CJS or JS? & other questions

[thgian]

Hello to all,
I need to clarify some things, so pls give me a hand.

I have a quite interested CMR dataset with small mammals (rodents). This came from a 12 month field work (monthly sampling) that took place in 8 stations along an altitudinal transient in two mountain massifs (400, 800, 1200 &1800m in each mountain).
The collected data, apart from the recaptures was sex, reproductive status, age (juvenile/adult), weight and other morphometric features such as body length etc.
In each station not only one species was collected and along with the above collected data, the following hypotheses could be checked:
- In one station, phi & p is the same (or defers) among the same species different sex.
- In one station, phi & p is the same (or defers) among different species
- Test if phi & p is constant or time dependence
- In different stations, phi & p among same species is the same (or defers)
If I use the Cormack-Jolly-Seber formulation, the procedure seems quite easy. I use the U-CARE for GOF test and in MARK I check my hypotheses.
Unfortunately, I cannot have the number of the population (N), neither the recruitment that a Jolly-Seber formulation can give. Also by using Jolly-Seber, I can have phi & p for the whole population (mark and unmark) and not only for the marked animals, but unfortunately I don’t know how to do the GOF test. Also, other problems have occurred (numerical convergence) when I tried to run my data in a POPAN formulation.

So, I am a little bit confused. Do you think that I could stay in CJS or this is not the adequate model?
Also, the hypotheses mentioned above are theoretically correct or they are too simple or wrong?

Thank you in advance.
I hope someone could give me a boost.

Thanos

[cooch]

Hello to all,
I need to clarify some things, so pls give me a hand.

I have a quite interested CMR dataset with small mammals (rodents). This came from a 12 month field work (monthly sampling) that took place in 8 stations along an altitudinal transient in two mountain massifs (400, 800, 1200 &1800m in each mountain).
The collected data, apart from the recaptures was sex, reproductive status, age (juvenile/adult), weight and other morphometric features such as body length etc.
In each station not only one species was collected and along with the above collected data, the following hypotheses could be checked:
- In one station, phi & p is the same (or defers) among the same species different sex.
- In one station, phi & p is the same (or defers) among different species
- Test if phi & p is constant or time dependence
- In different stations, phi & p among same species is the same (or defers)
If I use the Cormack-Jolly-Seber formulation, the procedure seems quite easy. I use the U-CARE for GOF test and in MARK I check my hypotheses.
Unfortunately, I cannot have the number of the population (N), neither the recruitment that a Jolly-Seber formulation can give. Also by using Jolly-Seber, I can have phi & p for the whole population (mark and unmark) and not only for the marked animals, but unfortunately I don’t know how to do the GOF test. Also, other problems have occurred (numerical convergence) when I tried to run my data in a POPAN formulation.

So, I am a little bit confused. Do you think that I could stay in CJS or this is not the adequate model?
Also, the hypotheses mentioned above are theoretically correct or they are too simple or wrong?

Thank you in advance.
I hope someone could give me a boost.

Thanos

Quick reply - estimates of N from open populations are not very robust. I'd suggest avoiding them altogether. I'd consider the Link-Barker parametrization of the Jolly-Seber model - you'll be able to compare phi and p (as per the bulk of your note), and lambda, which is estimated (as a derived parameter) far more precisely for open populations. You can run Link-Barker using finite mixtures to handle heterogeneity (fairly straightforward), or with random effects (less so). As for a GOF test, simply 'pretend' the encounter histories are CJS, and run the GOF under that assumption. Then, apply the estimated c-hat for your JS models (using Link-Barker).

I'd have a good read of Link-Barker in chapter 13, and the section on mixture models in chapter 14 (which focuses on application of mixtures to closed estimators, but the same principle applies).

[thgian]

Thank you very much for your reply, I think I got it. I had read up to Chapt 5, but reading Chapter 13 was an apocalypse.
I have a few more questions that came up after the close look of this chapter. I will try to be straight and comprehensive.

- Link-Barker formulation deals with f (per capita recruitment rate) and not lambda. I presume that you suggested lambda just because f and λ are connected (λi =φi + fi).
- There are "losses on capture" in my experiment. How do we handle with it. In Chapter 13, in the two examples, apart from mention it, it is not seem to be a specific manipulation.
- Why in the model p(*)phi(t)f(t) [or p(*)phi(t)b(t), doesn't matter], all the parameters are valid unlike the fully depended models where some estimates cannot be used because of confounding or non-identifiability. p (recapture) has something to do with it but I can't figure out the connection.
- Can I use the POPAN, the Link-Barker and the Pradel-λ formulations separately in order to calculate all the parameters? As it says in Chapter 13, phi and p are the same across these formulations except for some minor differences, and the other parameters are connected in such a way that you can indirectly estimate them by using one formulation. So, why don't use the three formulations separately just to gain time?
- You spoke about finite mixtures to hadle heterogeneity but reading Chapter 14 didn't helped me a lot. By having a constant p, the problem is solved? I cannot understand it.
- Finally, the estimated c-hat from the GOF test for all my groups are far below 1, (=0.3), showing inderdispersion of the data. I assume that I have to use the suggestion c-hat=1 as written in the manual.

Thank you again for your help. You are doing a great job.

Thanos

[gwhite]

The Link-Barker correctly handles losses on capture, whereas I did not program the Pradel models to handle losses on capture. The original Pradel (1996) paper included a separate parameter to model losses on capture, and I felt that made the model too complicated so left out this parameter. In contrast, the Link-Barker model can leave off the last section of the likelihood and thus handle the loss. So, you will obtain identical estimates with the Pradel and Link-Barker data types if you do not have losses on capture, but will NOT if you do have losses on capture.

