Closed population models, model selection or model averaging

[mariel]

Hello,

I have carefully read chapter 14 from Mark Book. I have compared models Mo, Mt, Mh and Mth to estimate abundance using AICc.

I would be happy to get some advices about model averaging and N estimation.

Model Mth has the smallest AIC followed by Mt (delta AICc = 2.8 between Mt and Mth), Mo (delta AICc = 31.0 between Mo and Mth) and Mh (delta AICc = 34.6 between Mh and Mth). AICc weight is 0.8 for model Mth and 0.2 for Model Mt.

I am wondering which is the most appropriate method to estimate N:
1) make a model averaging on Mth and Mt parameters

2) or select the appropriate estimator for model Mth, as it is the model with the smallest AIC, by examining the coefficient of variation of individual capture probabilities and the sample coverage defined as “the proportion of the total capture probabilities of the captured animals” (Chao et al. 1992, e.g. Poncelet et al. 2010). This part of the analysis will be done in Capture instead of Mark.

If 1) is the most appropriate method, I have also a few questions.
When I tried to do a model averaging on the 4 models, only model Mth appeared in the result sheet (with a weight of 1) and I did not manage to solve this problem.
To estimate CI, would you advice me to follow the calculation by hand detailed in chapter 14.10.1?

Thank you in advance for your help,
All the best,

Marie

[mariel]

I guess that I can not do model averaging as deltaAIC > 2?

Thanks,
Best wishes,

Marie

[cooch]

I guess that I can not do model averaging as deltaAIC > 2?

Thanks,
Best wishes,

Marie

It seems you're not understanding (fully) model averaging. First, you can only average over models with the same likelihood structure.If you've built finite mixture heterogeneity models, but also have models based on 'standard' models (which have different likelihoods), you can't average over the set of them (although there is a way to do it -- you can, with only a little work, build all of the standard models from the finite mixture starting point, simply by constraining the Pi parameter to 1).

Second, model averaging is just that, averaging -- if the AIC weight is small, relative to other models in the model set, then all that does is reduce the impact of that model's estimate on the overall average.

I'd suggest you read sections 4.4 and 4.5 of chapter 4 (if you haven't already).

[mariel]

Many thanks for your answer and your help. I have runned all the models under the full likelihood with heterogeneity.

To estimate population size, would advice me to do the model averaging to take model uncertainty into account or choose the estimators of Mth (only in the case where delta AICc of Mth with all other models > 2) using Capture and Chao's method (examination of coefficient of variation of individual capture probabilities and sample coverage) ?

I have another question, I read in Chapter 15, that MARK's default for closed models is to use a sin link for p's and c's and a log link for N and that the selected link function do not matter as a log link will be used on fo.

However, when I used a logit link, model Mt has an AICc 49.24 of and Mth an AICc of 46.44. When I used a sin link, model Mth has a higher AICc (Mth AICc: 50.67) than Mt (Mt AICc: 49.24 which is the same than with the logit link). This changed substantly the respective weight of the models.

I have read the sidebar of the chapter 6.4 but I have not found the answer to my question (or not get it). Which link function would you advice me to use?
I am also wondering why AICc changed for only Mth model when using sin or logit function.

Thank you in advance for your help.

Marie

[dhewitt]

Parameter counting might be an issue here when comparing AIC(c) values between models with no difference but link functions. To quote the great Paul Conn from a previous post:

"You should be okay comparing AIC between SIN and LOGIT link functions, provided that the number of parameters has been entered correctly. One issue that happens with the logit link is that when parameters are estimated on the boundary (zooming off to + or - infinity on the beta scale), MARK decides that it can't estimate a parameter and thus the AIC value you get will be off. In this case you're supposed to realize what is happening and adjust the number of parameters manually. This doesn't happen with the SIN link, ..."

- Dave Hewitt

[mariel]

Many thanks for your help. Parameter count seem to be the problem of the Mth model I have built.
However, I have difficulties to solve it.

I have 7 capture occasions.
For model Mth with a logit link, the last p for the two mixtures (p8 and p15) are not estimated, which is expected as a constraint is needed to estimate these parameters. p4 is not estimated as well.
With the Mth model and a sin link, only parameters for the first mixture (p4, p5, p7 and p8) are not estimated.

I set the parameters as follow:
pi: 1
p: 2,3,4,5,6,7,8
9,10,11,12,13,14,15
c: 3,4,5,6,7,8
10,11,12,13,14,15
N: 16

I do not know how to set the last parameter so that it is estimated (p8=c8 and p15=c15 so the last p should be constrained on the last c, no?).
N is not equal to Mt+1.

I would be happy to receive some help again.

Thank you in advance,

Marie

[dhewitt]

My experience with closed models for abundance is so limited I am no help. Sorry.

[mariel]

Many thanks for your answer.

I have not find how to solve the problem, if anyone else could help that would be great.

Marie