What’s the best model for count data, Poisson or negative binomial regression?

[JohnS]

I’m trying to decide if I should use a Poisson regression for my count data, but I’m not fully confident the variance equals the mean. My exploratory analysis shows the variance is a bit higher, which makes me wonder if a negative binomial model would be more appropriate here.

[AvaZT]

I tried Poisson regression and the variance clearly outpaced the mean, so overdispersion was obvious. I switched to a negative binomial and the standard errors calmed down a bit, and the coefficient estimates shifted.

[Grace.W]

I found that sometimes the extra variance comes from clustering or a few outliers rather than the model itself. I tried adding covariates, then a random intercept structure, and it helped in one chunk of data but not everywhere.

[Daniel.W]

Do you think the overdispersion is really about the mean model or about unobserved heterogeneity across groups?

[GregoryW]

I did a quick dispersion check and a quasi likelihood tweak, but the results stayed noisy and I still couldn't decide.