Hierarchical model with INLA

[houessou madjid]

Hi all,

I'm modelling bird spatio-temporal migration. I have two datasets. One  telemetry data and one citizen science data.  My goal is to integrate both datasets. To do so, i transform my telemetry data into presence/absence data. My idea is to use the probability of presence in telemetry data as weight in Log Gaussian Cox Process (citizen science) with spatio-temporal dependencies. 

Concretely, my model is defined like this  :

 \ln(\frac{p_i}{1-p_i}) = X(s_i,t)\beta+\{Z(s) \otimes Z(t)\}^Tu 

   \ln(\lambda(s_i,t)) &= X(s_i,t)\beta+\{Z(s) \otimes Z(t)\}^Tu
     
    with $u \sim \mathcal{N}(0,\sigma^{2}\mathbf{I})$ 

X(s_i,t)  :  environmental covariates in space and time (from daymet)

\beta : coefficients

Z(s) and Z(t) are spatial and temporal basis functions


Is possible to build this type of hierarchical model in INLA? If yes, any example would be extremely appreciate.

Thanks,

[Helpdesk (Haavard Rue)]

seems like it, yes. the space-time component is not exactly written in this form
but I guess you aim for a kronecker structure. since the two likelihoods are
from two families, you may want a scaling between the two linear predictors.

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[houessou madjid]

Thanks for your response?

How can I write it in order to implement it with INLA?

Any ressources or example of this type of model?

[Finn Lindgren]

Hi,

The ”group” model in the example i linkade to you in the other thread is such a kronecker precision/covariance model:

You probably want to use an ar1 model for the time aspect of the group model.

Note however that the appropriate way to merge telemetry and citizen science sightings data is not a settled thing and is an active research topic. E.g. it’s not clear that one should convert telemetry to presence/absence, or thin it and model it as an LGCP, and whether the citizen science data is appropriate to model as an LGCP. 

It _sounds_ like you’re intending to use the telemetry data to estimate a “preferential sampling” term for the citizen science data, but you need to write down the details of what model you want to use, as there is more than one approach, and you have to use your knowledge about your specific problem to judge which one might be appropriate.

Finn

On 17 Jul 2025, at 01:32, houessou madjid <hmad...@gmail.com> wrote:

Thanks for your response?

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