Gear specific detection histories

[Kleinzb]

I am using PRESENCE to analyze some fisheries data. I used three gear types (separate occasions) at 41 independent sites. One of my primary interests it to explain which gear is most effective by using probabilities of detection. I am interested in minimizing parameters so as to make more room for covariates. To that end I would like to model each gear type individually while using an additional cumulative column (detection histories of all other gears) to explain occupancy and thus inform detection.
Here is an example:
Let's say I fished a big net, a small net, and a fishing pole on 3 different events totaling 9 different occasions in a single season. I want to model each gear individually, like this:
Fishing pole
E1 E2 E3 C
0 0 0 1
0 1 0 0
0 0 0 1
0 0 0 1
0 1 1 0
0 0 1 1
1 0 0 0
1 1 0 1

Where E1, E2, and E3 are each event sampled with a fishing pole and C is the cumulative detection histories of big nets and small nets. Instead of modeling all detection histories together, like this:

Fishing pole
FP1 FP2 FP3 BN1 BN2 BN3 SN1 SN2 SN3
0 0 0 1 0 0 0 1 1
0 1 0 0 0 1 1 1 0
0 0 0 1 1 0 1 0 0
0 0 0 1 0 0 0 1 0
0 1 1 0 0 1 0 0 1
0 0 1 1 0 0 0 1 0
1 0 0 0 0 1 0 1 1
1 1 0 1 0 1 1 0 0

Will I be violating any assumptions or otherwise do something incorrectly if I do this?