Modeling NB Overdispersion parameter
hanna grock
Hi R-INLA community,
I am new to INLA and am modeling gridded spatial count data (number of animal locations, derived from GPS collared animals) using a negative binomial regression with SPDE barrier model to account for spatially correlated errors. While the model is performing well, we strongly suspect that the overdispersion parameter in the negative binomial distribution (parameterized with mean and overdispersion parameter) increases as a function of the number of animals that each grid cell is “exposed” to (i.e., number of unique animal home ranges that overlap with each grid cell). We are already using a related measure of exposure as an offset term, we expect that the number of unique animals will contribute additional count variation due to among-individual variation in habitat use. Therefore, we are hoping to model the overdispersion parameter as a linear function of a covariate (number of unique “exposures”).
While we know this idea (modeling NB overdispersion parameter as a linear function of covariates) can be implemented using glmmTMB, we are not sure if this is possible in R-INLA (and we would very much like to keep using INLA if possible). If so, we are hoping for some guidance in how to accomplish this. We also have one related follow-up question: is there a way in INLA to model the zero-inflation parameter as a function of covariates?
In glmmTMB, the syntax would look something like this (for covariates on dispersion and zero-inflation parameters):
m1 = glmmTMB(n_points ~ s(x1, k=5) + s(x2, k=10) + offset(offset),
ziformula = ~ x3,
dispformula = ~ x4,
data= df,
family=nbinom2(link="log") )
Please let us know if you would like additional clarification- and thanks in advance for any help you can provide.
Hanna
Helpdesk (Haavard Rue)
inla.doc("0poisson")
then adding an iid to the poisson of this will essentially give a negative
binomial
as of now, there is no easy way to make the variance of the noise to depend on
covariates. this what you're asking about as well ??? It can be added though if
needed
best
Havard
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Håvard Rue
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