multi method - high theta SE values

questions concerning analysis/theory using program PRESENCE

multi method - high theta SE values

Postby KerryK » Tue Sep 16, 2014 8:46 am

Hello again

I'm still in the early learning process of PRESENCE but I would appreciate some advice before I spend too much more time racking my brain trying to get this to work with my data. I would like to compare the detectability of two different methods, I have 285 sites, 4 surveys, method 1 is more much effective at detecting the species than method 2 so as a result some of the columns for the method 2 only have a few "1"'s and lots of "0"'s. I've been trying to run the multi method analysis on my data but despite my best efforts I keep getting numerical convergence although its always greater than the recommended minimum value in the FAQ's so not necessarily a huge problem, but in addition, one of my theta values and SE's are ridiculously high.... for example....

A4 theta3 : 25.540412 126178.322551
A5 theta4 : 0.287754 0.787783

If I run the data for the two methods separately using the single season analysis, I don't have this issue with numerical convergence. I am a little confused as to how the theta should be interpreted in the multi method analysis as looking at previous posts it seems that what is in the help file does not appear to be entirely accurate. So I have a few questions:

1) Should I just analysis the data separately and discuss the differences between the two methods without actually comparing them directly. Are there any issues with this?

2) Can I continue to model the data using the multi-method with this large theta value, and if so, how can I justify doing this?

3) Can I adjust the theta parameters at all to overcome this issue?

Thanks for any advice

Kerry
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Re: multi method - high theta SE values

Postby jhines » Tue Sep 16, 2014 10:50 am

Hi,

In the multi-method model, you can estimate survey-specific p's or theta's, but not both. One of them needs to be constrained to be constant in order for the model to be identifiable.

The multi-method model allows you to estimate 'local-presence', while the original single-season model does not. So, local-presence is combined with detection in the single-season model. You can run the single-season model on each method and test the difference between detection probabilties using a z-statistic (eg., as in program CONTRAST), but a better test would be to analyze both methods in a single-season model, with method as a covariate for p. Then, use AIC to test a model where both methods have the same p, versus a model where each method has a different p. Again, you'd be testing if the product of local occupancy and detection is different between the two methods.

The best case would be to use the multi-method model to test between methods. Then, you're really comparing the actual detection probabilities between the two methods. However, if the data are so poor that you can't get reasonable estimates with this model, then it simply may not be possible to tease apart detection from local-occupancy/detection. In that case, you could do the test described above (which would be equivalent to fixing the theta's to 1.0 in the multi-method model).

If you've constrained the p's to be constant over surveys, then the multi-method model should be able to estimate survey-specific theta's. A large beta estimate for theta3 only means that the actual theta3 parameter is very close to 1.0 (local-occupancy in survey 3 is 100%, or no sites are impossible to detect the species). That doesn't seem like a problem, unless you have some knowledge about the survey that indicates it shouldn't be that high.

If you'd like to estimate survey-specific p's, then you need to constrain the theta's to be constant among surveys (single column of 1's in the design matrix).

Jim
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Re: multi method - high theta SE values

Postby KerryK » Wed Sep 17, 2014 8:35 am

Dear Jim

Thanks so much for your comprehensive reply. It was really helpful. I just quickly ran the model constraining theta as you suggested and it seemed to have resolved the numerical convergence issue as well.

Thanks very much.

Best

Kerry
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Re: multi method - high theta SE values

Postby mdyson » Fri May 15, 2020 12:20 pm

Hi Jim,

I am developing multiscale models (to account for multiple cameras/site) for multiple different species and dealing with some large coefficient SEs for psi and theta for some species (SE >|100|). Almost all the cases for inflated thetas are for species that have low numbers of detections, so I suspect that has something to do with it (overfitting/boundary issue).

In the case where psi had a large SE, I have the species in question at all sites, so I fixed the parameter to 1 and am ignoring the SE estimate.

I am mostly interested in interpreting p for my models under the assumption that p is an index for activity or abundance at my sites (i.e., species that are more active or abundant will likely have a higher detection probability). Therefore, in developing my models, I have fit p first (using psi(.), theta(.)) and then proceeded to fit psi (with best p model), while leaving theta as an intercept only model to account for dependence between cameras at sites.

The values for p I am getting across species all make sense and have reasonable SEs and psi estimates are all also reasonable. However, for two species, I get theta estimates with very large SEs. Looking at the raw data for those species, there are very few times when the species is detected at a site on more than one camera (i.e., nearly all detections are at a single station at the site). Would it be reasonable to interpret the inflated theta estimates here to reflect this data separation and just ignore the inflated SEs? Alternatively, does this suggest that for these species, I could fit models at the station level without violating the independence assumption (i.e., not use multiscale)? Should I fix the theta parameter to 0 for these species?

I am hoping I am on the right track with this approach and interpretation, but if not, hopefully, someone might steer me in the correct direction. Thanks in advance for the feedback.

Matt
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