Co-occurrence models - independent detection

[zjfarris]

I have looked everywhere I can think of and have not found an answer to this question. Hopefully someone can help here.
When running co-occurrence (interaction) occupancy models MacKenzie et al. (2004) demonstrate that to test for independence in co-occurrence you set up two models (1. gamma or SIF is estimated and 2. SIF is set to 1). If delta AIC is >2.0 then they are independent.

However, I am interested in looking at co-detection (does the presence/detection of A impact detection of B, such that rB < pB). This is similar to what Bailey et al. 2009 did with their analysis.
To determine if rB < pB do I need to assess independence in a similiar fashion to co-occurrence such that I run and compare two models: 1. Delta or the Detection interaction factor is estimated and 2. Delta is set to 1.0?

I hope this makes sense. I am happy to try and clarify if needed.
Thanks in advance for any input you might be able to offer.