Should I use Poisson or negative binomial for overdispersed count data?

[Brian77]

I’m trying to decide if I should use a Poisson or a negative binomial model for my count data on website errors per day. The variance is about twice the mean, so I’m worried about overdispersion, but my sample size is fairly small.

[Grace_T]

With var about twice the mean, the Poisson model will understate variability; a dispersion-parameter family is a common fix, but with a small sample size the dispersion estimate can be unstable; a quick check is a quasi-Poisson approach.

[Luke66]

I tried something similar with a small dataset and the extra variability showed up as wide intervals once I switched to a dispersion model.

[Timothy84]

Maybe the issue isn't the extra variability at all but days with zero counts or holidays; sometimes a zero inflated or other time patterns explain it more.

[SophiaM]

Do you have covariates or known day effects that you could model, to help stabilize the dispersion estimate?