I'm performing occupancy modeling (wildlife science) to determine the difference between a change in control vs. treatment sites over time (before vs. after). I first calculated the occupancy odds from the Beta value, then calculate the odds ratio from this occupancy odds (control site after treatment/control site before treatment, and treatment site after treatment/treatment site before treatment). I want to report the confidence interval as well (and standard error would also be great). I think this should be a linear combination, but my numbers are coming out slightly off.
First I calculate the odds ratio from the beta estimate for psi (occupancy probability):
- Before value: psi/(1-psi) = 0.6122/0.3878 = 1.58
- After value: psi/(1-psi) = 0.6714/0.3286 = 2.04
- Odds ratio: 2.04/1.58 = 1.29
Here's an example of how I calculated CI limits:
- Lower CI limit of control site after treatment - Lower CI limit of control site before treatment: -0.2972 - (-0.3771) = 0.0798
- exp(0.0798) = 1.08.
- This should mean that the lower CI limit is 1.08.
- Through the same calculation, I get that the Upper CI limit is 1.55.
However, when I check this by calculating the standard error, also using the linear combination, and then subtract 0.5*SE from the odds ratio, the number doesn't match:
- Upper CI limit - Lower CI limit = 1.55-1.08 = 0.23.
- SE = 0.23/2 = 0.115
- Odds ratio - SE = 1.06
- Likewise, the odds ratio + SE = 1.53. These figures are close but don't match the CI limits I calculated above.
Any insights as to why these values don't match? Or tips on mistakes I don't realize I'm making? Thanks!