In this simulation, we demonstrate the effect of introducing "known absences" (sites where a species cannot be present) into an occupancy model. Specifically, we show that including such known absences can lead to incorrect inferences about changes in occupancy at sites where the species was detected at least once.
We simulate detections for a single species across some number of visits (specified by nvisit) at some number of sites (specified by nsite) across 2 eras. Each era may differ in detectability (respectively, detectabilities are p.1 and p.2).
One can see the effect of adding known absences by changing the parameter nsite.foreign from 0 to a non-zero value and also by varying p.1 and p.2.
By increasing the number of sites with known absences added to the model, one can see that the model-estimated change in occupancy at sites where the species was observed at least once becomes closer to the same value as estimated from the raw data, neither of which may reflect actual changes in true occupancy.