**A brief note on overdispersion**

Assumptions

Poisson distribution assume variance is equal to the mean.

Quasi-poisson model assumes variance is a linear function of mean.

Negative binomial model assumes variance is a quadratic function of the mean.

rstats implementation

#to test you need to fit a poisson GLM then apply function to this model

library(AER)

dispersiontest(object, trafo = NULL, alternative = c(“greater”, “two.sided”, “less”))

trafo = 1 is linear testing for quasipoisson or you can fit linear equation to trafo as well

#interpretation

c = 0 equidispersion

c > 0 is overdispersed

**Resources**

**Function description**from vignette for AER package.- Excellent
**StatsExchange description**of interpretation.