Overdispersion impact on precision

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Jamie McKaughan

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May 10, 2023, 8:00:08 AM5/10/23
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Dear all,

 

I have recently returned to a baboon density estimate analysis I did last year using CTDS and REM. In general the actual estimates are as expected, but the CTDS estimate in Survey 2 has significantly lower precision than that of Survey 1, or of REM in the same survey. I am trying to make sense of why this might be. Table of key figures below.

 

The number of sites at which baboons were detected between the two surveys were very different with Survey 1 catching them at 21/24 sites, with Survey 2 only 26/59, while the numbers were also more similar across the sites capturing them in S1, but a lot more varied in S2. My working theory is that the encounter rate variance is obviously the reason for the significantly higher imprecision of CTDS in S1, and that CTDS is more responsive to this overdispersion than REM, but I am unsure why exactly. My initial thinking was that the number of observations must cause greater variability in CTDS than REM, on account of REM only using first contacts, whereas baboons staying in front of CTs for long periods in CTDS will accumulate more observations with every passing snapshot interval/moment – something that would not occur with REM. Does this make sense as a possible reason for such a notable difference? Or is there another additional or alternative possibility that I have not thought of?

 

Obviously the group-living nature of chacma baboons combined with using CTs severely violates independence and creates greater overdispersion, so I have used QAIC, but I guess where the overdispersion is so severe the encounter rate variance will remain high regardless of whether the correct model was selected or not.

 

I also noted that for both surveys the CTDS estimate was higher than using REM, with effective detection angle smaller in both CTDS surveys than the REM survey, while detection distance was slightly smaller in REM too. These were calculated from the relative data sets, but I was thinking that perhaps these should both be consistent – and perhaps should come from the REM data as these would theoretically be the animals ‘triggering’ the camera, and thus those that would define the detection zone more accurately, while the CTDS data would have all observations at every snapshot, which would include many individuals that were not ‘effecting’ the detection zone. Is that sound thinking and justifiable? I had already used the same activity calculation using the contacts only because using all observations made very unrealistic activity results (i.e 100% or 3%).

Screenshot 2023-05-10 at 12.57.58.png

Many thanks in advance for your time to have a read of this!

Jamie

Eric Rexstad

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May 10, 2023, 8:36:59 AM5/10/23
to Jamie McKaughan, distance-sampling
Greetings Jamie.

I saw your recent paper in Ecological Solutions and Evidence using CTDS.  I see your concern regarding the CV of CTDS estimates in Survey 2 being 26. Before going down the road of overdispersion, can you describe how you arrived at that CV?  Was it produced analytically or via the bootstrap?

You are correct in your assessment that encounter rate variance is usually the major contributor to uncertainty in CTDS estimates. As a first approximation, the squared CV in the density is the sum of the squared CVs of a) the detection probability, b) encounter rate and for camera traps c) the activity multiplier. Would you be willing to pass along those three pieces of the puzzle (off list if you wish) so we can do a sense check of the CV S2 shown in your table.

From: distance...@googlegroups.com <distance...@googlegroups.com> on behalf of Jamie McKaughan <jamie.mc...@gmail.com>
Sent: 10 May 2023 13:00
To: distance-sampling <distance...@googlegroups.com>
Subject: [distance-sampling] Overdispersion impact on precision
 
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Jamie McKaughan

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May 29, 2023, 5:43:34 AM5/29/23
to distance-sampling
Hi all,

Eric and I discussed this further off the group, below is a summary.

The CV's I recorded were from bootstrapping. The analytical CV's were much more reasonable, but my initial analytical CV's were not including the activity CV as per the delta method. I removed the activity estimation from being included in the effort calculation and instead incorporated it later as a multiplier that would also enable me to include its CV in any precision estimation. The density CV did go up slightly as would be expected.

The differing density estimates and precision between CTDS and REM is most likely a result of the repeated data capture of the CTDS snapshot method compared to the REM use of only first contacts. The spikes in camera locations that occurred in data collection were considerably more pronounced in the CTDS data than the REM data, the latter of which would also only be using this data to estimated the detection zone, and so perhaps its CV plays a less pronounced role in REM CV overall given the other additional parameters it uses. When you then bootstrap the data, these disparities have the potential to be exacerbated given the random nature of bootstrap resampling.

I am hoping to try and simulate a comparison between solitary and group animals in both CTDS and REM. As and when I manage that I will try to remember to share results here!

Many thanks
Jamie
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