I'm modeling habitat suitability for a large, mobile animal using occurrence data (presence only - I have no true absence data in this case) collected from camera traps (stations with automatic motion/heat sensing cameras). At each camera trap location I have 0 to several occurrences recorded.
Typically, when such data is modeled, they are modeled as count data, and detection probability is included in order to mitigate for covariates that affect detection, which otherwise may be identified as covariates that affect suitability. For example, an area where detection is less likely due to, say, dense vegetation, may be mistaken as less suitable due to that vegetation structure when in fact that may not be the case (or even the opposite may be true).
My question is, if the count variable were to instead be used as a detection/no-detection variable (so, a binary) would the probability of detection have less of an effect on the model (*when modeling relative suitability, not probability of occurrence)? i.e. if you didn't account detection probability, would using a binary response variable give you a less biased estimate of habitat suitability than if you were to use count data? And if so, why? It doesn't seem like probability of detection would change, or would be more homogeneous across the study area with this change, but it seems like the effects would be smaller in magnitude by not reinforcing differences in detection probability with multiple occurrences.
Also, I understand that it's not desirable to toss out all the other occurrences assuming you can calculate detection probability. I'm asking this in an attempt to better understand the possible differences in outcome between these two modeling approaches when using such data, as I've seen both methods in the literature, but have not seen this question specifically addressed. If you could reference any publications that may shed light on this, I'd be very appreciative.