POPAN B*hat / N*hat results - "Not a number"

[jma803]

I have run several subsets of data in POPAN in an effort to obtain N*hat.

On several (but not all) of my phi(t)p(t)pent(t)N(t) models, one occassion of my B* hat reads "Not a number," and my N*hat also reads "Not a number." (I'm assuming the N*hat can't be computed because of the B*hat issue). If I run the model as a phi(.)p(t)pent(t)N(t) I do not encounter this issue so it doesn't seem like it's my data that's the problem.

If anyone can shed some light on this issue I would appreciate it!

[cooch]

I have run several subsets of data in POPAN in an effort to obtain N*hat.

On several (but not all) of my phi(t)p(t)pent(t)N(t) models, one occassion of my B* hat reads "Not a number," and my N*hat also reads "Not a number." (I'm assuming the N*hat can't be computed because of the B*hat issue). If I run the model as a phi(.)p(t)pent(t)N(t) I do not encounter this issue so it doesn't seem like it's my data that's the problem.

If anyone can shed some light on this issue I would appreciate it!

For many data types (not just POPAN), not all parameters are identifiable with fully time-dependent models, whereas, imposing a constraint on one or more structural parameters can sometimes resolve others. Notice in your case you're contrasting a time-dependent model (with the identifiability problem) with a 'dot' model, where things are identifiable. Your 'dot' model imposes a constraint on phi, which will change identifiability of other parameters.

[jma803]

Thanks Evan.

Are the other results from the time dependent model still reasonable? i.e. just because one occasion of the B*hat cannot be identified, does this affect the interpretability of the other results?

[cooch]

Thanks Evan.

Are the other results from the time dependent model still reasonable? i.e. just because one occasion of the B*hat cannot be identified, does this affect the interpretability of the other results?

We generally distinguish between parameters which are structurally non-identifiable, and those which may not be identifiable because of the data (in some fashion). What you need to do is look carefully at the chapter for the POPAN model (and the MARK helpfile_ to determine which parameters (if any) are structurally not identifiable. Once you know those, then you can better intret what you have. Also, there are often various constraints that people impose on some structurally non-identifiable parameters to reduce/eliminate bias in remaining parameters. Again, same point applies.

[cschwarz@stat.sfu.ca]

A NsN in B* is usally the result of a division by zero.

Are you sure you are interested in the B* (the gross births)? These are obtained from the B's by "inflating" them by a function of the survival rate (refer to the relevant chapter in GIM or my paper in CJFAS in 1993 on estimating escapement).

For "uniform" survival between intervals, the expansion factor is log(phi)/(phi-1). If phi-hat is 1, then you have 0/0 which is undefined. In actual fact, the limit as phi approaches 1 should be 1 which results in B* equal to B. You could try fixing the survival rate to .9999 which should led to a valid estimate of B*.

Check to see if the estimated phi for that interval is 1. A value of 0 also causes problems because then everything must die between occasions and then it is not clear how new animals can enter the population.

If that doesn't work, please send me the *dbf and *fpt files so that I can have a closer look. [I'm currently off teaching a workshop on Bayesian mehods for Ecologist so won't actually look at it until next week.]

Carl Schwarz