How to test for overdispersion in Poisson GLMM with lmer() in R?

Question

I have the following model:

> model1<-lmer(aph.remain~sMFS1+sAG1+sSHDI1+sbare+season+crop
  +(1|landscape),family=poisson)

...and this is the summary output.

> summary(model1)
Generalized linear mixed model fit by the Laplace approximation 
Formula: aph.remain ~ sMFS1 + sAG1 + sSHDI1 + sbare + season + crop 
         +      (1 | landscape) 
  AIC  BIC logLik deviance
 4057 4088  -2019     4039
Random effects:
 Groups    Name        Variance Std.Dev.
 landscape (Intercept) 0.74976  0.86588 
Number of obs: 239, groups: landscape, 45

Fixed effects:
              Estimate Std. Error z value Pr(>|z|)    
(Intercept)  2.6613761  0.1344630  19.793  < 2e-16 
sMFS1        0.3085978  0.1788322   1.726  0.08441   
sAG1         0.0003141  0.1677138   0.002  0.99851    
sSHDI1       0.4641420  0.1619018   2.867  0.00415 
sbare        0.4133425  0.0297325  13.902  < 2e-16 
seasonlate  -0.5017022  0.0272817 -18.390  < 2e-16 
cropforage   0.7897194  0.0672069  11.751  < 2e-16
cropsoy      0.7661506  0.0491494  15.588  < 2e-16

Correlation of Fixed Effects:
           (Intr) sMFS1  sAG1   sSHDI1 sbare  sesnlt crpfrg
sMFS1      -0.007                                          
sAG1        0.002 -0.631                                   
sSHDI1      0.000  0.593 -0.405                            
sbare      -0.118 -0.003  0.007 -0.013                     
seasonlate -0.036  0.006 -0.006  0.003 -0.283              
cropforage -0.168 -0.004  0.016 -0.014  0.791 -0.231       
cropsoy    -0.182 -0.028  0.030 -0.001  0.404 -0.164  0.557

It is probably overdispersed, but how exactly do I calculate this?

Thanks very much.

Try the qcc.overdispersion.test in [qcc](http://rss.acs.unt.edu/Rdoc/library/qcc/html/qcc.overdispersion.test.html) package. — Penguin_Knight, Apr 27 '13 at 03:36
I'm not well versed in using the lme4 package, but one way to find out if there is overdispersion when dealing with a Poisson model is to compare the residual deviance to the residual degrees of freedom. These are assumed to be the same, so if the residual deviance is greater than the residual degrees of freedom, this is an indication of overdispersion. There's also the Cameron & Trivedi test of the assumption of equidispersion, but again, I'm not sure if this can be performed by the lme4 package. — Graeme Walsh, Jun 26 '13 at 22:54
@Penguin_Knight: it doesn't look like `qcc.overdispersion.test` is appropriate (it tests for overdispersion in *raw* binomial data, not in a model) — Ben Bolker, Jul 21 '14 at 18:00

score 4 · Answer 1 · answered Apr 27 '13 at 14:38

4

Among many other useful tidbits on GLMM with lmer() and other GLMM fitting software, check out the section on the following web page called How can I deal with overdispersion in GLMMs?

http://glmm.wikidot.com/faq

answered Apr 27 '13 at 14:38

ndoogan

1,260
8
21

This is more of a comment than an answer. Could you expand it, perhaps by giving a summary of the information at the link? – gung - Reinstate Monica Sep 12 '18 at 15:17

score 0 · Answer 2 · answered Sep 12 '18 at 15:10

0

The package AER (p.33) has the Cameron & Trivedi test of the assumption of equidispersion that can be used with GLMs.

AER::dispersiontest(model1)

answered Sep 12 '18 at 15:10

daszlosek

121
8

2

Although implementation is often mixed with substantive content in questions, we are supposed to be a site for providing information about statistics, machine learning, etc., not code. It can be good to provide code as well, but please elaborate your substantive answer in text for people who don't read this language well enough to recognize & extract the answer from the code. – gung - Reinstate Monica Sep 12 '18 at 15:16

How to test for overdispersion in Poisson GLMM with lmer() in R?

2 Answers2