Inlcuding covariates in 2-sp models RPresence

posts related to the RPresence library, which may not be of general interest to users of 'classic' PRESENCE.

Inlcuding covariates in 2-sp models RPresence

Postby vls72 » Mon Nov 06, 2017 12:00 am

Hi,

I am hoping to get some clarity on how to incorporate covariates into 2-species (single season) occupancy models (psiBA conditional parameterization) in RPresence, specifically covariates on occupancy that have a by-species interaction.

If I want to include land cover covariates on occupancy (called NativeForest and Crops here) as well as an interaction by species, plus an occurrence-level interaction (psiBA not equal to psibA), would this be correct (for psi):
OccMod(model=list(psi~SP+INT+NativeForest+Crops+NativeForest*SP+Crops*SP,
p~SP)......

Or should the covariate interaction be between both SP and the occurrence-level interaction (INT)? would this just mean that in addition to an interaction by species, the covariate will interact with psiBA and psiBa differently? I imagine that would look something like this but I'm not sure...

OccMod(model=list(psi~SP+INT+NativeForest+Crops+NativeForest*SP*INT+Crops*SP*INT,
p~SP)......

Thanks for any/all help provided. Hopefully this question makes sense... In general I am just seeking clarification on the difference between covariate interactions with SP and INT, and whether/why it makes sense to include both in the same model or not.

-Vanessa
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Re: Inlcuding covariates in 2-sp models RPresence

Postby darryl » Mon Nov 06, 2017 2:39 am

Hi Vanessa
Here's the default coding for the SP and INT effects relative to the occupancy parameters for a 2 species model (although you can change it by specifying alternative contrasts):

parameter SP INT
psiA 0 0
psiBA 1 0
psiBa 1 1

If I just simplify it to one covariate, X, then:
psi~SP+X = effect of X is the same for both species, but with a consistent difference between species (on logit scale). Presence of species A has no effect on species B
psi~SP*X = effect of X different for both species (note we don't need to include main effects in the formula). Presence of species A has no effect on species B
psi~SP*X+INT = effect of X different for both species. Presence of species A has an effect on presence of species B, but the effect is constant with respect to X
psi~SP*X+INT*X = effect of X different for both species. Presence of species A has an effect on presence of species B, and the effect is difference with respect to X (ie the level of interaction depends on X).

Note that as INT is nested within SP, then any interaction model with SP*INT has undefined levels (ie the SPxINT interaction term = INT), so you wouldn't use SP*INT*X, but could do SP*X + INT*X.

Hope that helps!
Darryl
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