Informative priors for Productivity model in an IPM

[Diego Arévalo]

Dear all,

I'm fitting an Integrated Population Model for a long-lived species, the Griffon Vulture, using capture-recapture and recovery data, productivity, and counts of breeding pairs in three sites (sites A, B and C). The study period spans 13 years, but for some years I lack of productivity and count data in sites A and B. Specifically, 4 years of productivity information (years 2, 9, 10 and 11) and 10 years of counts at site A (years 2 to 5, 7 to 10, 12 and 13), and 11 years of counts at site B (years 2 to 9, and 11 to 13). 

Since I'm fitting a multi-state model and estimating the movement probability between sites, the information on breeding individuals is 'shared' when we allow that individuals move from a site to another, thus, making population size estimates identifiable (albeit with lower precision) for sites A and B in the years without data. However, for the years lacking productivity information at site A, the values are quite unrealistic. Given that the Griffon Vulture is a long-lived species and typically produces a single  egg per breeding season (if we ignore replacement clutches), productivity should range between 0 and <1, commonly around 0.5. In the missing years of productivity information at site A, the estimates reach values >1, which is entirely unrealistic. 

Since I'm modeling the log of productivity as a GLMM with a random time effect, I've tried using informative priors for the hypermean (dunif(0,1)), but mean estimates of years without data were >1. I've even tried truncating the temporal residual term using a reasonable range of values to reduce the deviation from the overall mean, but I've observed that this negatively bias the hypermean and positively bias annual productivity  in the years without information (>1.5).

Can anyone help me find a solution to 'correct' these productivity estimates? or is it statistically incorrect to force values in the absence of information into a preferred range?

 Thank you in advance!

Diego Arévalo

[Jose Jimenez Garcia-Herrera]

Dear Diego,

 

I'm sure Michael Schaub can give you some additional advice, but you can use a binomial instead of a Poisson if the productivity (as is your case with the griffon vulture) is going to be between 0-1.

 

Regards,

José

 

De: hmec...@googlegroups.com <hmec...@googlegroups.com> En nombre de Diego Arévalo
Enviado el: martes, 5 de marzo de 2024 22:13
Para: hmecology: Hierarchical Modeling in Ecology <hmec...@googlegroups.com>
Asunto: Informative priors for Productivity model in an IPM

 

No suele recibir correos electrónicos de dareva...@gmail.com. Por qué esto es importante

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[Michael Schaub]

Good morning,

 

It is certainly a good suggestion to use the binomial instead of the Poisson, perhaps this helps already. However, there may be too little information in the data because it seems that in some years where there is no productivity data, there is no count data. If this is the case (too little information), you may want to make your model more robust by introducing additional assumptions. For example, you could assume that productivity in the years with missing (productivity) data is the same as the long-term average that you estimate from the years with data.

 

Best

 

Michael

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[Diego Arévalo]

Hi all,

Thank you for all your replies. I finally found a solution following Thomas' suggestions, who wrote to me in private. It basically involved changing the log-link to a logit-link function to bound values between 0 and 1 for modeling productivity. This worked perfectly to those estimates with missing data, while the others remained very similar when using the log-link.

Thanks once again.

Best regards,

Diego

[Denis Valle]

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When: May 13 - May 16

 

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To view this discussion on the web visit https://groups.google.com/d/msgid/hmecology/ZR0P278MB07903CA8E4C486B0C430DD589A212%40ZR0P278MB0790.CHEP278.PROD.OUTLOOK.COM.