N-Mixture Models with R-INLA

[Tim Meehan]

Hi All,

Just in case you are interested, Haavard Rue, Nicole Michel, and I have been developing the capacity to analyze N-mixture models in a Bayesian framework using R-INLA. Due to some restrictions innate to the INLA approach, you can't analyze all types of N-mixture models, as you could with MCMC, but it is blazing fast for the types you can analyze. We wrote up a tutorial and it just got accepted to the Journal of Statistical Software. It won't be out for a while, but we archived a preprint here: https://arxiv.org/abs/1705.01581. Hope you find it useful.

If you are interested in computational statistics, check out the appendix where Haavard describes how likelihood is computed. 

Best,

Tim

[Kery Marc]

Dear Tim,

thank you very much and congratulations !

I think I had seen that a short while ago already, forgot where. Is it correct that you can only add site-level, but not observation-level covariates into the model for p ?

I must admit that I found this somewhat of a restriction, since so often we would like to account for the date of survey in the analysis, because that often has a big effect on p, for instance in breeding birds. Also other covariates such as survey duration. On the other hand, there may well be cases where this would not be so important and if at the same time one has a huge data set and wants to do spatial modeling, then sure being able to fit Nmix models in INLA is a great thing !

Best regards  ---- Marc

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Subject: N-Mixture Models with R-INLA

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[Tim Meehan]

Hi Marc,

Yes, you are correct about site- and site-by-year covariates only for p.  So if observation-level covariates have not been effectively dealt with in sampling design, then this is not the appropriate approach. We are hopeful that it will be useful to those who would explore assumptions, fits, and p-covariates using other methods, perhaps on subsets of data, and then use INLA for larger datasets, over broader extents. Also, there are some in the INLA community that are experimenting with using INLA in an iterative way to analyze models that aren't currently workable with INLA.  Perhaps folks could work to develop this approach for N-mixture models.

Best,

Tim

[Peter Solymos]

Tim,

This is really nice work.

I just wanted to send a quick note regarding your comment "and then use INLA for larger datasets, over broader extents". The broader extent is where the constant-p assumption most likely won't hold, e.g. we found the constant-p model to be best supported for only 1 out of 152 species (http://www.bioone.org/doi/10.1650/CONDOR-18-32.1).

Cheers,

Peter

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Alberta Biodiversity Monitoring Institute http://www.abmi.ca
Boreal Avian Modelling Project http://www.borealbirds.ca

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[Tim Meehan]

Thanks, Peter. This is good to know. 

It suggests that, when testing assumptions, it should be done on sub-samples that are stratified to cover the full range of conditions. Incidentally, using INLA, it is possible to specify both fixed and random effects for p, which could include exchangeable, spatially- or temporal-structured random effects.

Best,

Tim

[KC]

Hi Tim,

I just came across the tutorial you mentioned. I was wondering if it were possible to add spatio-temporal random effects for both p and abundance n-mixture models using INLA?

Thanks,

Kaylan 

[Tim Meehan]

Hi Kaylan,

You can add spatiotemporal random effects for p but not lambda. Sounds like a job for MCMC.

Good luck!

Tim