Confounding pent

[TimvdS89]

Hi everyone,

Novice here looking for some help...

I get a confounding parameter estimate for the probability of entry for occasion 3, see picture below, and I cannot understand why. Background story: 4 years of capture-recapture data on Risso's dolphin data, and I'm interested in knowing the super-population sizes of males (n=125) and females (n=113) over these four years. The best fitting model I get is phi(.)p(s*t)pent(s*t), however, as shown, pent for occasion 3 seems to be confounded, and, consequently influencing my population abundance (I think). Changing the 'pent' to be time-specific (t), sex-specific (s) or constant does not yield better results. I've gone through my data, but cannot find any problems with it.

As there are two groups, and 4 occasions (i.e., 3 probabilities of entry per group), the first three pents are MLogit(1), and the final three pents I did MLogit(2).

Does anyone know what I'm doing wrong? Any help is greatly appreciated!!

Thank you in advance!

- Tim

[TimvdS89]

Hi everyone,

Small update: I've now also fitted a model with an additive effect of sex and time (s+t) on the probability of entry. This has resulted in no parameter estimates being confounded (which is good I suppose!), however, with a much larger AIC value. Could someone explain to me what in this case would be the more appropriate model; the one that has a lower AIC value, but more confounding parameters, or the model without confounding parameters but a higher AIC value?

Again, thank you in advance for any help!!

- Tim

[cooch]

Hi everyone,

Small update: I've now also fitted a model with an additive effect of sex and time (s+t) on the probability of entry. This has resulted in no parameter estimates being confounded (which is good I suppose!), however, with a much larger AIC value. Could someone explain to me what in this case would be the more appropriate model; the one that has a lower AIC value, but more confounding parameters, or the model without confounding parameters but a higher AIC value?

Again, thank you in advance for any help!!

- Tim

Parameter probably isn't confounded, but simply cannot be estimated due to extrinsic limits in the data. You can check this by using the data cloning option (Appendix F in the MARK book). The reason it seems estimable when you fit an additive model is that the additive model takes the estimates from one group (which is estimable0 and applies an additive constant to the other estimates. Its the same constant for all time intervals, so thats why the final pent is now 'identifiable'. This is more or less analogous to what would happen if you fit a model with two groups (sexes), but constained pent to be a constant over time, or a function of a covariate.

[TimvdS89]

Thank you very much for your quick reply! I have tried cloning the data, but from the results (see below), it would appear that there is a problem with the parameter identifiability of this final pent (SE ratio is 13,62). It looks like the parameters is extrinsically non-identifiable, but I believe this also has implications for the population abundance of N2. Any ideas or suggestions on how I can account for this? I am a little uncertain whether this means there is a flaw in my data or my model selection, or where in the process I have to make the corrections.

Again, many thanks in advance!

[cooch]

Thank you very much for your quick reply! I have tried cloning the data, but from the results (see below), it would appear that there is a problem with the parameter identifiability of this final pent (SE ratio is 13,62). It looks like the parameters is extrinsically non-identifiable, but I believe this also has implications for the population abundance of N2. Any ideas or suggestions on how I can account for this? I am a little uncertain whether this means there is a flaw in my data or my model selection, or where in the process I have to make the corrections.

Again, many thanks in advance!

Several comments

1\ estimates of N from open populations are twitchy at best, verging on silly at worst.

2\ you don't make inference from a single model, but over multiple models -- and said model set should include only models where parameters are estimable -- meaning, it would seem in your case, dropping the full sex*time model from the candidate model set.

3\ the problem is that your data aren't insufficient to support the fully time-dependent model with interactions. Pure and simple. So, don't use that model.

[TimvdS89]

Ok, great, thank you very much!