I'm running POPAN models on a juvenile eel mark-recapture dataset with 11 sampling occasions over seven weeks. Due to sparse recaptures between individual sampling events (~1.8% recapture rate), I created an additional dataset by pooling detections into weekly intervals and generating capture histories at the weekly scale. I ran both model sets and selected the top-ranked models based on AIC.
I'm now checking for parameter identifiability in these top-ranked models using the data cloning approach described in Appendix F of MARK – A Gentle Introduction. I cloned the data 100 times and compared the standard errors (SE) between cloned and original datasets. Because some parameters are estimated near boundaries, I also examined profile likelihood confidence intervals (CIs) to assess whether the CIs shrink under cloning—following the approach in section F.1.2.
However, I’m confused by the following paragraph from page F-8:
“You can now see that the profile interval for parameter 14 has shortened considerably for the cloned data, with the lower bound changing from 0.732 to 0.997, indicating that this parameter was actually being estimated. In other words, parameter 14 was extrinsically non-identifiable.”
To me, this seems contradictory: if the profile CI shortens under cloning, that suggests the parameter is being estimated—so how can it be extrinsically non-identifiable?
In addition, could someone clarify:
What exactly does it mean for a CI to have "shortened considerably"?
When is a parameter considered “at the boundary” such that profile CIs are required to assess identifiability?
Here are two examples from my models:
1. In my top-ranked model using the original dataset (Φ(.) p(.) b(t)), one time-dependent pent (parameter 12) looks suspicious. Given the already narrow CI of the uncloned parameter I would say the CI of the cloned parameter shortened considerably, thus the parameter is being estimated?
2. In the top-ranked model for the pooled dataset (Φ(.) p(t) b(t)), several parameters look questionable (the intrinsically non-identifiable parameter is highlighted in red). For example, parameter 10 and 11 have an SE ratio below the expected ~10 but their profile CI shorten considerably in the cloned model. The estimates are 0.95 and 0.016, which isn’t strictly at the boundary, so is it valid to infer that these parameters are estimable?
Any help interpreting these outputs would be much appreciated!