Adjustment terms

[PABLO PALENCIA MAYORDOMO]

Dear distance sampling list,

I would like to deep into the adjustem terms. If I'm right, adjustments provide flexibility to the detection function. But, what are the practical implications of adding more than one adjustment (argument "nadj" in "ds" function) in a given model? If we add 2 adjustments, it means that the function will have 2 flexibility points?

In my experience, using more than one adjustment could lead to overfitting issues. For instance, if you have a slight increase of observations at further distances, then a model with 2 adjustments can fit this not -constant- decrease in detected animals. this would lead to a model selected on the basis of AIC, but penalized by the "non-increasing" criteria (again, if I'm right, a basic property when selecting a distance sampling model is to select a nin-increasing function of distance from the point).

Thus, a general recommendation could be to include only 1 adjs term? Otherwise, when is recommended to include more than one adjs term?

Thanks a lot
Pablo

[Eric Rexstad]

Pablo

You are correct, additional adjustments provide additional flexibility in the detection function model being fitted to detection distances. This flexibility is useful when there are perhaps unmodelled sources of variation in detection probability. But there are situations where such flexibility can lead to overfitting. With data of the form with which you work (camera trap images), constituting a form of point transect sampling, detection function modelling can be particularly tricky.  Another potential challenge with flexible models is the lack of monotonicity (the bumps in the shape that you describe).

Recognise that the family of detection function models are used to fit models not only point transect data, but line transect data as well. There are line transect data sets for which models with multiple adjustment terms are suitable.

Have a look at the lecture on "choosing a detection function" on our workshop website

https://workshops.distancesampling.org/online-course/syllabus/Chapter1/

---

From: distance...@googlegroups.com <distance...@googlegroups.com> on behalf of PABLO PALENCIA MAYORDOMO <palencia...@gmail.com>
Sent: 03 November 2022 13:39
To: distance-sampling <distance...@googlegroups.com>
Subject: [distance-sampling] Adjustment terms

 

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[Len Thomas]

Adding to Eric's response:

I think you're working on camera trap data, Pablo. In that case, we have found
that the overdispersed nature of the distance data (caused by things like
getting lots of images of the same animal encounter) can create problems when
trying to fit high-parameter models such as those with lots of adjustment terms.
We have found that limiting the number of parameters to 3 seems to be a good
compromise between having flexible models and not trying to fit every lump and
bump. So, for the uniform we use up to 3 adjustment terms, for the half-normal
up to 2 adjustment terms (because the key function has 1 parameter) and for the
hazard rate up to 1 adjustment term (because the key function has 2 parameters).
This is illustrated in our Duiker example project

https://examples.distancesampling.org/Distance-cameratraps/camera-distill.html

(.Rmd file available from https://examples.distancesampling.org/). That example
also illustrates a QAIC-based approach to model selection.

I agree with you that keeping the monotonicity constraints on (the default) is
helpful -- we do not expect detectability to increase with increasing distance!
Having said that, the monotonicity constraint implementation is not perfect --
it just checks at 10 distances that g(r(x)-1) >= g(r(x)) where r(x) is the
distance at the xth check point, and x=2...10. So it's possible to get
"wobbles" between the check points. Having only a few adjustment terms helps
avoid this also.

Hope this is useful! Cheers, Len

On 03-Nov-22 2:00 PM, 'Eric Rexstad' via distance-sampling wrote:
> Pablo
>
> You are correct, additional adjustments provide additional flexibility in the
> detection function model being fitted to detection distances. This flexibility
> is useful when there are perhaps unmodelled sources of variation in detection
> probability. But there are situations where such flexibility can lead to
> overfitting. With data of the form with which you work (camera trap images),
> constituting a form of point transect sampling, detection function modelling can
> be particularly tricky.  Another potential challenge with flexible models is the
> lack of monotonicity (the bumps in the shape that you describe).
>
> Recognise that the family of detection function models are used to fit models
> not only point transect data, but line transect data as well. There are line
> transect data sets for which models with multiple adjustment terms are suitable.
>
> Have a look at the lecture on "choosing a detection function" on our workshop
> website
> https://workshops.distancesampling.org/online-course/syllabus/Chapter1/

> <https://workshops.distancesampling.org/online-course/syllabus/Chapter1/>
> --------------------------------------------------------------------------------
> *From:* distance...@googlegroups.com <distance...@googlegroups.com>

> on behalf of PABLO PALENCIA MAYORDOMO <palencia...@gmail.com>

> *Sent:* 03 November 2022 13:39
> *To:* distance-sampling <distance...@googlegroups.com>
> *Subject:* [distance-sampling] Adjustment terms

> Dear distance sampling list,
>
> I would like to deep into the adjustem terms. If I'm right, adjustments provide
> flexibility to the detection function. But, what are the practical implications
> of adding more than one adjustment (argument "nadj" in "ds" function) in a given
> model? If we add 2 adjustments, it means that the function will have 2
> flexibility points?
>
> In my experience, using more than one adjustment could lead to overfitting
> issues. For instance, if you have a slight increase of observations at further
> distances, then a model with 2 adjustments can fit this not -constant- decrease
> in detected animals. this would lead to a model selected on the basis of AIC,
> but penalized by the "non-increasing" criteria (again, if I'm right, a basic
> property when selecting a distance sampling model is to select a nin-increasing
> function of distance from the point).
>
> Thus, a general recommendation could be to include only 1 adjs term? Otherwise,
> when is recommended to include more than one adjs term?
>
> Thanks a lot
> Pablo
>
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>
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Len Thomas (he/him) len.t...@st-andrews.ac.uk lenthomas.org @len_thom
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and School of Mathematics and Statistics
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[PABLO PALENCIA MAYORDOMO]

Hi Eric and Len,

Thank a lot for your response. I got it :)

Actually, I already saw the lecture you mentioned (but I forgot to attach the screenshot to my post). By the way, here it is (just in case that helps the rest of the group members to understand our discussion).

Yes, you are right. I was thinking of camera trap data in which bumps could be habitual, as you also mentioned

Thanks a lot

Pablo