Heterogeneity models

questions concerning analysis/theory using program MARK

Heterogeneity models

Postby TimvdS89 » Tue Oct 09, 2012 9:34 am

Hi all,

Quick question: I'm working on Risso's dolphin data, and I'm attempting to estimate a population abundance. I've divided the population into 6 age classes. I wanted to try to fit a closed population heterogeneity model on this data, but before doing so I wanted to ask how I would define the concept of mixture? I'm a little lost on this... In my particular case, I have 6 encounter groups, but does that also mean I have 6 mixtures? I've read and reread Chapter 14 over and over, but became non the wiser...

Thanks in advance!
TimvdS89
 
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Re: Heterogeneity models

Postby cooch » Tue Oct 09, 2012 10:44 am

TimvdS89 wrote:Hi all,

Quick question: I'm working on Risso's dolphin data, and I'm attempting to estimate a population abundance. I've divided the population into 6 age classes. I wanted to try to fit a closed population heterogeneity model on this data, but before doing so I wanted to ask how I would define the concept of mixture? I'm a little lost on this... In my particular case, I have 6 encounter groups, but does that also mean I have 6 mixtures? I've read and reread Chapter 14 over and over, but became non the wiser...

Thanks in advance!


6 groups, 2 mixtures per group = a lot of parameters to play with. The DM is going to be 'rather ugly'.
cooch
 
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Re: Heterogeneity models

Postby TimvdS89 » Tue Oct 09, 2012 11:01 am

cooch wrote:
TimvdS89 wrote:Hi all,

Quick question: I'm working on Risso's dolphin data, and I'm attempting to estimate a population abundance. I've divided the population into 6 age classes. I wanted to try to fit a closed population heterogeneity model on this data, but before doing so I wanted to ask how I would define the concept of mixture? I'm a little lost on this... In my particular case, I have 6 encounter groups, but does that also mean I have 6 mixtures? I've read and reread Chapter 14 over and over, but became non the wiser...

Thanks in advance!


6 groups, 2 mixtures per group = a lot of parameters to play with. The DM is going to be 'rather ugly'.


That's true...But why would I have 2 mixtures per group? Is it not so that the mixture is an ageclass? In other words, an individual can be found in 1 of 6 ageclasses, so that would leave me with 6 mixtures? Sorry..still lost on the concept of mixture.
TimvdS89
 
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Joined: Mon Aug 13, 2012 5:20 am

Re: Heterogeneity models

Postby cooch » Tue Oct 09, 2012 11:32 am

TimvdS89 wrote:
cooch wrote:
TimvdS89 wrote:Hi all,

Quick question: I'm working on Risso's dolphin data, and I'm attempting to estimate a population abundance. I've divided the population into 6 age classes. I wanted to try to fit a closed population heterogeneity model on this data, but before doing so I wanted to ask how I would define the concept of mixture? I'm a little lost on this... In my particular case, I have 6 encounter groups, but does that also mean I have 6 mixtures? I've read and reread Chapter 14 over and over, but became non the wiser...

Thanks in advance!


6 groups, 2 mixtures per group = a lot of parameters to play with. The DM is going to be 'rather ugly'.


That's true...But why would I have 2 mixtures per group? Is it not so that the mixture is an ageclass? In other words, an individual can be found in 1 of 6 ageclasses, so that would leave me with 6 mixtures? Sorry..still lost on the concept of mixture.


For each age class, you imagine 2 mixtures: say, low encounter probability and high encounter probability individuals. 6 age classes, 2 mixtures per age class. This assumes individuals are identifiable to age class. If you don't have that, you could try using 6 mixture groups, no age classes, under the assumption that the major axis of heterogeneity in p is 'age'. So, your thinking would be that estimate of the mixture parameter would tell you something about number of age classes, and so on. However, if you don't have known-aged individuals, then I'd suggest trying different models ranging number of mixtures from 2 -> 6. My suspicion would be that your 'best' models would have far fewer than 6 mixtures (indicating that age might not be the most parsimonious source of difference in detection rate).

