### Inestimable recovery parameter in Burnham model: use CJS?

Posted:

**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):

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.

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

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