GOF Testing (on CJS model) with Boundary Estimates

[epost16]

Hello everyone,

I am looking for some help understanding how to go about GOF testing with parameter identifiability problems and parameters estimated at the boundaries. I am very new to this, and apologize if I haven't quite wrapped my head around everything.

I am attempting to analyze annual survivorship in a population of turtles using a live-recapture CJS model. My data is unfortunately quite messy - it was collected from 2008-2025; however, there are 6 missed sampling occasions and several years with low survey effort (several candidate models account for this difference in survey effort). In total, the dataset consists of 516 individuals.

With ideal data, I know that GOF testing should be performed on the most general model (in my case, Phi(g*t)p(g*t), where g = sex). However, more constrained models should be tested if there are parameter identifiability problems.

Many of my parameter estimates from my most general model were suspect - estimates at either boundary with SEs of 0-1. I ran data cloning and computed profile likelihood confidence intervals followed by data cloning to investigate parameter identifiability. Based on the original data cloning, I have 15 (out of 42) parameters with potential extrinsic identifiability problems (and 4 intrinsically unidentifiable parameters). Of those 15 parameters, the profile likelihood confidence interval and data cloning exercise seem to indicate that 14 are truly being estimated near the boundaries. In some cases, this makes sense, but annual survival was often estimated at 1 which seems too high given our very low recapture rate (~10%).

On the forum, I have seen advice to fix the boundary parameters to 0 or 1 and "hold your nose".

My questions are:

1. When you fix parameters, do you include them in the parameter count? My understanding is that you don't, but when I fixed my 14 parameters and removed them from the count, my most general model suddenly became the best performing model, despite previously receiving little to no support.

2. Should I conduct GOF testing on my most general model, given that the profile likelihood CIs and data cloning suggest that nearly all of the wonky parameters are identifiable (just being estimated at a boundary)?

3. Alternatively, should I conduct the GOF testing on my most general model after having fixed the wonky parameters to 0 or 1?

Otherwise, I will use more constrained models with fewer identifiability problems for the GOF testing.

Thank you in advance for any advice you can offer!

[cooch]

There is no perfect solution (especially with missing occasions, which are always a PITA), but

1\ fixing boundary parameters will not generally change c-hat (try it and check for yourself - the quickest 'check' is to look at the Fletcher c-hat before/after fixing parameters). As such, no reason not to try te GOF on the version of your model with fixed parameters.

2\ and may help improve your estimates for the other parameters

3\ fixing a parameter will lower the parameter count by the number of fixed parameters. Simply watch the parameter count when you do, and you'll see this is the case.

As an aside, quite often I've found this problem arises when the study sampling interval is such that the true survival probability over the sampling interval really is ~1. I've often pointed out to students that the optimal sampling interval is one that is logistically feasible/practical, while also logically connected to something biologically meaningful. For example, 'annual survival' doesn't make much sense for something with a very short lifespan (e.g., a fruit fly). It might also not make much sense for something extremely long-lived (say, an elephant, where I once helped with an analysis where annual survival was ~0.99999 over the ages 12-65 years).

[epost16]

Thank you so much, this is very helpful! I really appreciate your insight about considering survivorship over longer timeframes - that makes a lot of sense!