Lambda is produced as a derived parameter from the Link-barker model, so you can in fact get lambda, as well as use the variance components analyses.

All of the Jolly-Seber parameterizations can be obtained with the Change Data Type menu choice under PIMs. The likelihoods for the Pradel and Link-Barker models are comparable, but not with the Pradel or Burnham parameterizations.

With all the Jolly-Seber parameterications, the first p is confounded with the recruitment parameter, and the last phi, p, and recruitment parameter are confounded. So, if you model p with a covarariate or a dot model, making the first and last p identifiable, you can then get estimates of the first recruitment parameter, and the last phi and the last recruitment parameter.

Gary

[cooch]

- Link-Barker formulation deals with f (per capita recruitment rate) and not lambda. I presume that you suggested lambda just because f and λ are connected (λi =φi + fi).

Correct, more or less. See the Pradel chapter for some background.

- There are "losses on capture" in my experiment. How do we handle with it. In Chapter 13, in the two examples, apart from mention it, it is not seem to be a specific manipulation.

Chapter 2. Losses coded in input file.

- Why in the model p(*)phi(t)f(t) [or p(*)phi(t)b(t), doesn't matter], all the parameters are valid unlike the fully depended models where some estimates cannot be used because of confounding or non-identifiability. p (recapture) has something to do with it but I can't figure out the connection.

See Gary's answer.

- Can I use the POPAN, the Link-Barker and the Pradel-λ formulations separately in order to calculate all the parameters? As it says in Chapter 13, phi and p are the same across these formulations except for some minor differences, and the other parameters are connected in such a way that you can indirectly estimate them by using one formulation. So, why don't use the three formulations separately just to gain time?

The models are effectively redundant. And, saving time should not be a motivation. Robustly estimating your question(s) should be.

- You spoke about finite mixtures to hadle heterogeneity but reading Chapter 14 didn't helped me a lot. By having a constant p, the problem is solved? I cannot understand it.

Then you didn't understand Chapter 14.

- Finally, the estimated c-hat from the GOF test for all my groups are far below 1, (=0.3), showing inderdispersion of the data. I assume that I have to use the suggestion c-hat=1 as written in the manual.

Unless you have a strong biological rationale for underdispersion, set c-hat to 1.0 in that case.

[thgian]

- You spoke about finite mixtures to hadle heterogeneity but reading Chapter 14 didn't helped me a lot. By having a constant p, the problem is solved? I cannot understand it.

Then you didn't understand Chapter 14.

Ok, you haven't finished with me yet, I will came back when I finally understand the chapter (even if I need to read it for 50 times)
(that means: thank you very much for your advice. All your suggestions have been recorded)

Another question (hope not boring)
As U-CARE didn't gave me results (probably lack of data, or sparse data, even if in some cases I have more than 50% recapture), I assume that I cannot use the global full-time-dependent model as my general model.
But...
I can use some other reduces models as Phi(.)p(.)f(.) just to check my hypothesis, is that correct? In that case I could use another method to calculate c-hat (bootstrap-median c-hat), again correct? Besides that, I don't want to check if the φ changes through time but to check if there is a difference in φ between two species (constant φ).

edit: one more question (I can' find the answer in the Manual, nor in the help file)
There is an option under the Adjustment menu, the "Effective sample size". When I change the number of the effective sample size, the 2d model become 1st in the result window (when working with AIC). How can I calculate the appropriate effective sample size? (Notation: when I use BIC instead of AIC, the two models doesn't change raw, and the 1st model remains 1st whatever the effective sample size is).

I hope I haven't mix them up

Thanos

[cooch]

Another question (hope not boring)
As U-CARE didn't gave me results (probably lack of data, or sparse data, even if in some cases I have more than 50% recapture), I assume that I cannot use the global full-time-dependent model as my general model.
But...
I can use some other reduces models as Phi(.)p(.)f(.) just to check my hypothesis, is that correct? In that case I could use another method to calculate c-hat (bootstrap-median c-hat), again correct? Besides that, I don't want to check if the φ changes through time but to check if there is a difference in φ between two species (constant φ).

Two comments:

1. you can estimate a median c-hat for any model within the CJS (and some other) data types. Whether it is time-dependent, or not, won't matter to the estimation.

2. however, if your data are so sparse that you can't do a GOF for a fully time-dependent model, then you might have to accept that you simply don't have sufficient data to do much of anything (let alone estimate c-hat).

edit: one more question (I can' find the answer in the Manual, nor in the help file)
There is an option under the Adjustment menu, the "Effective sample size". When I change the number of the effective sample size, the 2d model become 1st in the result window (when working with AIC).

Don't change the effective sample size - in a very few instances, where you have deep insights as to the models, you might need to, but in most instances, leave it alone.

How can I calculate the appropriate effective sample size? (Notation: when I use BIC instead of AIC, the two models doesn't change raw, and the 1st model remains 1st whatever the effective sample size is).

The fact that you're bouncing back and forth between AIC and BIC suggests you might simply be data dredging. Don't. Pick one or the other (after thinking hard about which is appropriate - this is not a trivial question), then work from there. I'd suggest a thorough read of Chapter 4 (to start), then any of the 'big books' on multi-model inference, information theoretic model selection, and a priori construction of candidate model sets.