th0pi parameter in the Hines correlated detection model

questions concerning analysis/theory using program PRESENCE

th0pi parameter in the Hines correlated detection model

Postby lstarcevich » Fri Mar 12, 2021 2:34 pm

Hi - I'm working with the multi-season correlated detection model in PRESENCE. The Hines et al. (2014) manuscript states that:

pi = Pr(species local presence in unsurveyed replicate 0 | sample unit i occupied.

The PRESENCE output contains a derived parameter defined as:

th0(1) = th0pi*th0 + (1-th0pi)*th1 = Pr(1st segment is used),

which I assume is conditional only on site occupancy at that time period.

Is th0pi the probability that a site was available in both segment 0 and 1 given occupancy, or something else?

Thank you.
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Re: th0pi parameter in the Hines correlated detection model

Postby jhines » Fri Mar 12, 2021 11:43 pm

th0pi is the proportion of sites where the "previous" site is locally occupied (used). It is a "nuisance" parameter which is not of any use except to get the local occupancy of the 1st site.
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Re: th0pi parameter in the Hines correlated detection model

Postby lstarcevich » Thu Mar 18, 2021 1:45 am

Thank you for your response. Is th0pi used in a different parameterization from the one using the equilibirum of theta1 and theta0, theta0/ (theta0 + (1-theta1))? In other words, are these two valid but separate parameterizations of the initial segment probability of local occupancy?

--- theta_mean[1] <- th0pi*theta1 + (1-th0pi)*theta0
vs
--- theta_mean[1] <- theta0/ (theta0 + (1-theta1))

Then the Hines et al (2014) parameterization simply models the initial segment probability as pi?

--- theta_mean[1] <- pi

Thanks again.
lstarcevich
 
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Re: th0pi parameter in the Hines correlated detection model

Postby jhines » Thu Mar 18, 2021 8:06 pm

It's the same parameterization, with a constraint. In one case, we estimate the proportion of initial segments where the previous segment is occupied as th0pi. In the other case, we don't estimate th0pi, but fix it to the equilibrium value (theta0/(theta0+1-theta1)), which was used in the paper (and called pi). It is a "nuisance" parameter which only use is to allow a slightly better model fit when estimated.
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Re: th0pi parameter in the Hines correlated detection model

Postby lstarcevich » Fri Mar 19, 2021 1:49 pm

Thanks so much for the clarification.
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