Inestimable recovery parameter in Burnham model: use CJS?

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Inestimable recovery parameter in Burnham model: use CJS?

Postby jbauder » Tue Nov 14, 2017 6:32 pm

Hi everyone,
I am analyzing a joint PIT-tagged/telemetry data set using Burnham's joint encounter/recovery model. I have 145 individuals over 12 capture occasion (six years). Twenty individuals were telemetered (and some of those individuals were recaptured prior to receiving transmitters). I have used time-varying individual covariates to fix p=1 for telemetered individuals on occasions when they had working transmitters and to model S based on whether or not an individual carried a transmitter during a given interval. I only have three "recoveries" (i.e., known mortalities), all from telemetered individuals. Recapture rates for non-telemetered individuals are also pretty low (13 non-telemetered snakes were ever recaptured).
I thought I was good to go (famous last words, right!) but in the vast majority of my models (and all the "best supported" models), the recovery parameter appears inestimable (here's an example of the beta's from the AIC-best model):

Code: Select all
# f_p fixes p=1 for telemetered individuals
# F is also fixed at 1
# SVL is snout-vent length
                estimate           se           lcl          ucl
S:(Intercept)  6.0272944    1.0610798     3.9475780    8.1070108
S:SVL         -1.5378567    0.9239332    -3.3487657    0.2730523
p:(Intercept) -1.1391430    0.5865451    -2.2887714    0.0104854
p:f_p         26.1607560  127.6432800  -224.0200700  276.3415900
p:SVL         -1.5013974    0.7175832    -2.9078604   -0.0949343
p:Time        -0.7041631    0.1907288    -1.0779916   -0.3303345
p:SVL:Time     0.5230500    0.2193364     0.0931506    0.9529494
r:(Intercept) 15.0627770 3885.2844000 -7600.0949000 7630.2204000


I really don't think my recovery probability is 0.99999 so my first question (and initial guess) is might r be confounded with other parameters to the point of being inestimable, particularly since my only recoveries were for telemetered individuals with p=1? My high survival estimate is also unusually high (0.997). Also, I would not have expected survival and recapture to decrease with increasing body size. But my first thought is that maybe my data are insufficient to reliably estimate all the parameters in a Burnham joint model. Could the high estimated recovery rate be contributing to high survival estimates?

My next question was, is it logical to move to a CJS model and continue to use time-varying individual covariates to fix p=1 for telemetered individuals? I know others have used this approach but when I tried it (using the same covariates as in my Burnham model example), the time-varying individual covariate for fixing p is not forcing the beta estimate to some large positive number. Moreover, using the exact same set of candidate models I returned a completely different set of model rankings (AIC-best CJS model shown below). Once again, I can tell a good story about each parameter estimate (survival is lower during the winter and p varies by den site and increases with body size/SVL), although I “believe” these survival estimates more than those from the Burnham model.

Code: Select all
                   estimate        se        lcl        ucl
Phi:(Intercept)   3.5497445 2.2674916 -0.8945391  7.9940281
Phi:SeasonWinter -2.3109444 2.2730155 -6.7660550  2.1441661
Phi:Time         -0.6372828 0.1954899 -1.0204431 -0.2541225
p:(Intercept)    -2.7997817 0.6553911 -4.0843483 -1.5152150
p:f_p             3.3820915 0.8027085  1.8087829  4.9554001
p:DenA        1.9293446 0.6965248  0.5641559  3.2945333
p:DenB      2.5904624 0.7590309  1.1027619  4.0781629
p:DenC           1.4631332 0.6987793  0.0935257  2.8327408
p:SVL             0.5000798 0.2036470  0.1009317  0.8992279
 


Does anyone have any ideas why 1) I can fix p=1 in the Burnham model but not the CJS model and 2) there are such differences in model rankings/parameter estimates between these two model types? Would the safest thing to do be to assume my data are insufficient to fit a Burnham joint model and report estimates from the CJS model (provided I can fix p=1)?

Thanks so much,
Javan
jbauder
 
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Re: Inestimable recovery parameter in Burnham model: use CJS

Postby Bill Kendall » Tue Nov 14, 2017 7:05 pm

First, I didn't know you could fix parameter values based on individual covariates. Are you letting it estimate the parameters and they come out to 1?

More importantly, from your description it's not clear how you're handling the fact that some of your individuals are sometimes telemetered, sometimes not. Your recovery estimate might be so high because you have few recaptures and r is being dominated by the telemetered deaths, which I assume are monitored with certainty.

