0
$\begingroup$

My dependent variable (count) shows signs of overdispersion (mean 2.50, Variance 6.60), which led me to use a negative binomial model. This seems to fit better compared to the Poisson regression (lower AIC). However, few of the significant effects I found when using the Poisson regression become highly non-significant when using the negative binomial model.

Is that normal? should I stick with the Negative Binomial regardless?

Thank you

Improve this question
$\endgroup$

1 Answer 1

Reset to default
6
$\begingroup$

You can run both and perform a likelihood ratio test to test whether the negative binomial is to be preferred. In almost all cases, it is. Remember that overdispersion matters for the conditional outcome, not the outcome itself, so examining the mean and variance in the outcome prior to fitting the model does not tell you which model will be preferred.

One reason you have significance in the Poisson and not in the negative binomial is that in the presence of overdispersion, Poisson standard errors are too small. You may be tempted to go with the model that proves your hypothesis, but you should do everything you can to ensure that that is a valid choice.

Improve this answer
$\endgroup$
3
  • $\begingroup$ thank you for your answer. When deciding the best model based on the likelihood ratio or AIC, should I run them with intercept only (thus, dependent variable only) or including the independent variables (which are quite a few - 8 to be precise)? Thanks $\endgroup$
    – John Walk
    Jun 16, 2020 at 11:03
  • 3
    $\begingroup$ With all your predictors. You want to compare two models, and unless comparing intercept-only models is relevant to your research question, there's no use in doing it. Because the models are nested, you should use the LR test, not just compare AIC. Honestly you should just use the NB model. If a Poisson is appropriate, then you've wasted one parameter. Not a big deal. If you were to use a Poisson model and the NB was appropriate, you would make a huge statistical error. It's perfectly fine to just choose the NB without dmonstrating it's better than the Poisson for your data. $\endgroup$
    – Noah
    Jun 16, 2020 at 18:39
  • $\begingroup$ Thank you for the clarification. That was very helpful! $\endgroup$
    – John Walk
    Jun 17, 2020 at 10:21

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge that you have read and understand our privacy policy and code of conduct.

Not the answer you're looking for? Browse other questions tagged or ask your own question.