GOF and Model Robustness

[Karin]

I have done a capture-recapture experiment in a hibernating species (for 3 years). Therefore I have only data (once a month) during the summer time, while those animals were active. The aim of this study is to compare summer and winter (hibernation) survival.
For the GOF-testing I (or better MARK) estimated for the full model [phi(t*sex*age)p(t*sex*age)] the median c-hat with 1.17, which I think is quite good. Unfortunately Test3.RS and Test2.CT turned out to be significant for some groups (but I had insufficient data for some of the tests). And, even worse, it seems they are due to an inappropriate model and not to binomial variation. I have heterogeneous capture histories due to some transients and those who stayed in the area turned out to be trap-happy.

So, I’m not sure what to do next:

1) Ignore Test 2 + 3 because my c-hat indicates that my model fits quite well.

2) Point out that a heterogeneous capture histories have only a negligible effect on survival rate estimates (Carothers 1973 and 1979) and that trap-happiness even increases the precision of the survival rate estimator (Pollock 1990, p. 25) and continue with my model (I don’t want to estimate N). I hope I understood those authors correctly…

3) Start with a different model: e.g. instead of a whole time dependent model I look only for differences between the years and summer/winter differences. For this model the median c-hat does not change much (1.16).

4) Reject the CJS model and choose another one. In this case: which?


And I have some questions as well:

a) Are Test 2 + 3 reliable when I have unequal time intervals (I have a longer interval during winter)?

b) Does insufficient data in Test 2 + 3 mean that I don’t have enough data for my model or for Test 2 + 3?

c) Does it make sense to adjust c-hat when the cause for the lack of fit is an inappropriate model? (Given that I should continue with this model)


Thanks to anyone who takes the time to answer my questions
Karin

[cooch]

I have done a capture-recapture experiment in a hibernating species (for 3 years). Therefore I have only data (once a month) during the summer time, while those animals were active. The aim of this study is to compare summer and winter (hibernation) survival.
For the GOF-testing I (or better MARK) estimated for the full model [phi(t*sex*age)p(t*sex*age)] the median c-hat with 1.17, which I think is quite good. Unfortunately Test3.RS and Test2.CT turned out to be significant for some groups (but I had insufficient data for some of the tests). And, even worse, it seems they are due to an inappropriate model and not to binomial variation. I have heterogeneous capture histories due to some transients and those who stayed in the area turned out to be trap-happy.

So, I’m not sure what to do next:

1) Ignore Test 2 + 3 because my c-hat indicates that my model fits quite well.

2) Point out that a heterogeneous capture histories have only a negligible effect on survival rate estimates (Carothers 1973 and 1979) and that trap-happiness even increases the precision of the survival rate estimator (Pollock 1990, p. 25) and continue with my model (I don’t want to estimate N). I hope I understood those authors correctly…

3) Start with a different model: e.g. instead of a whole time dependent model I look only for differences between the years and summer/winter differences. For this model the median c-hat does not change much (1.16).

4) Reject the CJS model and choose another one. In this case: which?


And I have some questions as well:

a) Are Test 2 + 3 reliable when I have unequal time intervals (I have a longer interval during winter)?

b) Does insufficient data in Test 2 + 3 mean that I don’t have enough data for my model or for Test 2 + 3?

c) Does it make sense to adjust c-hat when the cause for the lack of fit is an inappropriate model? (Given that I should continue with this model)


Thanks to anyone who takes the time to answer my questions
Karin

You need to establish whether lack of fit is due to an inappropriately structured general model (i.e., a model with a structure that is simply not appropriate for your data), or data 'sparseness', or both. You might want to run your data through U-CARE in addition to what you did with RELEASE - U-CARE has a richer set of diagnostic tools to allow you to establish whether the lack of fit is structural. If the reason is data sparseness, then your only option is to reduce the complexity of your general model. While there is a near-reflexive tendency to assume that your general model needs to be fully time-dependent, in the face of data sparseness, this is clearly not a good strategy. Note that RELEASE and U-CARE both assume the model your fitting is time-dependent, so if you end up using a reduced parameter general model, then you can't use U-CARE or RELEASE to do much with them. At that point, all you can do is estimate c-hat, and apply the correction.

The problem with simply applying the correction is that this is arguably only meaningful if the lack of fit is extra-binomial. C-hat is estimated in MARK under the assumption that lack-of-fit is extra-binomial. If in fact the major reason for lack of fit is structural, then applying a c-hat estimated assuming lack of fit is sampling error is not entirely appropriate.

More directly, your general model is not CJS - it has age in it. As such, you can't use the standard RELEASE output (which is generated for a CJS model) directly - there are ways you can sum over some of the component tests - see the table on p. 23 of Chapter 5.

I suspect you have already, but if not - read section 5.8 of Chapter 5.