Psi estimate < naive Psi?

questions concerning analysis/theory using program PRESENCE

Psi estimate < naive Psi?

Postby Kate » Tue Nov 08, 2011 4:32 pm

Hello,
I am a new PRESENCE user and apologize in advance if my elementary question is below the level usually seen in this forum. I have 3 years of data with 3 surveys/year and would like to use multi-season models to estimate Psi and P for several bird species (without using covariates at this time). For one species, the model estimates a Psi value (0.134) that is less than the naive Psi value (0.225). Does this make sense or does it mean that there may be a problem with my dataset? (I feel fairly confident that the dataset is correct, and less confident in my ability to interpret results.)
Thank you for your help,
Kate
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Re: Psi estimate < naive Psi?

Postby darryl » Tue Nov 08, 2011 4:43 pm

Hi Kate,
Ignore the naive psi value that's reported with the multi-season model, I think Jim Hines has included it there by accident. The value that is being reported is the fraction of sites were the species was EVER detected (ie over all 3 years in your case), where as the estimated psi applies to only the first year.

Cheers
Darryl
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Re: Psi estimate < naive Psi?

Postby Kate » Tue Nov 08, 2011 5:11 pm

Thank you for your help!!
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Re: Psi estimate < naive Psi?

Postby Gavin M Jones » Sat Aug 25, 2018 2:55 pm

Apologies for resurrecting a 7-year-old post, but the subject/topic is spot-on.

I am using a single-species, multi-season occupancy model with detection/non-detection data from 74 sites/25 years. Some sites were surveyed all 25 years, a few sites were surveyed as few as 5 years, but most sites were surveyed between 15-20 years. I want to structure a model with a fixed effect for 'site' so that in essence the model will estimate the proportion of years each site was occupied, corrected for detection probability. To do this I'm using an indicator variable for each site and structuring the design matrix to estimate one beta per site that is constant across years.

I started by using a simple model structure psi(site), gamma(.), p(.)

The model produced a real estimate for gamma = 0.26 and p = 0.76. Most estimates for the 'site' fixed effect for psi were reasonable, but I noticed that in about 1/3 of cases the estimated psi was lower than naive psi. I didn't think this was possible. Below I've pasted naive and estimated psi for the first 15 sites, as an example, and I bolded cases of interest:

naïve estimate
1.000 1.000
0.360 0.395
0.619 0.559
0.905 0.847
0.591 0.796
0.720 0.841
1.000 1.000
0.667 0.468
0.400 0.517
1.000 1.000
0.786 0.644
0.563 0.366
1.000 1.000
1.000 1.000
0.429 0.453

Does anyone have any ideas as to why/how this could occur? I'm a bit puzzled.

Thank you,
Gavin
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Re: Psi estimate < naive Psi?

Postby jhines » Sat Aug 25, 2018 7:55 pm

Interesting question, but how did you run that model in Presence? To have a different initial occupancy for each site, you would need 74 covariates. The occupancy estimates from Presence are the probabilities of each site being occupied each season. To get the estimated proportion of years of occupancy per site, I think you could just add the probabilities of occupancy for each site over all years.

You're right that naive occupancy should always be less than estimated occupancy. The results suggest that something is wrong with the model, either how it is specified, or a data-bounds problem. With the psi(t)gamma(t) parameterization, problems sometimes arise in the optimization when the computation of epsilon results in a value which is > 1.0.

If you send me your most recent backup zipfile in your project folder, I'd be happy to take a look.

Cheers,

Jim
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Re: Psi estimate < naive Psi?

Postby Gavin M Jones » Mon Aug 27, 2018 10:51 am

Hi Jim,

Thanks for your reply and your kind offer to help out. I sent you the backup zipfile via email.

You are correct that I used 74 covariates - a different intercept for each site, but I constrained Psi to be constant through time for each site. My thinking was this would behave like a 'dot' model for each individual site. But it sounds like I've made some type of error in either model structure or interpretation. I look forward to your thoughts!

Thank you,
-Gavin
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Re: Psi estimate < naive Psi?

Postby jhines » Mon Aug 27, 2018 1:33 pm

Gavin,

Thanks for sending the data. The naive estimates don't make sense because the
multi-season model estimates yearly occupancy where occupancy in year t+1
depends on occupancy in year t. You have occupancy different for each site and
constant over years, but extinction is constant among all sites and years, so
the occupancy estimate for each site is affected by the extinction and
colonization parameters.

To obtain the quantity you're interested in (proportion of years occupied), I
think you need to either run a model where colonization equals 1 - extinction,
or re-structure the data where you treat each site/year combination as a
different site (row in detection history matrix) and run a single-season model
with site as a covariate.

If you run the colonization=1 - extinction model, you'll need to check the 4th
parameterization option in the run window and you'll see that the 1st design
matrix contains psi and all gamma's. Before doing that, you can copy the
design matrix from the model you ran by retrieving the previous model, click
on the 1st cell in the occupancy design matrix, then right-click and select
"Copy". Then paste it to Excel, then paste all but the 1st column back into
the design matrix for psi/gamma. You should end up with a design matrix like this:

-,a1,a2,a3,a4,a5,a6,a7,a8,
psi1 C1 C2 C3 C4 C5 C6 C7 C8 ... C74
gam(1) C1 C2 C3 C4 C5 C6 C7 C8 ... C74
gam(2) C1 C2 C3 C4 C5 C6 C7 C8 ... C74
gam(3) C1 C2 C3 C4 C5 C6 C7 C8 ... C74
gam(4) C1 C2 C3 C4 C5 C6 C7 C8 ... C74
gam(5) C1 C2 C3 C4 C5 C6 C7 C8 ... C74
gam(6) C1 C2 C3 C4 C5 C6 C7 C8 ... C74
:
:

Cheers,

Jim
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Re: Psi estimate < naive Psi?

Postby Gavin M Jones » Mon Aug 27, 2018 3:41 pm

Hi Jim,

Your suggestion to use the [gamma = 1 - epsilon] parameterization worked perfectly. This model produced output where estimated occupancy is always higher than naive occupancy (in terms of the proportion of years that each site is occupied). Here are the same 15 sites as before:

naïve estimate
1.000 1.000
0.360 0.363
0.619 0.626
0.905 0.908
0.591 0.592
0.720 0.724
1.000 1.000
0.667 0.686
0.400 0.409
1.000 1.000
0.786 0.796
0.563 0.564
1.000 1.000
1.000 1.000
0.429 0.443

Thank you so much for your help.
-Gavin
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