# [R-sig-ME] underdispersion glmer/MCMCglmm

Simone Messina S|mone@Me@@|n@ @end|ng |rom u@ntwerpen@be
Tue Apr 20 10:36:27 CEST 2021

```Dear all,

I am running binomial models based on infection rates, but I have some doubts which I hope you can kindly help me to solve.

Briefly, I want to test for the effect of forest type (2 levels) on birds� infection rate (proportion data). My dataset is composed by 2 rows per each species (one row per each type of forest). Sample sizes per species in each forest type are mostly below 10, except for one species over 20.

Question 1: Is it possible that my model is under-dispersed (see below)?
To deal with under-dispersion shall I get the model estimates as in Quasi-distribution?

glm1<-glmer(infection ~ forest + (1|species), data=dataset, family=binomial, weights = SampleSize)

> summary(glm1)
Generalized linear mixed model fit by maximum likelihood (Laplace Approximation) ['glmerMod']
Family: binomial  ( logit )
Formula: infection ~ forest + (1 | species)
Data: dataset
Weights: Size

AIC      BIC   logLik deviance df.resid
96      100      -45       90       25

Scaled residuals:
Min      1Q  Median      3Q     Max
-1.2925 -0.4949  0.1130  0.6178  1.1473

Random effects:
Groups  Name        Variance Std.Dev.
species (Intercept) 1.763    1.328
Number of obs: 28, groups:  species, 14

Fixed effects:
Estimate Std. Error z value Pr(>|z|)
(Intercept)  -0.2969     0.4515  -0.657    0.511
forestUNL    -0.5426     0.3875  -1.400    0.161

Correlation of Fixed Effects:
(Intr)
forestUNL -0.414

Then I test for under- / over-dispersion, and I detect under-dispersion:
> overdisp_fun(glm1)
chisq   ratio   rdf     p
14.729  0.589  25.000  0.947

Hence, I calculated model estimates as in Quasi-distribution.

> printCoefmat(quasi_table(glm1),digits=3)
Estimate Std. Error z value Pr(>|z|)
(Intercept)   -0.297      0.347   -0.86    0.392
forestUNL     -0.543      0.297   -1.82    0.068 .

Question 2: in case I decide to run the model with MCMCglmm (to include phylogeny), shall I consider under- / over-dispersion? How? Is there a way to get estimates as in Quasi-distribution in MCMCglmm models?

The only info I could get so far is that MCMCglmm automatically accounts for over-dispersion in count data with poisson distribution, but I don�t understand if this is valid also in case of proportion data with binomial family.

Thank you very much for your attention and explanations.

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