conditional Poisson regression model with INLA?

[Marc Marí-Dell'Olmo]

Hi, all

 

Does anyone know it is possible to implement conditional Poisson regression model with INLA?

I would like to replicate the example of this article:
http://bmcmedresmethodol.biomedcentral.com/articles/10.1186/1471-2288-14-122
http://www.ag-myresearch.com/bmcmrm2014b.html

Best Regards

 

Marc

[Håvard Rue]

On Fri, 2016-08-05 at 01:00 -0700, Marc Marí-Dell'Olmo wrote:
> http://bmcmedresmethodol.biomedcentral.com/articles/10.1186/1471-2288
> -14-122

see attached screenshot. so you can do this using a multinomial model
ie, by adding a stratum spesific intercept to the logistic regression?

-- 
Håvard Rue
Department of Mathematical Sciences
Norwegian University of Science and Technology
N-7491 Trondheim, Norway
Voice: +47-7359-3533 URL : http://www.math.ntnu.no/~hrue
Mobile: +47-9260-0021 Email: havar...@math.ntnu.no

R-INLA: www.r-inla.org

[Marc Marí-Dell'Olmo]

Yes, I think that it is similar to perform the unconditional Poisson model as specified in formula 3 (that can be easily implemented with INLA). But this model fits a parameter (intercept) for each stratum and with conditional poisson model it is not necessary. As you can see in the table 4, to solve the same problem with Unconditional Poisson model have to be fitted 421 parameters while with Conditional poisson only 2 parameters are estimated. This is very important for me, because I want to perform a multiple time series analysis, where the number of parameters to be estimated with unconditional poisson could be very large and its estimation could be (computationally) impossible.

Perhaps including a constraint in the intercepts of the uncionditional Poisson model could be equivalent to the conditional poisson... I don't know...

Thank you!

[Håvard Rue]

...and there is no way to 'estimate' this stratum spesific intercept
upfront? 

On Fri, 2016-08-05 at 03:00 -0700, Marc Marí-Dell'Olmo wrote:
> Yes, I think that it is similar to perform the unconditional Poisson
> model as specified in formula 3 (that can be easily implemented with
> INLA). But this model fits a parameter (intercept) for each stratum
> and with conditional poisson model it is not necessary. As you can
> see in the table 4, to solve the same problem with Unconditional
> Poisson model have to be fitted 421 parameters while with Conditional
> poisson only 2 parameters are estimated. This is very important for
> me, because I want to perform a multiple time series analysis, where
> the number of parameters to be estimated with unconditional poisson
> could be very large and its estimation could be (computationally)
> impossible.
>
> Perhaps including a constraint in the intercepts of the
> uncionditional Poisson model could be equivalent to the conditional
> poisson... I don't know... 

[Marc Marí-Dell'Olmo]

I don't know, I will explore it ...

[Steffi]

Dear Havard and Marc

I'd be very interested to hear if there were advances with the question regarding the conditional Poisson regression where it is not needed to estimate stratum-specific intercepts... I have a dataset with over 4000 strata, and other examples may contain even more.

Any hints are moste welcome.

Thanks in advance!
Steffi

[Håvard Rue]

On Sat, 2017-04-15 at 04:59 -0700, Steffi wrote:
> Dear Havard and Marc
>
> I'd be very interested to hear if there were advances with the
> question regarding the conditional Poisson regression where it is not
> needed to estimate stratum-specific intercepts... I have a dataset
> with over 4000 strata, and other examples may contain even more.
>

I don't know what this ended up with.

[INLA help]

On Sun, 2017-04-16 at 09:13 +0300, Håvard Rue wrote:
> On Sat, 2017-04-15 at 04:59 -0700, Steffi wrote:
> > Dear Havard and Marc
> >
> > I'd be very interested to hear if there were advances with the
> > question regarding the conditional Poisson regression where it is
> > not
> > needed to estimate stratum-specific intercepts... I have a dataset
> > with over 4000 strata, and other examples may contain even more.
> >
>
> I don't know what this ended up with. 

and I do not understand it really. is this using a multinomial
likelihood for the conditional poisson???

--
Håvard Rue
he...@r-inla.org

[Steffi]

and I do not understand it really. is this using a multinomial
likelihood for the conditional poisson???

 

Somehow, yes, but not quite. In my case I actually have binary data, where one success (1) is grouped with nine failures (0) to one stratum (btw, the data stem from animal movement behaviour, where at each step of a given location (1), a fixed number of possible locations (0) is added.)

Thus the response y is binary, and ten points build up a stratum. The likelihood for the analysis would be the conditional logisitic. A trick to do the analysis is to use cox regression, where all event times are set to 1. I therefore tried something like this:

formula <- inla.surv(rep(1,nn), y) ~  x1 + x2 + x3 +   strata(ID) + random terms

and used the coxph family. However, this is very inefficient, because INLA then approximates the baseline hazard by piecewise constant Poisson models, which is quite inefficient, especially because the numbers of strata is large.

Another trick is to use
formula <- y ~  x1 + x2 + x3 +   strata(ID) + random terms

and then the Poisson family, which is again giving the same results, but the problem now is that stratum-specific intercepts need to be estimated.

I'm not sure, however, if there is a way to use the Poisson family and circumvent the estimation of intercepts of each stratum... Interest does not center around them, so maybe they can be somehow fixed, but I don't see how.