Polygon search: extremely wide CIs

[Granjon]

Hello,

I am running SECR models to estimate the number of chimpanzees in a population from opportunistically collected feacal samples in Uganda in an area of about 50km2. I am trying out different assumptions for D and g0, and while most models worked fine, I find myself with extremely large confidence intervals for g0~h2.

> Ngogo<-read.capthist('CaptXY full.txt', 'Perimeter.txt', fmt = 'XY', detector = 'polygon')
No errors found

My first, most basic model gives seemingly reasonable results:
>ngogo.full.ECM=secr.fit(Ngogo, trace=FALSE, buffer=5000, method='BFGS')
> predict(ngogo.full.ECM)
link estimate SE.estimate lcl ucl
D log 1.516138e-02 1.899798e-03 1.187119e-02 1.936349e-02
g0 log 2.602691e+00 3.010776e-01 2.076267e+00 3.262586e+00
sigma log 1.589340e+03 1.015496e+02 1.402443e+03 1.801143e+03


But my second models gives very surprising results:

> ngogo.full.TIRM=secr.fit(Ngogo, trace=FALSE, buffer=5000, model=g0~h2, method='BFGS')
> predict(ngogo.full.TIRM)
$`session = Ngogo, h2 = 1`
link estimate SE.estimate lcl ucl
D log 3.204532e-02 0.2385743 6.256999e-04 1.6412057
g0 log 2.884242e-01 681.5110558 1.273612e-04 653.1700477
sigma log 1.531781e+03 98.7854385 1.350079e+03 1737.9380833
pmix logit 6.774748e-01 0.5365195 1.678445e-02 0.9961459

$`session = Ngogo, h2 = 2`
link estimate SE.estimate lcl ucl
D log 3.204532e-02 0.2385743 6.256999e-04 1.6412057
g0 log 3.134584e+00 0.6275551 2.125386e+00 4.6229807
sigma log 1.531781e+03 98.7854385 1.350079e+03 1737.9380833
pmix logit 3.225252e-01 0.5365195 3.854093e-03 0.9832156


I do not have a lot of recaptures in my data file (most individuals were captured 1, 2 or 3 times, and up to 11 for one individual), but most models are working fine. I am especially concerned as I had run that same model=g0~h2 before I corrected a tiny mistake in the data, and the results were perfectly fine. These incredible estimates with g0~h2 happened only after a single line was corrected (one individual captured once ended up being the same as another already captured twice). If anything, that correction should have improved the estimate?

This makes me wonder whether there is not something more inherently wrong in my analysis. Similar things happen when I use sex as 'Sessions' in order to estimate the number of males and females.

Thanks for your help,
Celine

[murray.efford]

Hi Celine

Mixture models are fragile (sometimes the likelihood maximisation can get stuck on a local peak), and it's possible you have struck a numerical problem like that. Or there could be a bug or something else - hard to say.

If you don't want to go the whole hog (the slow profile likelihood check in the secr-finitemixtures pdf) I suggest first trying a different method (method = 'Nelder-Mead') and then trying specified starting values (start = model0 where model0 is the name of your original model fit, the one that worked, even if the data have changed).

Murray

[Granjon]

Hi Murray,

thank you for your reply. In my post I had forgotten to say that I had already tried the Nelder-Mead method, but the calculation had failed.

Using the previous fitted model as starting values did work, but to be honest I do not really understand what really happened. Also, it might be a silly question, but what starting values should I have used if I had not had another fitted model with wrong data to start with?

[murray.efford]

Hi
I'm sorry that I cannot add anything very useful. Finite mixture models simply are harder to fit than more simple models, and more prone to errors during fitting. There are also cases where they are not needed even if heterogenety is present, because heterogeneity in g0 and sigma can be compensatory. If you suspect something is going wrong, you always have the option of directly specifying different starting values (start = list(D = , g0 =, sigma =)).

It may also be that 'polygon' methods are less robust than an equivalent analysis in which the searched area is discretized as a set of pixels and each pixel is treated as a detector. I have not investigated this - it's just a suspicion. Discretizing the search area also avoids the constraint on the shape of the polygon (see http://www.otago.ac.nz/density/pdfs/secr-polygondetectors.pdf p6).

Murray

[Granjon]

Thank you very much for the additional information. The model also worked fine when I specified the starting values manually, and the results are pretty much the same, so I am relieved there was not some inherent issue with my data.

Best
Celine