POPAN Dealing with confounding parameters

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POPAN Dealing with confounding parameters

Postby JWithers » Wed Feb 20, 2019 12:01 pm

I am running a JS POPAN model and am struggling with how to deal with confounded parameters and parameters at boundaries. I have 7 years of mark-recap data for a rare species so p should be around .05 and its a long-lived species so Phi should be approaching the upper boundary (0.9-0.97).

My “base” model p(t), phi(t), pent(t) produces results with what appears to be confounding between Phi and Pent parameters (Beta SE’s = 0 or very large) with Phi real parameter estimate near their boundary (1) and only 13 of 20 parameters suggested to be included in the model.

By modifying the model to p(t), phi(.), pent(t) the AIC score improves but still only 10 of 15 parameters are suggested to be included in the model and pent parameters appear confounded (SE=0) while Phi(.) is at a boundary.

Finally, I fixed p parameters to produce my best model p(f), phi(.), pent(t) with the highest AIC score. It produces a realistic Phi estimate (94.6) and N estimate; however, only 5 of the 8 parameters are recommended to be counted and three of the beta pent SEs appear very large (which I assume means they are still confounded). (see below for best model output)

Npar : 8 (unadjusted=5)
-2lnL: 246.482
AICc : 263.1644 (unadjusted=256.76235)

Beta
estimate se lcl ucl
Phi:(Intercept) 2.870229 1.1321729 0.6511703 5.0892882
pent:(Intercept) 1.140485 0.4572359 0.2443027 2.0366675
pent:time3 -20.070176 2369.2567000 -4663.8134000 4623.6731000
pent:time4 -15.878127 964.4521000 -1906.2043000 1874.4480000
pent:time5 -2.522932 2.9541384 -8.3130434 3.2671792
pent:time6 -1.547736 1.1041636 -3.7118968 0.6164245
pent:time7 -16.313364 1495.8260000 -2948.1324000 2915.5057000
N:(Intercept) 6.542054 0.2654187 6.0218331 7.0622746


Real Parameter Phi
all.diff.index par.index estimate se lcl ucl fixed
Phi g1 a0 t1 1 1 0.946355 0.0574773 0.6572741 0.9938753
Phi g1 a1 t2 2 1 0.946355 0.0574773 0.6572741 0.9938753
Phi g1 a2 t3 3 1 0.946355 0.0574773 0.6572741 0.9938753
Phi g1 a3 t4 4 1 0.946355 0.0574773 0.6572741 0.9938753
Phi g1 a4 t5 5 1 0.946355 0.0574773 0.6572741 0.9938753
Phi g1 a5 t6 6 1 0.946355 0.0574773 0.6572741 0.9938753


Real Parameter p
all.diff.index par.index estimate se lcl ucl fixed
p g1 a0 t1 7 3 0.05108 0 0.05108 0.05108 Fixed
p g1 a1 t2 8 3 0.05108 0 0.05108 0.05108 Fixed
p g1 a2 t3 9 3 0.05108 0 0.05108 0.05108 Fixed
p g1 a3 t4 10 3 0.05108 0 0.05108 0.05108 Fixed
p g1 a4 t5 11 4 0.05556 0 0.05556 0.05556 Fixed
p g1 a5 t6 12 5 0.04000 0 0.04000 0.04000 Fixed
p g1 a6 t7 13 6 0.05769 0 0.05769 0.05769 Fixed


Real Parameter pent
all.diff.index par.index estimate se lcl ucl
pent g1 a1 t2 14 7 6.201100e-01 1.241639e-01 3.674799e-01 8.209906e-01
pent g1 a2 t3 15 8 1.191522e-09 2.823021e-06 -5.531929e-06 5.534312e-06
pent g1 a3 t4 16 9 7.882892e-08 7.602671e-05 4.385005e-316 1.000000e+00

pent g1 a4 t5 17 10 4.974770e-02 1.419869e-01 1.452745e-04 9.496557e-01
pent g1 a5 t6 18 11 1.319154e-01 1.341091e-01 1.507510e-02 6.013907e-01
pent g1 a6 t7 19 12 5.101112e-08 7.630376e-05 2.837588e-316 1.000000e+00

My questions are:
1) Since the model states “5 of the 8 parameters were counted” and beta pent SEs look confounded does this mean some of the pent parameters may still be confounded and/or are unreliable?

2) If so, do I need to adjust (lower) the number of parameters in my model or leave all in and state that these three pent parameters are confounded and thus suspect? Ultimately, is this model output still valid?

3) After calculating my annual N (N.occ) I find similar estimates across all years except the initial year. Is there a need to/way to correct the first year’s estimate (See below)?

N.Occ N SE LCL UCL
1 176.1707 58.42451 61.65869 290.6828
2 717.8004 78.20456 564.51944 871.0813
3 679.3071 64.03990 553.78895 804.8254
4 642.8784 74.10274 497.63699 788.1197
5 652.6358 99.04877 458.50025 846.7714
6 734.8267 78.55290 580.86304 888.7904
7 695.4206 84.43953 529.91907 860.9220
JWithers
 
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Re: POPAN Dealing with confounding parameters

Postby jlaake » Fri Mar 08, 2019 1:43 pm

I suggest that you read through Chapter 12 of the Cooch and White book. Did you consider a p(.) model? How did you devise the the fixed values for p? The 3 pent parameters are at boundaries saying that no new animals entered the population during those intervals. Is that not possible? The values of pent are consistent with the estimates of N that you are getting. It is estimating that most of the animals entered between occasions 1 and 2 which is why your estimates for N jump up and then stay fairly stable with survival being nearly 1. Long lived species require LONG time series to get useful estimates of survival especially when p is very small.
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Re: POPAN Dealing with confounding parameters

Postby JWithers » Fri Mar 08, 2019 3:06 pm

Thank you for your reply. Previously, I had not considered a p(.) model but have incorporated two new models that use this parameter; one of which ranks fairly high. However, though my new p(.)Phi(.)Pent(time) model ranks high, the Nocc estimates it produces have larger 95% CIs than those produced by my p(fixed)Phi(.)Pent(time) model; which makes sense. I'm calculated my p(fixed) parameters from telemetry data. And yes, it is possible that no new individuals entered the population during those time periods. Thank you again!
JWithers
 
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Re: POPAN Dealing with confounding parameters

Postby jlaake » Fri Mar 08, 2019 8:27 pm

Think about this for a minute. Saying you know the values p fixed adds information and reduces uncertainty. You don't know those values so you are adding information that doesn't exist. So yes your uncertainty of N will increase.
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