Overdispersion occurs when the observed variance is higher than the
variance of a theoretical model. For Poisson models, variance increases
with the mean and, therefore, variance usually (roughly) equals the mean
value. If the variance is much higher, the data are "overdispersed".
Interpretation of the Dispersion Ratio
If the dispersion ratio is close to one, a Poisson model fits well to the
data. Dispersion ratios larger than one indicate overdispersion, thus a
negative binomial model or similar might fit better to the data. A p-value <
.05 indicates overdispersion.
Overdispersion in Poisson Models
For Poisson models, the overdispersion test is based on the code from
Gelman and Hill (2007), page 115.
Overdispersion in Mixed Models
For merMod
- and glmmTMB
-objects, check_overdispersion()
is based on the code in the
GLMM FAQ,
section How can I deal with overdispersion in GLMMs?. Note that this
function only returns an approximate estimate of an overdispersion
parameter, and is probably inaccurate for zero-inflated mixed models (fitted
with glmmTMB
).
How to fix Overdispersion
Overdispersion can be fixed by either modeling the dispersion parameter, or
by choosing a different distributional family (like Quasi-Poisson, or
negative binomial, see Gelman and Hill (2007), pages 115-116).