Beta interpretation

[Kleinzb]

]I was recently asked by a reviewer to provide beta estimates from my top models from my candidate suite of models. I am inclined to transform my beta estimates from the log-odds scale to the odds scale and then interpret them as I would any logistic regression estimate. However, as a graduate student, I am forever convinced I am doing something wrong...Any insight would be appreciated. Here is some background.

I sampled a single species of fish at 41 sites with three gear types. I was primarily interested in the probability of detection because I wanted to use it as a metric for comparing the effectiveness of each gear. I used a single-species, single-season model to limit the number of parameters I needed to estimate. I first modeled occupancy as a constant and with a suite of habitat covariates. I used AIC to select the top model and then used that model for the rest of the modeling exercise. I then modeled detectability as a constant and with gear and habitat covariates. I again used AIC to select the "best" models (Delta AIC < 2). I have compiled a table of my beta estimates from my top models which are presented on the odds scale.

Again, any help would be greatly appreciated. Thanks and farewell.

Model Covariates Estimate Confidence limits
Lower Upper
[i]Ψ (BankTalus), p ̂ (gear, VelocityMean)[/i]
Ψ 1.77548 0.56759 5.55391
Ψ (BankTalus) 7290.15400 0.00316 16831080000.00000
HN6.4 (VelocityMean) 0.00021 0.00000 0.03957
HN19 (VelocityMean) 5.68828 0.00168 19237.77000
EF (VelocityMean) 197.49160 0.34181 114107.50000
HN6.4 23.40882 2.82166 194.20220
HN19 0.11362 0.00505 2.55765
EF 0.09226 0.00665 1.27955
[i]Ψ (BankTalus), p ̂ (gear, Proximity)[/i]
Ψ 1.51323 0.55135 4.15325
Ψ (BankTalus) 85.39359 0.13704 53209.60000
HN6.4 (Proximity) 0.00816 0.00055 0.12168
HN19 (Proximity) 26.12976 0.38649 1766.58000
EF (Proximity) 2554.99600 94.25436 69259.46000
HN6.4 5775.35500 41.16451 810278.70000
HN19 3.67750 0.01006 1343.76100
EF 0.00221 0.00002 0.23253

I cannot get the table to look good on the post, but the actual values should not change the interpretation. Following each habitat covariate or gear type are the parameter estimates, and the lower and upper confidence limits. Thanks again.