Chapter 15 Poisson GLMM

Given the mean-variance relationship, we will most likely need a model with over-dispersion.

To understand why, let’s start with a Poisson model.

To run a GLMM in R we will use the glmer() function from the lme4 package:

# Poisson GLMM Given the mean-variance relationship, we
# will most likely need a model with over-dispersion.  To
# understand why, let's start with a Poisson model.
mp1 <- glmer(total.fruits ~ nutrient * amd + rack + status +
    (1 | popu) + (1 | gen), data = dat.tf, family = "poisson")

Random effects: (1|popu) and (1|gen). We model random intercepts for both factors so that total fruit production can vary among populations (popu) and genotypes (gen).

Over-dispersion check

We can check for overdispersion using the overdisp_fun() function (Bolker et al. 2011) which divides the Pearson residuals by the residual degrees of freedom.

The function tests whether the ratio is greater than 1.

Let’s run the test:

# Download the glmm_funs.R code from the wiki page and
# source it to run the function
source(file = "data/glmm_funs.R")  # This line will vary depending on where your data is saved
# Over-dispersion check
overdisp_fun(mp1)

##       chisq       ratio           p        logp 
## 15755.86835    25.57771     0.00000 -6578.47028

# Ratio is significantly > 1

Ratio is significantly > 1

As expected, we need to model a different distribution where the variance increases more rapidly than the mean.