Check overdispersion of GL(M)M'sSource:
check_overdispersion() checks generalized linear (mixed)
models for overdispersion.
Fitted model of class
Currently not used.
A list with results from the overdispersion test, like chi-squared statistics, p-value or dispersion ratio.
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
is based on the code in the
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
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).
Bolker B et al. (2017): GLMM FAQ.
Gelman, A., and Hill, J. (2007). Data analysis using regression and multilevel/hierarchical models. Cambridge; New York: Cambridge University Press.
Other functions to check model assumptions and and assess model quality:
library(glmmTMB) data(Salamanders) m <- glm(count ~ spp + mined, family = poisson, data = Salamanders) check_overdispersion(m) #> # Overdispersion test #> #> dispersion ratio = 2.946 #> Pearson's Chi-Squared = 1873.710 #> p-value = < 0.001 #> #> Overdispersion detected. m <- glmmTMB( count ~ mined + spp + (1 | site), family = poisson, data = Salamanders ) check_overdispersion(m) #> # Overdispersion test #> #> dispersion ratio = 2.324 #> Pearson's Chi-Squared = 1475.875 #> p-value = < 0.001 #> #> Overdispersion detected.