I've used a multistate approach (live/dead, perhaps telemetered/not) to run similar analyses. However, I think you could use the Burnham model effectively if you use two groups (telemetered and not), setting p=1 and r=1 for telemetered, and p estimated and r = 0 for PIT tagged. For the case where you apply a transmitter to a PIT tagged individual, censor that individual from the PIT tagged group at that point (i.e., fill out the rest of the history with 0's and use -1 for the capture frequency), and start its history in the telemetered group.

Your small sample sizes will continue to be a challenge, though.
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Re: Inestimable recovery parameter in Burnham model: use CJS

Postby jlaake » Tue Nov 14, 2017 8:06 pm

Bill-

You can't. It is the latter. He has posted about this on the RMark sub-forum. Tags fail so he is using a time-varying covariate. He could use the approach you suggest but would then need to use loss on capture and start a new capture history when the tag failed and it was no longer telemetered. With only 3 recoveries I don't think it is worth trying to use the Burnham model. With only 12 recaptures of non-telemetered animals be careful of pushing your data too far.

--jeff
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Re: Inestimable recovery parameter in Burnham model: use CJS

Postby jbauder » Tue Nov 14, 2017 8:52 pm

Hi Jeff and Bill,

Thanks for your suggestions (especially regarding the multi-state approach), and that makes me feel a lot better to get some more opinions regarding the sparseness of my data! I have a few other data sets I am working with that have more recoveries (but never more than six recoveries) and the Burnham model seems to work better there (i.e., betas are not 0 or 1 and SE's are reasonable).

I am still unsure why this time-varying individual covariate won't work with a CJS model, even though I use the same covariates and encounter histories (just changing the LD history to a LL format). Is there something about the CJS model or its assumptions that would cause the time-varying individual covariate approach not to work?

Thanks,
Javan
jbauder
 
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Re: Inestimable recovery parameter in Burnham model: use CJS

Postby jlaake » Tue Nov 14, 2017 9:01 pm

I'm a bit confused. I thought it did work with CJS and it certainly can. But as Bill pointed out you aren't fixing the parameter. You are letting the parameter go to a boundary which then estimates that p=1. But it is an estimation which is numerical and can go awry with sparse data. Using the group approach allows you to fix the real parameter value so there is no estimation involved with the fixed real parameter. But it does require you to restructure your data somewhat with groups and using a freq=-1 when the animal changes from one group to the next and starting a new capture history in the new group.
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Re: Inestimable recovery parameter in Burnham model: use CJS

Postby jbauder » Tue Nov 14, 2017 9:25 pm

Sorry for the confusion! The beta estimate in the CJS model when f_p=1 (when an individual was telemetered) was about 3.4 with the CJS model which corresponds to a real estimate of about 0.97 (and the real estimate for other group levels, like a different sex or den, would often push the real estimate much lower). In contrast, the beta estimate in the Burnham model is always much larger (>20). So it is working in the right direction with the CJS model, but just not estimating a large enough beta to produce p=1.

It seems odd that it would work with the more parameter-rich Burnham model and not the CJS model. But I definitely see your point that I am not truly fixing a parameter and if sparse data can cause the numerical approach to go awry then this particular data set meets that criteria! I think the grouping approach you and Bill described makes sense and I will give that a try.

Thanks again for your prompt responses!
Javan
jbauder
 
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Censoring individuals to fix p in CJS model

Postby jbauder » Wed Nov 15, 2017 11:48 am

I had another quick follow up question to Jeff and Bill's suggestion for using censoring and groups to fix p=1 in a CJS model, rather than a time-varying individual covariate, when using a mix of PIT-tagged and/or telemetered (I would like to make sure I am implementing this correctly!).
If I have an encounter history of 11001111 where the individual was telemetered on occasions 1 and 2 (so p=1) but then the transmitter died after occasion 2. The individual was recaptured and given another transmitter on occasion 5 and then located with telemetry on occasions 6-8. The individual was alive and technically in the PIT-tagged group for occasions 3 and 4 but wouldn't splitting the encounter history as shown below ignore the fact that the individual was alive for occasions 3 and 4?
Code: Select all
ch freq group
11000000 -1 Telem
00001111  1 Telem

Would this be correct instead?
Code: Select all
ch freq group
11000000 -1 Telem
01001000 -1 PIT
00000111  1 Telem

Thanks again for your help!
Javan
jbauder
 
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Re: Inestimable recovery parameter in Burnham model: use CJS

Postby jlaake » Wed Nov 15, 2017 12:02 pm

It would be the second set except the last one should have a 1 for occasion 5 because that was when it was released with the tag.

--jeff
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Re: Inestimable recovery parameter in Burnham model: use CJS

Postby jbauder » Wed Nov 15, 2017 12:07 pm

Got it, thanks!
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