vastly different density estimates from secr and oSCR

[Rahel Sollmann]

Hi all,

I am helping someone analyze camera trap data with a multi-session SCR model. Initially, I used oSCR for the analysis but I have now re-analyzed the data with secr and am getting density estimates an order of magnitude lower.

I am taking into account the different spatial resolutions of the two packages and fitting structurally the same model to the same data. It's a 'vanilla' model: Euclidean distance, no telemetry data, Poisson observation model... 

I have more experience with secr than oSCR (the secr estimates are also much more in line with previous analyses of subsets of the same data), so am assuming I am doing something wrong in the oSCR analysis. But I have been scouring the data and code and cannot find my mistake.

I have attached an Rmarkdown report showing data comparison and model fitting for the two packages. This is only for a single-session subset of the data, to speed up computations, but the problem persists when analyzing all sessions. The data aren't mine to share publicly, but I would be happy to share the data subset and script used for the report off-list if it helps figuring out what is going wrong.

Thanks in advance!

Best,

Rahel

[Jeffrey Royle]

hi Rahel,

 This is interesting. I'm curious what is the area of the state-space and does the implied population size make more sense for one or the other?

 from what I can tell the other model parameters are more or less consistent, right?

 regards

andy

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[Jeffrey Royle]

If my interpretation is correct, the estimated sex probability parameter is quite off

 -3.56 for oSCR and -1.37 for SECR. 

That's peculiar.

[Rahel Sollmann]

Hi Andy,

it's one of those study areas where the trap array really spans the entirety of the population (a national park) and the buffer is habitat that animals use to some degree (so you can't really remove it from S) but you'd expect a much lower density. But if you calculate abundance for the area of the trap array based on the two density estimates, the secr one is quite low (apprx 1200km2 *0.3/100km for 3.6 animals) whereas the oSCR one is absurdly high (9/100km2 for >100 animals).

And you're right, even though the detection parameters look good, the sex ratio is off as well.

Best

Rahel

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[Chris Sutherland]

What is the sex ratio of the observed individuals?

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[Jeffrey Royle]

it's 50/50 I think:

covariates(dat.secr)[ord,] ## [1] M M F F M F F M M F ## Levels: F M dat.oSCR$indCovs[[1]]$sex ## [1] 1 1 0 0 1 0 0 1 1 0

I don't like the sex ratio parameter that oSCR is spitting out which seems very low.  But the capture probabilities of the sexes are vastly different too , and with a 50/50 observed sex ratio I'm thinking oSCR is probably finding a bad MLE.

Rahel: would be cool if you could re-run oSCR but use the SECR estimates as starting values.....

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[Rahel Sollmann]

I tried it with the secr starting value for density but yes, I can re-run using all secr estimates as starting values. Should have results in about 20 mins. More soon.

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[Rahel Sollmann]

Nope... here are the estimates from the model using secr mle as starting values

       parameters       mle    std.er
1  p0.(Intercept) -7.409839 0.5860361
2         p0.male  1.638126 0.5532573
3 sig.(Intercept)  8.373094 0.1728995
4     sig.sexmale  1.100368 0.1946630
5     t.beta.road  2.297829 0.3958878
6  d0.(Intercept) -2.345398 0.5514381
7    psi.constant -3.561123 0.7819642

[Jeffrey Royle]

this is interesting.   I guess what the oSCR model is thinking is that the Pr(capture a male) is about 1.0, whereas Pr(capture a female) is very low, so the population has a whole bunch of uncaptured Females out there but not many uncaptured males. That makes sense just looking at the data.  But the SECR results are somewhat consistent in telling the same story, just less extreme. 

There's one way to get to the bottom of this, but I don't see how to do this easily:  you need to compute the likelihood either using the oSCR or SECR likelihood for both sets of parameters and see which one is best.  I think it could be done by hacking the oSCR.fit function (you use the MLE as starting values and just return the evaluation of the likelihood).  Not sure about SECR....

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[Rahel Sollmann]

Hi Andy,

ok, thanks, I will look into that. As a side note, this data subset was analyzed previously using JAGS and results were pretty consistent with what secr is producing.

Best

Rahel

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[Jeffrey Royle]

just fyi I think the likelihood is very flat in the psi.sex dimension and the algorithm is stopping too soon (one or the other) or else there's multi-modes to the likelihood which would NOT be surprising given the sparsity of F captures and the fact that you have 3 parameters to describe the F data!

[Jeffrey Royle]

that's interesting and good to know. 

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[Rahel Sollmann]

Hi Andy,

I agree about the sparse data but - in the full analysis we have 4 years of data and we're not estimating session specific sex ratios or detection parameters, and still, the estimates from oSCR are 10x higher than those from secr.

Cheers

Rahel

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[Jeffrey Royle]

eeek, ok, very strange then!   

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[Daniel Linden]



I’m wondering if there is a problem with the ndays offset. That appears to be one difference between the model fit approaches right now…

[Rahel Sollmann]

Hi Daniel,

I was wondering about that. The secr vignette about varying effort states that in a Poisson model, the usage (here, number of active days for each camera) is used as an offset in the linear predictor for encounter rate lambda such that

lambda= lambda0*usage (ignoring additional covariates)

I assumed that oSCR does the same when using +offset(ndays), where ndays is log(number of active days). Is that not the case?

Best

Rahel

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[Rahel Sollmann]

Hi Andy,

so I think I calculated the log-LL values under secr and oSCR for estimates from both model versions (no guarantee that I got the oSCR hacking right, it is Friday afternoon...):

The nice thing is, secr outputs the LL values as it runs the model so that one was easy.

secr LL:

         (1) for estimates from secr: -258.723

         (2) for estimates from oSCR: -29489.761

oSCR LL (assuming oSCR spits out the negLogLik, I multiplied the output by -1):

         (1) for estimates from secr: -1951.324

         (2) for estimates from oSCR: -1710.763

So... very weird, no?

Any other thoughts?

Thanks and happy weekend,

Rahel  

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[Daniel Linden]

It should be the same, but I recall some strange behavior in the past with the offset function (maybe something oSCR specific).

What happens if you fit an estimated coefficient for log(ndays)?

[Rahel Sollmann]

OMG that's it!

parameters        mle    std.er
1  p0.(Intercept) -15.953186 9.8017950
2         p0.male   1.616551 0.5768182
3 sig.(Intercept)   8.354778 0.1645539
4     sig.sexmale   1.191043 0.1847156
5    t.beta.ndays   3.020891 2.2159025
6     t.beta.road   2.351929 0.3994432
7  d0.(Intercept)  -5.827147 0.3793804
8    psi.constant  -1.376643 0.6428632

> exp(-5.827147)*100
[1] 0.2946471

Thanks so much! So better stay away from offsets in oSCR then...

Best

Rahel

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[Daniel Linden]

Sweet!  Yeah, the offset seems like a reasonable constraint that obviously saves you a parameter.  But is also makes an explicit assumption about the relationship between effort and encounter, which may not turn out to be reasonable.

There must be some bug in how formulas are used in oSCR that causes problems for the offset.  But again, given your estimate is very different from 1, I'd be hesitant to use an offset either way.

[Jeffrey Royle]

thanks Dan, I'm glad you figured this out!   I remember now that it came up once a few years ago.

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