Closed capture models

[RBoys]

Hello,

I have a couple of questions that I am hoping someone can answer.

1. I have data for a closed capture model where there seems to be full heterogeneity between individuals but no known covariates for this heterogeneity. I have been running Full Likelihood Heterogeneity pi, c and p models for this and then removing the mixture column in the design matrix and fixing the pi parameter to equal 1. Firstly does this sound correct? Secondly I am also running models without the heterogeneity ie. Full Likelihood p and c models, and the output of these models is identical to those with heterogeneity, eg. M0=Mh, Mb=Mbh etc.. Is this because the Full Likelihood p and c models are really just a simple model with a single heterogeneity mixture? Or is there something wrong? If these are correct, should I be using the models with heterogeneity or without?

2. Next, I would like to use multiple consecutive days as a single sampling occasion in my closed model, however, some sampling days are not consecutive and so these would be a single day sampling occasion. Does anyone know what the effects would be of using multiple days as a single sampling occasion? And what happens if the sampling occasions vary in the number of days?

Thank you

[egc]

It seems clear from the gist of your question that you're using MARK. As such, I'm going to move your question over to the MARK subforum.

[cooch]

Hello,

I have a couple of questions that I am hoping someone can answer.

1. I have data for a closed capture model where there seems to be full heterogeneity between individuals

Your assessment of heterogeneity is based on what?

but no known covariates for this heterogeneity. I have been running Full Likelihood Heterogeneity pi, c and p models for this and then removing the mixture column in the design matrix and fixing the pi parameter to equal 1.

Why? If you think there is heterogeneity, why are you 'turning off' the structures in the model that will give you some capability of testing for heterogeneity (unless you're comparing the fits of models with an without heterogeneity -- but you don't make a pint of this).

Secondly I am also running models without the heterogeneity ie. Full Likelihood p and c models, and the output of these models is identical to those with heterogeneity, eg. M0=Mh, Mb=Mbh etc.. Is this because the Full Likelihood p and c models are really just a simple model with a single heterogeneity mixture? Or is there something wrong? If these are correct, should I be using the models with heterogeneity or without?

Goes back to earlier question. I'd suggest the following as a starting point. Re-start your analysis, selecting 'Huggins Full Likelihood Heterogeneity pi, c and p' as the data type. Then, after making sure you fully understand what you're doing (careful study of relevant sections of Chapter 14 in the MARK book), run all 8 of the pre-defined models as described n the - sidebar - beginning on p. 14 of Chapter 14. Look at the output, and see what evidence you have across those models for/against heterogeneity, and go from there.

2. Next, I would like to use multiple consecutive days as a single sampling occasion in my closed model, however, some sampling days are not consecutive and so these would be a single day sampling occasion. Does anyone know what the effects would be of using multiple days as a single sampling occasion? And what happens if the sampling occasions vary in the number of days?

Thank you

If the population is closed, it won't make much of a difference, but it will limit your ability to build certain models. A clever approach might be to treat it like a robust design, and simply fix the gamma and survival parameters accordingly.

[RBoys]

In regards to the heterogeneity, we believe that it exists between individuals due to the capture probability, 76% of the individuals are transients.
I thought that the heterogeneity mixture should be 1 in this case because I do not have specific covariates to know how many mixtures, the sample only contains adults and we don't have sex information. So I thought that it was only heterogeneity due to capture probability and therefore 1 mixture.
Why is it best to use the Huggins Full Likelihood, rather than the Otis models?

Thank you

[cooch]

In regards to the heterogeneity, we believe that it exists between individuals due to the capture probability, 76% of the individuals are transients.

If the population is closed, then whether or not an individual is a transient is irrelevant, unless you believe that transient individuals have a different detection probability that resident individuals. If so, then (i) you might reasonably assume heterogeneity, and (ii) a discrete, finite mixture model is a very reasonable starting point.

If the transients depart over your sampling frame, then the population isn't closed, and you have other things to contend with. See chapter 8, section on transients for some discussion.

I thought that the heterogeneity mixture should be 1 in this case because I do not have specific covariates to know how many mixtures, the sample only contains adults and we don't have sex information.

It would seem you don't understand mixtures. In fact, in the absence of covariates, trying a finite mixture model as a first approximation handling heterogeneity is precisely what you should do.

So I thought that it was only heterogeneity due to capture probability and therefore 1 mixture.

Thats all mixtures model anyway in a closed abundance model.

Why is it best to use the Huggins Full Likelihood, rather than the Otis models?

Huggins ends to work better, in my experience, but it probably makes precious little difference.

I strongly suggest you read a fair bit of the literature first. My sense is you don't really have a good grasp of the basic concepts. One starting point is Chapter 14, but there are others.

[RBoys]

That is true, I am still trying to get to grips with everything.

So if I have run both models with and without heterogeneity and they have exactly the same outputs, which is better fitting, those with heterogeneity or without?

Thank you

[cooch]

So if I have run both models with and without heterogeneity and they have exactly the same outputs, which is better fitting, those with heterogeneity or without?

If they have exactly the same output (more or less), then this implies little to no heterogeneity, meaning -- for the heterogeneity (mixture models), pi should be estimated at or very close to 1.0 (meaning, 100% of the individuals are in the single mixture group).

if that is the case, then make your life simpler, and focus on models without heterogeneity.