Differences in Covariate Estimates: Logistic & Occupancy

[Bird Counter]

Hello Everyone,

I’ve been working on an exploratory analysis on a small data set in which I compared the betas (intercept + 1 covariate of interest) from logistic models and occupancy models using two survey methods with different detection rates. I did this for a number of species. I wanted to see how far apart the estimates generated by the different models for species with high and low detectability are. I am interested in some feedback on my approach and thinking on the subject.

The dataset was modest: n = 49 sites.
All of the sites were in the same kind of habitat so habitat-based differences in detectability are not expected.
The two survey methods covered ~same area per site, but one survey method was passive (point counts* 3 surveys/season) and one was intensive (area searches*2 surveys per season).
I also collected information on the breeding status of the species at all 49 sites.
Covariates were normalized prior to the analyses.

I then calculated the percent difference in the estimates between the beta values (β(0) + β(1)cov) generated with logistic regression and occupancy models:

((Occupancy – Logistic)/Logistic)*100

As expected, for species with high detectability (p > 0.77 (0.05) D = 0.99 over 3 surveys), the estimates of covariate effects generated by logistic and occupancy modeling were close (<5% difference). For species with low detectability, the estimates were quite different.

Model naïve psi p B(1) B1 SE B(0) B(0)+B(1)
PC_Logistic 0.33 NA 1.14 0.41 -1.02 0.12
Area_Logistic 0.37 NA 2.54 0.71 -1.11 1.43
*PC_p 0.33 0.21 (0.66) -- -- -- --
Area_p 0.37 0.68 (0.09) 3.66 1.36 -1.24 2.42
PC+Area_Logistic 0.43 NA 2.76 0.80 -0.71 2.05
PC+Area_p 0.43 0.46 (0.05) 2.99 0.85 -0.59 2.40

* This species is very poorly detected on point counts

In each model, the effect of the covariate B(1) was positive and significant (95% CI did not include 0) so the overall conclusions did not change.

When I compare the difference in the estimates using the formula above, I get a range of values (e.g., the difference between using modeling only the area search data using logistic models versus modeling area search data using occupancy modeling is 69%. In this case, the overall probability of detecting the species in 2 surveys was 0.90).

My first question: Does taking this approach make sense? I am looking for a way to talk about how the addition of a detectability component affects the estimated magnitude of covariate effects. The difference in estimates derived from the two survey methods is stark, but I’ll leave the reason for later.

I know Evan Cooch will be upgrading the site next week, but I'd appreciate any feedback in the mean time.

Thanks.

[darryl]

Hi Misty,
It seems like a reasonable way of going to demonstrate the difference for this particular dataset, but for a more general result you could think about trying to evaluate the bias in the effect size caused by imperfect detection analytically with a bit of algebra.
Cheers
Darryl

[Bird Counter]

Thanks for your reply, Darryl. I did this little analysis based on a conversation with a friend. I haven't had time or energy to think about it more deeply.

I'll touch base on this issue within the forum in the future.

Thanks again.

Misty