Interpretation of GLMM output in R

From the output, I conclude that both predictor variables have an effect on pollinator offspring. Is it reasonable to do the LRT for testing the predictor variables? Is there any chance to get an effect size of how much the predictor variables explain variance in the response variable? Since I know they have an effect, interpreation would be different when the effect of one variable is small or large. 

Date: Sun, 2 Aug 2015 00:08:35 +0200 
Subject: Re: [R-sig-ME] Interpretation of GLMM output in R 
From: thierry.onkelinx at inbo.be 
To: pauljohn32 at gmail.com 
CC: yvonne.hiller at hotmail.de; r-sig-mixed-models at r-project.org 
 
 
Paul, 
 
Note that exp(beta0 + beta1*parasitoids + btree) is equivalent to  
exp(beta0 + beta1*parasitoids)*exp(btree). So the relative effect of  
tree doesn't depend on the other effects. 
 
I tend to look at the ratio of the 97.5% and 2.5% quantiles of the  
random effect. exp(q*sigma)/exp(-q*sigma) or simplified exp(2*q*sigma)  
with q =1.96 (97.5% quantile of a normal distribution) and sigma= the  
standard deviation of the random effect. exp(2*1.96*0.3261) ~ 3.5 So  
the 97.5% quantile tree has about 3.5 times the number of pollinators  
of the 2.5% quantile tree. 
 
Best regards, 
 
Thierry 
 
Op 1-aug.-2015 15:43 schreef "Paul Johnson"  
<pauljohn32 at gmail.com<mailto:pauljohn32 at gmail.com>>: 
Hi 
 
Your message comes through with weird line breaks, you should turn off 
the HTML compose option in your mail program, just write text. 
 
On Fri, Jul 31, 2015 at 8:42 AM, Yvonne Hiller  
<yvonne.hiller at hotmail.de<mailto:yvonne.hiller at hotmail.de>> wrote: 

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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