Psi estimates of 1.

[hbooker]

Hi everyone,
I am very new to PRESENCE and am attempting to run single-season, single-species models with constant p and variable p for felid species with low detections.The problem is, I keep getting psi estimates of 1. I have 4 transects and 5 sampling occasions/transect. For jaguars, the first time I ran the analysis the transects were divided into 50m segments so I had 160 survey sites and only 5 detections. For the constant p model I received a psi estimate of 1, a naive psi of 0.03 and a p of 0.0062. The second time I ran it, I compressed the transect segments so that I had a total of 20 sites with 5 detections, a psi estimate of 0.4471, naive psi of 0.2 and a p of 0.1118. I thought that I had figured out the issue but when I ran the analysis for puma with the compressed sites, I again received a psi estimate of 1. When I did not compress the sites for puma I had 160 survey sites with 10 detections, psi estimate of 0.2372, naive psi of 0.0563, and a p of 0.0527. I am now completely confused because either way I am receiving psi estimates of 1 with super small SE and CIs of almost 0 - 1.0. Does anyone have any ideas of what I am doing wrong or are the detections just too low to produce reliable occupancy estimates?
Thank you,
Holly

[jhines]

With the single-season, constant detection model, without covariates, there isn't much that you can do wrong. If you have 5 detections from 160 sites, the naive occupancy of .03 makes sense. Obviously, we know that our occupancy estimate must be at least that big. Unfortunately, information about detection probability only comes from the 5 sites with detections (assuming the 5 detections were all at different sites). This makes the estimation of occupancy problematic as the likelihood function gives very similar results when occupancy is high and detection very low, versus low occupancy and moderately low detection. This is why the SE's are so big and conf. intervals so large.

Sometimes pooling the surveys and/or sites can help, but that may redefine what the occupancy and detection parameters represent. A possible solution that I often recommend is to combine data of similar species. They don't have to be physically similar, but if they have similar probability of detection (ie., very low), perhaps the data can be combined with a covariate to indicate species. Then, it would be possible to share the detection parameter among the 2 species, while estimating separate occupancy parameters.



Jim

[darryl]

Hi Holly,
I'm not trying to be flippant about it, but these methods are statistical and not magical. Like Jim says, when you've got few detections there's not a lot of information there to disentangle occupancy and detection. You always need a certain amount of information for any stats method to work properly. Occupancy estimates can tend to be estimated as very close to 1 when you've got few detections. A key consideration is how the few detections are grouped across different sampling units. If there's only a maximum of 1 detection per site, thats when the estimates tend to get a bit flaky, but if you've >1 detection per unit (at units with detections) then things can work better. Massaging your data in different ways for different species may alter how those few detections are spread across your units which may be why things seemed to work better for jaguars but not pumas.

Cheers
Darryl

[hbooker]

Hi Jim and Darryl,
Thank you very much for the suggestions. I will work with my data as you've suggested and see where that gets me.
Holly

[hbooker]

Hello again,
I wanted to get your opinions on what I have done and if it is a valid method of analysis. I combined data for jaguar and puma in one model and then jaguarundi and ocelot together in another model, with the species itself being a covariate. These were the results.

constant p jaguarundi+ocelot (psi)0.7009 (SE)0.6633 (p)0.0303 (psi CI)0.0047-0.9991
variable p jaguarundi+ocelot (psi) 0.6737 (SE)0.6348 (p)variable (psi CI)0.0071-0.9983
constant p jaguar+puma (psi) 0.5434 (SE)0.5098 (p) 0.0345 (psi CI) 0.0208-0.9852
variable p jaguar+puma (psi)0.5027 (SE)0.4674 (p)variable (psi CI) 0.0253-0.9753

The CI's were so large so I then I used the p estimate from the combined species constant p models above and entered it into individual models for each species as a fixed p ie. jaguar fixed p of 0.0345, ocelot fixed p of 0.0303. These were the results.

constant, fixed p jaguarundi (psi) 0.526 (SE)0.146 (p)0.0303 (psi CI)0.2604-0.7776
constant, fixed p ocelot (psi)0.3068 (SE)0.1134 (p)0.0303 (psi CI)0.1347-0.5573
constant, fixed p jaguar (psi)0.1941 (SE)0.0854 (p)0.0345 (psi CI)0.0763-0.4126
constant, fixed p puma (psi)0.3494 (SE)0.1131 (p)0.0345 (psi CI)0.1684-0.5875

These results seem to make more sense; however, I am not sure if this is a valid way of running this analysis.
Thank you again,
Holly

[jhines]

Entering a fixed value of p will cause the variance of psi to be underestimated, especially if the SE(p) is large, or p is small. I suggest combining all 4 species with species indicator covariates, then run models where all species have the same psi and p. Then, run models where psi and/or p is different for each species. If you had a pre-conceived thought that jaguarundi and ocelot had similar psi and/or p, you could add models where those two species had the same psi and/or p, but different from jaguar and puma. I suspect that AIC results will show that a very simple model is 'best' since the detections are so sparse. Hopefully, the top model will have lower SE's (and tighter CI's) than the results you listed.

