Negative binominal regression, sample size and the rule of the events per variable

[John Ressman]

Hello, I am trying to find references about sample size in relation to my negative binominal regression model (nbreg). When it comes to a logistic regression model the rule of ten events per variable can be applied but how about the nbreg? Regarding the logistic regression I find a lot of good scientific references but not for a nbreg. Is there someone who knows if I can apply this rule for my nbreg model (as they all are from the same family, GLM) and if there is a good scientific reference for this? Best regards, John Ressman

[Tiago Pereira]

There isn’t a rule of thumb that fits every situation. But I think you’re referring to how many observations per predictor one should use logistic regression or a negative binomial model for multivariable modelling?

[John Ressman]

Yes, and the question was if you could apply that rule on nbreg. There is a lot of references on that rule for logistic regression.

[Leonardo Guizzetti]

There isn't a rule of thumb I've seen for negative binomial regression. That said, nbreg is similar to Poisson regression, which can be reasonably similar to linear regression for the purposes such rules of thumb. There, it's often said a minimum of 10 observations per variable are needed. However, these rules of thumb should not be taken seriously, and should probably be ignored entirely. I've seen model fits that work well with 5 observations per variable, and I've also seen poor model fits from 30 observations.per variable. It is your responsibility to assess model fit and how well it does (or doesn't) fit a particular purpose, rather than the assume that if you meet some rule of thumb this will magically improve model fit.

[Joao Santos Silva]

I agree with Leonardo that those rules should not be taken seriously. The results in Portnoy (1988) suggest that it is the ratio of the square of the number of parameters over the sample size that should be "small," at least for the asymptotic distribution to be well approximated by a normal. See the example in the first page of the paper.

[Tiago Pereira]

I agree with Leonardo. For the negative binomial model, it is very possible that the degree of overdispersion and zero inflated data may also play a role in the number of participants necessary for a decent fit.

[Jeff Wooldridge]

I’m not sure the issue is “fit.” I can get a perfect fit if n = k. I think it’s about when you can trust the asymptotic inference. I’m not sure but I know I’d use Poisson and not NegBin.

[Tiago Pereira]

Indeed, Jeff. Suboptimal choice of term. "a decent model".

[John Ressman]

Thank you for all the answers and your involvement in the issue.