quantile regression with negative binomial distribution for overdispersed count data

[Ruilin Chen]

Dear INLA users,

I asked this question in another thread related to quantile regression, but maybe it deserves its own separate thread. 

I am really interested in the idea of "model-aware quantile regression", and have been experimenting with INLA for that topic. My research uses negative binomial regression a lot because I am dealing with overdispersed count data. But I realized that most of the existing examples or demos of model-aware quantile regression using INLA are based on Poisson regression. 

Specifically, I checked out Tullia's toy demo on this under this link: https://github.com/tulliapadellini/INLA-quantreg

I was able to replicate it and also applied it to my own count data. But I keep getting error messages when I change the distribution family from "poisson" to "nbinomial". 

The error message is  "inla.mkl: src/inla.c:17794: inla_parse_data: Assertion `0 == 1' failed. Aborted (core dumped)" 

I forgot where I read it, but I remembered seeing somewhere that says INLA allows the quantile option for poisson, negative binomial as well as binomial distribution. It didn't return error messages when I changed it to "binomial", but it somehow didn't work for "nbinomial". 

My question is: 

•  Is this because the quantile option for negative binomial distribution is not yet supported in INLA? Or is this caused by some other bug either on my side or on INLA's side?
• Also, if it is not yet supported, does anyone have any idea how I could estimate a negative binomial quantile regression using the existing framework? 

Thank you! 

ruilin 

[Helpdesk]

I checked the code and the quantile for nbinomial is not yet
implemented. I'm a bit reluctant about the neg.binomial as its
essentially just a poisson with an iid normal random effect (well,
techically its a log of a Gamma(a,a) distribution, but they are more or
less the same). so the question is if Poisson is the correct choice even
for nbinomial.

I'm happy you like the idea of the model-aware q-regression. from the
response we got about this work, very few seems to understand/appriciate
it.

Best
Håvard

On Thu, 2021-12-16 at 09:58 -0800, Ruilin Chen wrote:
> Dear INLA users,
>
> I asked this question in another thread related to quantile
> regression, but maybe it deserves its own separate thread. 
>
> I am really interested in the idea of "model-aware quantile
> regression", and have been experimenting with INLA for that topic. My
> research uses negative binomial regression a lot because I am dealing
> with overdispersed count data. But I realized that most of the
> existing examples or demos of model-aware quantile regression using
> INLA are based on Poisson regression. 
>
> Specifically, I checked out Tullia's toy demo on this under this
> link: https://github.com/tulliapadellini/INLA-quantreg
> I was able to replicate it and also applied it to my own count data.
> But I keep getting error messages when I change the distribution
> family from "poisson" to "nbinomial". 
> The error message is  "inla.mkl: src/inla.c:17794: inla_parse_data:
> Assertion `0 == 1' failed. Aborted (core dumped)" 
>
> I forgot where I read it, but I remembered seeing somewhere that says
> INLA allows the quantile option for poisson, negative binomial as well
> as binomial distribution. It didn't return error messages when I
> changed it to "binomial", but it somehow didn't work for "nbinomial". 
>
> My question is: 

>  *  Is this because the quantile option for negative binomial

> distribution is not yet supported in INLA? Or is this caused by some
> other bug either on my side or on INLA's side?

>  * Also, if it is not yet supported, does anyone have any idea how I

> could estimate a negative binomial quantile regression using the
> existing framework? 
> Thank you! 
>
> ruilin 
>

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--
Håvard Rue
he...@r-inla.org