Multi-method: Model theta and psi with covariate separately?

questions concerning analysis/theory using program PRESENCE

Multi-method: Model theta and psi with covariate separately?

Postby BrynEvans » Wed Oct 11, 2017 1:25 pm

Hello all,

I am hoping for some clarity on the meaning behind 3 different scenarios for modeling theta and/or psi in a multi-method model suite in Presence. I would like to be able to understand the influence of a habitat parameter on both the local availability and the overall occupancy. When incorporating this habitat parameter in Presence, it seems to me that there are three options:

1)
______a1 a2 a3
Psi____1 0 HABITAT
theta1 0 1 HABITAT
theta2 0 1 HABITAT
theta3 0 1 HABITAT
...

2)
Psi____1 0 HABITAT
theta1 0 1 0
theta2 0 1 0
theta3 0 1 0
...

3)
Psi____1 0 0
theta1 0 1 HABITAT
theta2 0 1 HABITAT
theta3 0 1 HABITAT
...

The model output for both 1 and 2 above give the intercept estimates for Psi and theta1, and a slope for Psi.HABITAT, but the values are markedly different. Only option 3 provides the slope for theta1.HABITAT. I understand that theta is conditional on the overall occupancy status, but would like to be very clear about if/how to interpret the role of covariates separately.

One last note, the default notation for naming models is “psi,theta(), p()”, but in a detailed example from a USGS Patuxent workshop (on Nutria in Maryland) models are named “psi(),theta(),p()”. Is there substantial difference in the meaning? Is there a way to indicate the conditional nature of theta of psi if modeling only one with a covariate at a time?

Thank you!
-Bryn
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Re: Multi-method: Model theta and psi with covariate separat

Postby jhines » Wed Oct 11, 2017 2:32 pm

In the 1st model, overall occupancy (psi) and local availability (theta) are different from each other, but the effect of habitat is the same. So, "better" values of habitat give higher probabilities of occupancy and higher probabilities of local availability, but still different from each other. If you imagine a plot of habitat versus occupancy (psi), it might be a line with a positive slope. Plotting local availability on the same graph would be another line with a positive slope, parallel to the 1st line, but different. The difference would be the difference between the 1st 2 beta parameters.

In the 2nd model, occupancy depends on habitat, just like the 1st model, but local availability does not (local availability is the same for all habitat types. If you graphed these estimates, the occupancy line might have a positive slope, and the availability line would be a horizontal line (same value for all habitat values).

In the 3rd model, occupancy is the same for all habitat values, but local availability varies with habitat. A graph of these two lines would be a horizontal line for occupancy, and a line with a slope for local availability.

Of course, the logit link function will bend the lines so they don't surpass zero or one, and the slopes could be negative if the species doesn't prefer 'good' habitat.
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Re: Multi-method: Model theta and psi with covariate separat

Postby BrynEvans » Sun Oct 15, 2017 2:22 pm

THANK YOU so much for the speedy and thorough reply! Very good to know I can evaluate and interpret all three scenarios. I've spent a bit more time looking at my preliminary output, and just have a small follow up:

Is it correct to think of the slope value given for the model psi(HABITAT), theta(HABITAT), p(....) as the average influence of habitat on the two scales? This seems like a valid conclusion from the numbers, but if there was arithmetic I was missing I didn't want to assume. I'm suspicious that in cases where modeling only psi or only theta indicate very different influences I have some problems with covariates well outside of the model itself, though I'll be carrying on investigating if there might actually be reasonable conclusions where local availability and overall occupancy respond differently!

Again, thank you, I'll continue mulling it over off the air.

Sincerely,
Bryn
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Re: Multi-method: Model theta and psi with covariate separat

Postby darryl » Sun Oct 15, 2017 3:24 pm

Hi Bryn
It's going to be some combination of the values that you get from the other models, but not necessarily an average. Strictly speaking, it's simply the value of the effect if the effect is the same for both occupancy and availability. So the more pertinent question is whether it's biologically reasonable for the effect of habitat (in the case) to be exactly the same on these two processes.

Note that there is also a fourth option you didn't mention, where habitat is included for both, but with different effects:

Psi 1 HABITAT 0 0
theta1 0 0 1 HABITAT
theta2 0 0 1 HABITAT
theta3 0 0 1 HABITAT

Cheers
Darryl
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Re: Multi-method: Model theta and psi with covariate separat

Postby BrynEvans » Mon Oct 16, 2017 4:28 pm

Thank you both so much!
I am excited to forge ahead with a better understanding of the options, very much appreciate your time.
Take care,
Bryn
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