[hbooker]

Thank you again Jim for the recommendations. I will try those models out and see how it goes.
Holly

[hbooker]

Sorry...it is me again. I don't know anyone who has used PRESENCE so I am lost. I wanted to confirm that once I have combined all the detection histories for felids together (jaguar, puma, jaguarundi, and ocelot) that I am adding species covariates correctly, as I still am getting psi estimates of 1. I tried it 2 ways. The first was species as a site covariate with 0 detections, multiple species detected, jaguar,puma, jaguarundi, and ocelot all as covariates. I ran psi(.)p(spec), psi(.)p(.), psi(spec)p(spec), and psi(spec)p(.). Psi estimates were either 1 or 0 or 1 or 0.0104 with CI's of 0-1 and ridiculous SEs.

ie. Matrix 2: rows=6, cols=8
-,b1,b2,b3,b4,b5,b6,b7,
P[1] 1 Spec0 SpecM SpecJ SpecP SpecJI SpecOc
P[2] 1 Spec0 SpecM SpecJ SpecP SpecJI SpecOc
P[3] 1 Spec0 SpecM SpecJ SpecP SpecJI SpecOc
P[4] 1 Spec0 SpecM SpecJ SpecP SpecJI SpecOc
P[5] 1 Spec0 SpecM SpecJ SpecP SpecJI SpecOc

The second way I tried was to make each species a sampling covariate with their individual detection histories as the covariate. Again I got psi of 1.
i.e. ,b1 1, b2jag, b3puma, b4jaguarundi, b5ocelot

Should I just create 1 covariate as a site covariate and identify each species as a 1, 2, 3, 4, multiple species detected as 5, and no detection 6?

Thank you very much.
Holly

[jhines]

Hi Holly,
When I run occupancy models (or any sort of models), I usually start with the simplest model, then work my way up to more complicated models. If you cannot get reasonable estimates from the psi(.),p(.) model, then I suspect that you have very sparse data for all 4 species, and there isn’t much hope for getting more complicated models to run. If you would like to send me a copy of your data off-list, I would be happy to see if there is anything I can think of to get it to work.

Your second way of making species a sampling covariate, instead of a site covariate, should produce the exact same output.

The idea of creating a single covariate with a number for each species, and multiple species=5, and no detection=6 would imply that you want to build a model where there is an order to the species (ie., p(species1)<p(species2)<p(species3)<p(species4)<p(multiple species)<p(no detections), or p(species1)>p(species2)>p(species3)>p(species4)>p(multiple species)>p(no detections)). I can’t think of any justification for this model. Even if you had a hypothesis that there is an order of the detection probabilities among the 4 species, the difference between detection probabilities among the species would have to be nearly constant, and you would not want to include the multiple species(5) or no detections (6). I don’t think I’ve ever heard of anyone who has used such a model.

The design matrix in your post has a couple of problems. First, it is overparameterized. To estimate a detection probability for each of the 4 species, there should be 4 columns. You can either estimate an intercept and 3 species effect parameters(a), or 4 species intercepts (b).

Code: Select all

(a)
ie. Matrix 2: rows=6, cols=5
-,b1,b2,b3,b4,b5,
P[1] 1 SpecJ SpecP SpecJI SpecOc
P[2] 1 SpecJ SpecP SpecJI SpecOc
P[3] 1 SpecJ SpecP SpecJI SpecOc
P[4] 1 SpecJ SpecP SpecJI SpecOc
P[5] 1 SpecJ SpecP SpecJI SpecOc
(b)
ie. Matrix 2: rows=6, cols=5
-,b1,b2,b3,b4,b5,
P[1] SpecJ SpecP SpecJI SpecOc
P[2] SpecJ SpecP SpecJI SpecOc
P[3] SpecJ SpecP SpecJI SpecOc
P[4] SpecJ SpecP SpecJI SpecOc
P[5] SpecJ SpecP SpecJI SpecOc

Second, you cannot estimate psi or p for sites with no detections, since it is impossible to determine if there are no detections due to non-occupancy, or occupancy with no detections. The model needs to assume detection for sites with no detections is the same as sites with detections. Including a covariate (Spec0) will cause the model to try to estimate a separate p for those sites.

Also, using ‘SpecM’ as a covariate will cause the model to try to estimate different detection probabilities for sites with multiple species detected versus sites with only 1 species detected. If you were trying to estimate a different detection probability for sites with multiple species present vs only one species present, it is not possible with this model, since there is no way to know for sure from the data whether one or multiple species are present at a site. Using this covariate in conjunction with the species covariates will add complexity to the model, without obtaining anything useful to estimate.
Jim