Linear constraints in POPAN

questions concerning analysis/theory using program MARK

Linear constraints in POPAN

Dear Phi Dot Forum,

I have started my analysis of some shark mark-recapture data by exploring p and phi using a CJS model. The 'best' model is one where p is constrained by a measure of sampling effort (and so I know that in my study the level of effort affects capture probability). All credit to "The Gentle Guide..." for teaching me how to do this....

Anyway, my next step is to estimate abundance using a POPAN model. Working from my earlier CJS analysis I have constructed a model where p is again constrained by a measure of effort; but I have hit a hurdle. I can't quite get to grips with how many parameters it should be estimating.

So I have 24 capture sessions, and in my CJS "effort" model {phi[.]p[time - effort constrained]} I get 3 parameter estimates: 1 phi, and 2 p (intercept and slope). Correct?
But in my POPAN model {phi[.]p[time-effort constrained]b[time]N} how do I work out the number of parameters that should be estimated? Is it 1 phi, 2 p, 23 b and 1 N?

I'm sorry to ask, but the Guide doesn't cover linear constraints in POPAN models. Any thoughts/answers will be much appreciated.

Tim
timkdavies

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Joined: Wed May 20, 2009 11:24 am
Location: Silwood, UK

Re: Linear constraints in POPAN

I have a similar question about sampling effort constraints in POPAN models. I'm looking at 6 sampling occasions, assessing time varying p while accounting for sampling effort (miles surveyed each session). To model constant survival, time varying p, accounting for sampling effort's affects on p, time varying pent, and N - I think I would set the design matrix up like this - but I'm not sure - I can't find the answer to this earlier post by Tim.

B1 B2 B3 B4 B5 B6 B7 B8 B9 B10 B11 B12 B13 B14
phi 1 0 0 0 0 0 0 0 0 0 0 0 0 0
p 0 1 1 0 0 0 0 412.84 0 0 0 0 0
p 0 1 0 1 0 0 0 509.92 0 0 0 0 0
p 0 1 0 0 1 0 0 172.49 0 0 0 0 0
p 0 1 0 0 0 1 0 151.97 0 0 0 0 0
p 0 1 0 0 0 0 1 294.83 0 0 0 0 0
p 0 1 0 0 0 0 0 127.51 0 0 0 0 0
pent 0 0 0 0 0 0 0 0 1 1 0 0 0 0
pent 0 0 0 0 0 0 0 0 1 0 1 0 0 0
pent 0 0 0 0 0 0 0 0 1 0 0 1 0 0
pent 0 0 0 0 0 0 0 0 1 0 0 0 1 0
pent 0 0 0 0 0 0 0 0 1 0 0 0 0 0
N 0 0 0 0 0 0 0 0 0 0 0 0 0 1
shannonbarbermeyer

Posts: 24
Joined: Tue Aug 05, 2008 1:32 pm
Location: Wailuku, HI

Re: Linear constraints in POPAN

Starting with the more recent question,

You appear to have tried to model capt. prob as year-specific AND as a function of yearly effort. Unless you have individual covariates, there is no replication to get those estimates. For the p(yearly effort) model, you should have 2 columns in the design matrix in the rows for p, one for the intercept, and one for the effect of effort. So, the matrix would be:
Code: Select all
`        B1      B2      B3      B4      B5      B6      B7      B8      B9phi     1       0       0       0       0       0       0       0       0p       0       1       412.84  0       0       0       0       0   0p       0       1       509.92  0       0       0       0       0   0p       0       1       172.49  0       0       0       0       0   0p       0       1       151.97  0       0       0       0       0   0p       0       1       294.83  0       0       0       0       0   0p       0       1       127.51  0       0       0       0       0   0pent    0       0       0       1       1       0       0       0       0pent    0       0       0       1       0       1       0       0       0pent    0       0       0       1       0       0       1       0       0pent    0       0       0       1       0       0       0       1       0pent    0       0       0       1       0       0       0       0       0N       0       0       0       0       0       0       0       0       1`
jhines

Posts: 587
Joined: Fri May 16, 2003 9:24 am
Location: Laurel, MD, USA

Re: Linear constraints in POPAN

So I have 24 capture sessions, and in my CJS "effort" model {phi[.]p[time - effort constrained]} I get 3 parameter estimates: 1 phi, and 2 p (intercept and slope). Correct?

>>>Yes

But in my POPAN model {phi[.]p[time-effort constrained]b[time]N} how do I work out the number of parameters that should be estimated? Is it 1 phi, 2 p, 23 b and 1 N?

>>> Yes. If the phi, p, and b parameters are all time-specific, some of them at the beginning and end will be confounded, but with phi constant, that isn't the case here as phi is constant. Also, since p is a function of effort, it is not fully time-specific. So, you should be able to estimate all 23 entry parameters.

I'm sorry to ask, but the Guide doesn't cover linear constraints in POPAN models. Any thoughts/answers will be much appreciated.

>>> You shouldn't be sorry for asking questions after you've looked for answers
jhines

Posts: 587
Joined: Fri May 16, 2003 9:24 am
Location: Laurel, MD, USA

Re: Linear constraints in POPAN

I'm sorry to ask, but the Guide doesn't cover linear constraints in POPAN models. Any thoughts/answers will be much appreciated.

I echo Jim's comments, but will add -- the presumption is that by the time you get to *any* chapter following chapter 6 (the linear models chapter), that if you've really worked through and understood chapter 6, you'll be able to figure out the DM for *any* of the data types that follow, without having examples of the DM for every possible data type. There are occasionally nuances (like shared vs separate intercepts) that are covered in other chapters, which require looking at explicit DM structures, but otherwise.

Carl's POPAN chapter makes the same assumption. But, it looks like Jim has given you enough to get you pointed in the right direction.
cooch

Posts: 1604
Joined: Thu May 15, 2003 4:11 pm
Location: Cornell University

Re: Linear constraints in POPAN

Thank you so much, Jim! I don't take your help lightly - I had first read (and felt I had good understanding) and done all examples in the mark book chapters 1-7, 12, 14, 15, and some of 18 - checked various publications that were analyzing similar data with similar models (and their supplementary info), and searched posts on this forum. One would think that should be enough to set me straight - but I was unfortunately still confused about coding p in this situation (as evidenced by my faulty DM) - so thank you so very much for explaining why I couldn't do both varying by year and also sampling effort and how to properly structure my DM in the POPAN application. I sooooo appreciate the help!!! Shannon

jhines wrote:Starting with the more recent question,

You appear to have tried to model capt. prob as year-specific AND as a function of yearly effort. Unless you have individual covariates, there is no replication to get those estimates. For the p(yearly effort) model, you should have 2 columns in the design matrix in the rows for p, one for the intercept, and one for the effect of effort. So, the matrix would be:
Code: Select all
`        B1      B2      B3      B4      B5      B6      B7      B8      B9phi     1       0       0       0       0       0       0       0       0p       0       1       412.84  0       0       0       0       0   0p       0       1       509.92  0       0       0       0       0   0p       0       1       172.49  0       0       0       0       0   0p       0       1       151.97  0       0       0       0       0   0p       0       1       294.83  0       0       0       0       0   0p       0       1       127.51  0       0       0       0       0   0pent    0       0       0       1       1       0       0       0       0pent    0       0       0       1       0       1       0       0       0pent    0       0       0       1       0       0       1       0       0pent    0       0       0       1       0       0       0       1       0pent    0       0       0       1       0       0       0       0       0N       0       0       0       0       0       0       0       0       1`
shannonbarbermeyer

Posts: 24
Joined: Tue Aug 05, 2008 1:32 pm
Location: Wailuku, HI