rgampois seems to be incorrectly defined ( with respect to neg_binomial_2 from stan)

[rmcelreath]

rgampois seems to be incorrectly defined ( with respect to neg_binomial_2 from stan)

[stevejburr]

Just found this bug myself - I was going to post an issue but found this one.

Rethinking will fit an NBD model correctly using rgampois - I can get results to match brms() glm.nb() and match the model parameters for some simulated data. (I can share detail on this if helpful)

However, if you run sim() on the fitted rethinking model, then the simulated data won't be right as there's a mismatch between the different parameterisations. To get the correct simulations, you need to take the fitted values and pass them to the built in rnbinom function with different transformations.

I agree with rgampois_proposed() as above for getting the right numbers out.

[rmcelreath]

Thanks. If I understand right, the issue is just that the internal Stan function has a different parameterization than is assumed to be consistent with random number generator function? The map2stan model seems to be working fine.

[grepinsight]

You are right.

Based on my observation, I think the parameterization of negative binomial in stan and rethinking are different as follows:

Using X ~ Gamma(a, b) where E[X]= a * b, Var[X]=a* b^2 as a reference gamma distribution(where a is a shape parameter and b a scale parameter),

1. In rgampois of rethinking, the focus is mu and b( which is the scale parameter of the above gamma distribution), hence its function definition.
2. In neg_binomial_2 of stan, the focus is on mu and a(which is a shape parameter of the above gamma distribution), which is also an inverse dispersion parameter. The critical insight I learned while debugging this is that the notion of dispersion is embeded in a as opposed to b.

I was a bit confused initially, because when I think of negative binomial(or gamma-poisson mixture), I always think of poisson + overdispersion. So I automatically assumed that "scale" represented the parameter for the overdispersion, when in fact it's not.