Boundary estimates and link functions

[ehileman]

Hi all,

I am hoping someone can help me with a confusing issue I encountered recently. Here is a little background information first. I am working with a small data set: 117 snake captures with 73 uniquely mark individuals and 44 recaptures. I am using a CJS model with two groups (Adults and young) and 5 occasions. Sampling occasions were ~ 49 days long, and data were collected over two seasons. My global model is a constrained time model with eight parameters including the interactive terms Phi (age*winter) and p (age*summer). Winter occurred between occasions 2 and 3 (i.e., interval 2) and summer occurred during occasion 4. I can give background on the a priori rationale behind this model if needed, but in model design, it's very similar to the {sex+flood+sex.flood} example in chapter 6 of the GI.

I built it in the DM like this:
(Phi)
1 1 0 0
1 1 1 1
1 1 0 0
1 1 0 0
1 0 0 0
1 0 1 0
1 0 0 0
1 0 0 0

(p)
1 1 0 0
1 1 0 0
1 1 1 1
1 1 0 0
1 0 0 0
1 0 0 0
1 0 1 0
1 0 0 0

Constructing the global model using the default Logit Link resulted in 15:p (i.e., parameter 8:p) being inestimable (i.e., identified at its 1 boundary with a SE of 0, CIs = 1,1). I constructed the equivalent of this model in the PIMS using the default SIN Link, and that resolved the issue; all parameters are now estimable.

However, one of the nested additive models I built in my candidate set, Phi (age+winter) p (age*summer), has the same (15:p)issue. This model was constructed by deleting Phi B4 from the global model in the DM above and using the default Logit Link. Thinking that this was possibly a Logit Link function issue, I reran the additive model using the Parm-specific Link, intending to use one of the other (0,1) bound link functions (loglog, or Cloglog) for 15:p, and this is where I get confused. On a lark, I reran the model using the Parm-specific Link while maintaining the original settings (i.e., all on Logit Link). When I looked at the real parameter estimates output from this, all of the parameters were estimated and the parameter count (7) was correct. I reran it again just to confirm that this wasn't an error and I got the same results. Isn't running the Parm-specific Link with all parameters set to Logit Link the same as using the default Logit Link? Anyone know what is going on here? Thanks in advance for your help!

Eric

[ehileman]

Hi all,

Thanks to Gary White for helping me resolve this issue. I am posting Gary's reply to my initial query here as it may be helpful to other MARK users. His response is specific to my data, but his point regarding starting values may be of general interest to others for trouble shooting purposes, particularly for folks with boundary parameter estimate issues.

The question:
Is running the Parm-specific Link in the DM with all parameters set to Logit Link the same as using the default Logit Link? The reason I ask is that I had a inestimable parameter in the additive CJS model Phi (age+winter) p (age*summer) using the Logit Link that was resolved by using the Parm-specific link (with all settings left on Logit Link), and I don't understand why this happened.

The answer:

The differences are all due to the starting values being different for the 2 sets of link functions. Two parameters are locking up on boundaries with the default logit link specified. But if you start the default logit link with the results from the parm-specific model, you get identical results.

Cheers!

Eric

[cooch]

Hi all,

Thanks to Gary White for helping me resolve this issue. I am posting Gary's reply to my initial query here as it may be helpful to other MARK users. His response is specific to my data, but his point regarding starting values may be of general interest to others for trouble shooting purposes, particularly for folks with boundary parameter estimate issues.

The question:
Is running the Parm-specific Link in the DM with all parameters set to Logit Link the same as using the default Logit Link? The reason I ask is that I had a inestimable parameter in the additive CJS model Phi (age+winter) p (age*summer) using the Logit Link that was resolved by using the Parm-specific link (with all settings left on Logit Link), and I don't understand why this happened.

The answer:

The differences are all due to the starting values being different for the 2 sets of link functions. Two parameters are locking up on boundaries with the default logit link specified. But if you start the default logit link with the results from the parm-specific model, you get identical results.

Cheers!

Eric

This is a known problem/solution, but I guess I never managed to squeeze it into the book (I'll add it at some point before the next 'build'). In part because whenever I run into boundary issues in my own work, I try a variety of approaches, including using simulated annealing, which generally 'solves' the starting value problem. There are other tricks (like changing the structure of the DM --- see the - sidebar - beginning on p. 80 of chapter 6) which can help, but Gary's suggestion is obviously the most direct way (still, I'd be interested what you find if you use the simulated annealing approach on your data).

[ehileman]

Hi Evan,

Thanks for the feedback and suggestions. By the way, I reran the model using simulated annealing and got identical (within rounding error) results compared to the model run using different initial starting values. Now I have a couple more tools to use when dealing with those pesky boundary estimates. Thanks!

Eric