Counting parameters

questions concerning analysis/theory using program MARK

Counting parameters

Postby Hope132 » Mon Aug 07, 2017 7:29 am

Hello,
I'm using MARK for the first time and I got confused about the parameter counting as described in the addenum of Chapter 4 and Appendix F of the book. As far as I understood I need to correct the number of estimatable parameters in order to get the right weightings for the models.

I'm doing a Burnham Joint live encounter and dead recovery analysis, which has the parameters S (survival), p (properbility live resight), r (properbility of dead report), and F (dispersal from the sample).

First I want to fit a basic model by trying all combinations of constant, time, and/or group dependent parameters. Then I will check for age dependence of this model in a similar fashion.
For both these steps I don't specify a design matrix, so I can use the sin link funktion. According to chapter 4 this is quiet good for getting the right parameter count.
As I understood, as soon as one of the parameters is constant, all parameters are estimatable. For the other cases I should use the procedure from chapter 4, and count unique parameters in the table of saturated capture histories.

In the second step i want to include individual covariates. Since this includes using a design matrix, the logit link funktion has to be used. MARK seems to make far more errors with this one.
For a basic Model with at least one constant parameter, can I use the number of columns in the DM as the number of estimatable parameters?

So can I use this procedure?:
no individual covariates -> At least one constant parameter: number of parameters= estimatable parameters
No constant parameter : use table of saturated encounter histories
individual covariates -> Number of collumns in DM= estimatable parameters

Thank You!
Hope132
 
Posts: 3
Joined: Sun Aug 06, 2017 12:54 pm

Re: Counting parameters

Postby cooch » Mon Aug 07, 2017 7:24 pm

Hope132 wrote:Hello,
I'm using MARK for the first time and I got confused about the parameter counting as described in the addenum of Chapter 4 and Appendix F of the book. As far as I understood I need to correct the number of estimatable parameters in order to get the right weightings for the models.

I'm doing a Burnham Joint live encounter and dead recovery analysis, which has the parameters S (survival), p (properbility live resight), r (properbility of dead report), and F (dispersal from the sample).

First I want to fit a basic model by trying all combinations of constant, time, and/or group dependent parameters. Then I will check for age dependence of this model in a similar fashion.
For both these steps I don't specify a design matrix, so I can use the sin link funktion. According to chapter 4 this is quiet good for getting the right parameter count.
As I understood, as soon as one of the parameters is constant, all parameters are estimatable. For the other cases I should use the procedure from chapter 4, and count unique parameters in the table of saturated capture histories.

In the second step i want to include individual covariates. Since this includes using a design matrix, the logit link funktion has to be used. MARK seems to make far more errors with this one.
For a basic Model with at least one constant parameter, can I use the number of columns in the DM as the number of estimatable parameters?

So can I use this procedure?:
no individual covariates -> At least one constant parameter: number of parameters= estimatable parameters
No constant parameter : use table of saturated encounter histories
individual covariates -> Number of collumns in DM= estimatable parameters

Thank You!


While there are some formal (i.e., mathematical) approaches to evaluating the number of identifiable parameters for any particular model, they are not the easiest to understand/apply. As such, I generally recommend a numerical approach, which goes as follows:

1\ simulate the model(s) you are interested in, using the simulation capabilities in MARK (Appendix A in the 'book'). Simulate using large numer of releases, and a high 'encounter' probability. With enough data, and a high enough encounter probability, all parameters that are identifiable should be counted 'correctly' by MARK. Do this, and you'll know how many parameters are intrinsically identifiable for your model(s). Learning how to simulate data is a *very* useful skill for any number of reasons, including the issue under discussion here.

2\ Then, look at what MARK reports for those same models using *your* data. If MARK reports fewer, you'll know what to adjust to. But, you'll also want to know the reason why a parameter might not be identifiable. A parameter might not be estimated correctly by MARK either because it is intrinsically nonidentifiable (because of the structure of the model), or extrinsically (because of limitiations of the data). This is discussed in some detail in Appendix F (where the method of 'data cloning' is proposed as an omnibus tool to help figure out the source of the non-identifiability).
cooch
 
Posts: 1628
Joined: Thu May 15, 2003 4:11 pm
Location: Cornell University

Re: Counting parameters

Postby Hope132 » Mon Aug 14, 2017 6:38 am

Thank You very much for the quick answer :D . That approach sounds fairly easy, quick and understandable, but I'm still struggling. The parameter count in the simulations is always lower, than in the models from my acual data.

I tried setting all the p (live encounter properbility) and r (recovery of dead), later also S (survival) and F (dispersal, staying in sample) to 0.99, using the 'Fix Parameters' option. Likewise I set all the Beta values to 0.99 (for the identity link function). Then I used the 'All RD' button to set my models as esimation models. For some of the files, which had many Models, this caused an error message.
In these files the Simulation reported a high number of failures and ran so long, that I decided to abort it. Over all my computer (really really bad computer, but still) takes suspiciously long even if I only run few Simulations.
I set thee number of releases to 1000 per occaision (except for the last of course).
The result was, that among 5 Simulation a given Model usually had one or two of the Parmeter counts differend from the other simulations of this model. For example the Model Simulation gave Numpar: 55, 56, 55, 55, 55. However MARK's parameter count with the data was 57 (Which is also the number of parameter indices).
What step am I misunderstanding here?

Also, since MARK warns about this, will simulating work for the Models containing covarites as well?

This is for my master thesis, and I tried differend combinations of the settings for the Simulation, throughout the past week. They take quiet long and I think I'm missing something I won't find by chance.
Thank You again.
Hope132
 
Posts: 3
Joined: Sun Aug 06, 2017 12:54 pm


Return to analysis help

Who is online

Users browsing this forum: No registered users and 9 guests