Also, be advised that if your species has strong social structure, then you might need to think hard about violating assumptions about independent fates (e.., if mom and baby are likely to be sighted together, this violates a key assumption).
cooch
 
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Re: Heterogeneity models

Postby TimvdS89 » Tue Oct 09, 2012 3:41 pm

Thanks a lot, I can definitely work with this! I will first try with less mixtures, and then work my way up to 12 mixtures (2 mixtures per age class - the individuals are identifiable to an age class), and see what the differences are. However, the species does show strong social structure as you said, so I will have to see how I work my way around that.
TimvdS89
 
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Re: Heterogeneity models

Postby TimvdS89 » Thu Oct 11, 2012 8:53 am

Hi again,

Before working on Heterogeneity models with mixture and ageclasses, I first wanted to make sure that the DM I make with Closed capture models and ageclass are correct. For models Mo, Mt and Mb I think constructing the DM is no problem, as designing them for a population in which I make no differentiation between ageclasses (i.e. 1 grand population), the AICc values and deviances overlap nicely.

However, there is a slight problem, because when I split my population into ageclasses, there is a (miniature) difference between either the deviances and/or the AICc values, and I wonder whether or not this difference is "significant"?

Image

edit: I see this picture is too long. As clarification:
deviance of {N, p(t) = c(t)} - PIM = 227, and the number of parameters is 29.
deviance of {N, p(t) = c(t)} - DM = 258, and the number of parameters is 14.

For the model {N, p(t) = c(t)} the AICc values do not differ so much, but deviance and # of parameters differs a lot. Below I have uploaded the pictures from my DM and PIM, I hope somebody can tell me what I have done wrong!

PIM:
Image

DM:
Image
Image

Sorry for asking these questions and in this format, but I feel as though this forum is the only place I can ask questions regarding these issues. I've read the bible countless times, but I can't for the life of me understand why these models are not equal in AIC value/deviance, and I believe I have to understand this before moving on to Mh models and Heterogeneity models/mixturse.

Thanks in advance,
Tim
TimvdS89
 
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Re: Heterogeneity models

Postby cooch » Thu Oct 11, 2012 9:51 am

Try using the logit link for both 'types' of models (DM, PIM). Also, consider trying simulated annealing as the optimization routine.
cooch
 
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Re: Heterogeneity models

Postby TimvdS89 » Thu Oct 11, 2012 10:25 am

cooch wrote:Try using the logit link for both 'types' of models (DM, PIM). Also, consider trying simulated annealing as the optimization routine.


Hi Cooch,
thanks for the quick reply. I tried using the Logit Link for both types, but it only seems to make a difference for the outcome of the DM. Was there perhaps a fault in the PIM / DM structures I created?

Image

Kind regards,
TimvdS89
 
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Re: Heterogeneity models

Postby TimvdS89 » Sun Oct 14, 2012 1:06 pm

Hello,

Sorry to 'press' a little on this matter - but could someone tell me whether or not the structure of my PIM or DM is incorrect? I keep thinking I must've made a mistake with one or either of the structures, and I keep attempting to "fix" them, without knowing if there is a fault with either one of them.

I would be really grateful!
TimvdS89
 
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Joined: Mon Aug 13, 2012 5:20 am

Re: Heterogeneity models

Postby TimvdS89 » Mon Nov 12, 2012 6:17 am

Hello,

when reading the "Help" file under MARK, I read that apparently only models M0, Mt, Mb and Mtb are possible to design (either through DM or PIMs), but that to design the Mh model, one needs to use the "Full closed population models with Heterogeneity", as this incorporates the pi parameter. Is this true, because I believed I was also able to construct the Mh DM by deleting the interaction with time columns. Would like to have some feedback on this matter, as I assumed that for my data the Mh model was the best, but as it turns out I may not have constructed it properly.

If needed, I can also upload a picture of my Mh model.

Thanks again,
Tim
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