I'm dealing with traffic volume count data. The Poisson is a good fit for the data when I determined using chi-square test but the dispersion index is slightly overdispersed.
How to deal with this? Can it be possible that the data is a Poisson fit but still it is overdispersed? If so, what does it mean?
The index of dispersion is coming to 1.15 ( ideally should be 1 for Poisson) Also, I have data for 360 intervals - 30 seconds each ( i gathered data for 3 hours from the same place, same time).
Partially answered in comments:
Several possibilities arise. Might it just be due to random variation? If the overdispersion is seen unconditionally, this may simply reflect a mix of Poissons with different means; any heterogeneity in the mean will lead to overdispersion. If you have any explanatory variables, conditioning on these may remove the apparent overdispersion. If that doesn't get rid of it, it's possible using GLMs to fit quasi-poisson models that can incorporate overdispersion (though in a slightly hand-wavy way; I tend to consider Negative Binomial models at that point). How much overdispersion is there?
– Glen_b
In comments OP says the index of overdispersion is about 1.15, that is close enough to 1 that for many purposes the Poisson could be a good enough approximation. Maybe.
