pollinator
= pollinator offspring

Parasitoids = parasitoid offspring

volume = fig fruit size measurement

tree = Tree ID

I have data from trees in the forest and in the
farmland, as well as data of the rainy and dry season. I have chosen to perform
lmer for each season and habitat separately. For each tree, I have collected 10
fig fruits to count offspring of wasps at the trophic level (pollinator,
parasitoid) and to measure the size of the fruit (volume). As I have 10 fig
fruits per tree, I would use tree as a random effect, to account for unmeasured
variance between trees. I have found different approaches to that in
literature. For instance: We did not include? tree ? and ?
syconium ? as random factors, because wasps were free to move between syconia
on the same tree, and between trees.

Therefore,
I am not sure if I have to use GLMM with trees as a random effect or if it?s
also possible to use GLM without the random effect.

The inclusion of
fig volume in this manner removed the need to use ?fig? as an additional nested
factor within ?tree?. Is that right?

Here, I
present the model with the random effect.

So, lets start with the model of the farmland during
the dry season:

fad <- lmer(Pollinator~Parasitoids+volume+(1|tree),family="poisson",verbose=TRUE)

summary (fad)

Generalized linear mixed model fit by the Laplace
approximation

Formula: Pollinator ~ Parasitoids + volume + (1 |
tree)

   Data:
fad.data

  AIC  BIC logLik deviance

 1166 1175
-578.9     1158

Random effects:

 Groups
Name        Variance Std.Dev.

 tree   (Intercept) 0.10634  0.3261

Number of obs: 80, groups: tree, 8

Fixed effects:

Estimate Std. Error z value Pr(>|z|)

(Intercept)
2.3167867  0.1632747  14.190
<2e-16 ***

Parasitoids -0.0046908
0.0021686  -2.163   0.0305 *

volume
0.0069525  0.0006108  11.383
<2e-16 ***

---

Signif.
codes:  0 ?***? 0.001 ?**? 0.01 ?*? 0.05
?.? 0.1 ? ? 1

Correlation of Fixed Effects:

(Intr) Prstds

Parasitoids -0.160

volume
-0.657 -0.107

1. Random effects: What does the Random
Effect table - the Variance, Std. Dev. and Intercept tells me?

Your model assumes that the outcome is Poisson with expected value
exp(beta0 + beta1*parasitoids + btree)

btree is a unique added amount for each tree.  The estimate of the
number btree's variance across trees is 0.1.

What that 0.1 means in terms of the predicted outcome?  Well, that
mostly depends on how big beta0 + beta1*parasitoids is.  If that
number is huge, say 1000, then adding a thing with variance 0.1 won't
matter much.

On the other hand, if it is 0.01, then the random effect at the tree
level is very large, compared to the systematic components in your
model.  When the link function gets applied, the distribution of
outcomes changes in an interesting way.

If you run ranef(), it will spit out the estimates of the random
differences among trees (btree "BLUPS").  If you run the predict
method, you can see how those map out to predicted values (exp(beta0 +
beta1 parasitoids + btree)
So it says that the
between?tree variability is fairly large. But I don?t understand to what it
relates. Does it mean that pollinator offspring variance is high between
trees and might be overestimating the explanatory variables?

2. What can I
conclude from the model regarding the fixed effects and how to report about it
(with or without p-values, z-values, estimates)?

So of what I know is that
the p-value is only a guide and that it is rather a comparison of two models.
What are the two models and can I compare them.

I am puzzled why you see p values at all. In the version of lme4 I'm
running now, I don't see p values.

Lets compare versions, since I'm pretty sure p values were removed
quite a while ago.
sessionInfo()
R version 3.1.2 (2014-10-31)
Platform: x86_64-pc-linux-gnu (64-bit)

locale:
 [1] LC_CTYPE=en_US.UTF-8       LC_NUMERIC=C
 [3] LC_TIME=en_US.UTF-8        LC_COLLATE=en_US.UTF-8
 [5] LC_MONETARY=en_US.UTF-8    LC_MESSAGES=en_US.UTF-8
 [7] LC_PAPER=en_US.UTF-8       LC_NAME=C
 [9] LC_ADDRESS=C               LC_TELEPHONE=C
[11] LC_MEASUREMENT=en_US.UTF-8 LC_IDENTIFICATION=C

attached base packages:
[1] stats     graphics  grDevices utils     datasets  methods   base

other attached packages:
[1] lme4_1.1-8   Matrix_1.2-2

loaded via a namespace (and not attached):
[1] grid_3.1.2      lattice_0.20-33 MASS_7.3-43     minqa_1.2.4
[5] nlme_3.1-121    nloptr_1.0.4    Rcpp_0.12.0     splines_3.1.2
[9] tools_3.1.2

Anyway...

If you had a huge sample, those p values would be accurate.

You have a small sample, there are other, more computationally
intensive ways, to get p values.  Read the Jrnl Stat Software paper b
y the lmer team, they describe profiling and bootstrapping. You have
small enough sample, could do either one.
4. What does the
correlation of fixed effects tells me?

It is a hint about multicollinearity & numerical instability, so far as I know.

5. Is it right
that the estimates tells me whether the relation of the fixed effects to
pollinator offspring is positive or negative?

Best way to get answer is to plot the predicted values from the model.
Use the predict function to plot for various values of the predictor.
6. Can I
calculate an effect size on each explanatory variable?

Only if you think the term "effect size" is meaningful.  And if you
have a formula for one.  In my experience with consulting here, it
means anything the researcher wants to call a summary number.

I've come to loathe the term because somebody in the US Dept. of
Education mandated all studies report standardized effect sizes,
forcing everybody to make Herculean assumptions about all kinds of
model parameters to get Cohen's D or whatnot.

I would highly appreciate your feedback on this.
Thanks so much in advance.

Good luck.  Next time, use a text only email composer and try to ask 1
specific question. You are more likely to get attention if people can
easily read the message and see what you want.  This one was difficult
to read (for me at least) and also somewhat vague.

Best wishes,

Yvonne Hiller

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Interpretation of GLMM output in R

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