Hello all,
I am hoping for some clarity on the meaning behind 3 different scenarios for modeling theta and/or psi in a multi-method model suite in Presence. I would like to be able to understand the influence of a habitat parameter on both the local availability and the overall occupancy. When incorporating this habitat parameter in Presence, it seems to me that there are three options:
1)
______a1 a2 a3
Psi____1 0 HABITAT
theta1 0 1 HABITAT
theta2 0 1 HABITAT
theta3 0 1 HABITAT
...
2)
Psi____1 0 HABITAT
theta1 0 1 0
theta2 0 1 0
theta3 0 1 0
...
3)
Psi____1 0 0
theta1 0 1 HABITAT
theta2 0 1 HABITAT
theta3 0 1 HABITAT
...
The model output for both 1 and 2 above give the intercept estimates for Psi and theta1, and a slope for Psi.HABITAT, but the values are markedly different. Only option 3 provides the slope for theta1.HABITAT. I understand that theta is conditional on the overall occupancy status, but would like to be very clear about if/how to interpret the role of covariates separately.
One last note, the default notation for naming models is “psi,theta(), p()”, but in a detailed example from a USGS Patuxent workshop (on Nutria in Maryland) models are named “psi(),theta(),p()”. Is there substantial difference in the meaning? Is there a way to indicate the conditional nature of theta of psi if modeling only one with a covariate at a time?
Thank you!
-Bryn