modelling transients

[Eleni Papadatou]

Hi everyone,

I would greatly appreciate any help with this, as I am rather getting confused!

I am trying to model the adult population of a bat species (single-state). I have seven occasions, each representing a season. I ran GOF of simple CJS model in UCARE separately for the group of females and the group of males, and found a significant result on transients for females only, i.e. test 3.SR was not significant, but the test for transients was.

My questions concern initial global model I should use and how estimate a c-hat for the global model.

So…should I use a global TSM model for both groups ie taking into account transients for both females and males, although males did not have a significant transient affect? In which case, the model would look something like: phi(sex*a2-t/t)p(sex*t).
Or would it be better if I started with a model not taking into account transients for males? In which case it would look something like: phi(female*a2-t/t,male*t)p(t).
In fact, I assessed best model fit for females only and the best one was phi(a2-c/c)p(t), so I thought I could use phi(female*a2-c/c,male*t)p(t) as a global model, which again I am not sure if it is right.

Given initial model has been decided, which GOF would be best applied and how would estimate c-hat?
I know that GOF accounting for transients is done by adding component test results minus test 3.SR and this is c-hat estimate is based on this, but I am a bit confused as to how to apply this in my case.

Thanks very much for your help in advance

[cooch]

...
My questions concern initial global model I should use and how estimate a c-hat for the global model.

So…should I use a global TSM model for both groups ie taking into account transients for both females and males, although males did not have a significant transient affect? In which case, the model would look something like: phi(sex*a2-t/t)p(sex*t).

Well, to some degree, you've 'put the cart before the horse' - what is your a priori expectation for the presence/absence of transients in this system? Is there any reason to expect transients in one sex, or another?

The general model should be one that is biologically plausible, but sufficiently parameterized to fit the data. If you believe there may be transients in the data (which you obviously do, otherwise you wouldn't be looking for them), then a TSM model for both sexes as a general model seems like the appropriate starting, general model. The fact that you subsequently find that there are 'no transients' in males doesn't change the utility of this starting model - most (all) general) models are over-parameterized, but they do fit the data, which is the point.

So, I'd suggest a TSM model for both sexes, and then derive your estimate of c-hat for this model. How best to do that is up to you - you can (and probably should) compare/contrast estimates from RELEASE, U-CARE, and the median c-hat approach. Undoubtedly, they'll all differ - at which point you have the philosophical choice of preference of being overly liberal (taking the lower c-hat of the three) or potentially being overly conservative (by taking the higher c-hat of the three).

[Christian Ramp]

Hi Evan

Sorry to come back to this subject, but I still have a couple question about the GOF testing/c hat business.

As in Eleni’s case my CJS model gets rejected, by TEST3 components. The chi2 value of TEST.3Sr is huge, while TEST3.Sm is slightly under the significance level.
That makes sense I do have calves (higher mortality) and transients in my data set.
Removing the calves first sighting (not independent observation since they follow their mothers) moves TEST3.Sm slightly over the 5% level, but TEST.3Sr is still rejected.

I followed both methods suggested by Pradel – the ad hoc method of left truncating the data set, and as he suggests the age class model phi (2a*t) p(t).

The latter one has to be tested if it (as the ‘new’ general model) fits the data adequately well. So far so good, but how?

Eleni mentioned in the first message that one subtracts the chi2 values of TEST.3.SR from the overall chi2 value to get a test result plus a c hat estimate? This is the first time I have heard this. If this is so, where is this described in detail?

What about the LRT approach as mentioned in Pradel’s paper (also used by Lebereton et al 92)?
I tested the (rejected) CJS as the reduced model against my new more general model phi(2a*t) p(t) and it got rejected (chi2=163, df=14, p<0.0001).
My pooled test results (RELEASE) for the CJS were chi2= 180, df=44, whereas TEST3.SR already accounted for 136 of the chi2 value alone. Unless I got everything wrong, subtracting the LRT values result in a non significant GOF test and c hat <1.

Is that O.K.?

The alternative – the ad hoc method by Pradel (deleting all first sightings of all animals) – basically gave me the same result. Although the overall GOF test was fine (0.2) TEST3.SR was still significant (0.02) and the c hat was 1.22. Estimates (and SE/CI) of both approaches were up to the 4 decimal identical.

Which way is preferable?

And a last one, is there any further description of the ‘median c hat’ option in MARK, I have to admit I was lost with the help file description.

Thanks in advance.
Christian

[cooch]

I'd suggest both of you read Chapter 5 thoroughly (not claiming it is perfect, or a complete treatment of the subject of GOF testing - far from it). But, a large number of your questions are answered there.

The estimation of 'fit' has two purposes: (1) how good (or poorly) does my general model fit the data - and what is a measure of any lack of fit (the ubiquitous c-hat), and (2) why does the model not fit? The c-hat is used in a quasi-likelihood adjustment of whatever statistics you use (regardless of your paradigm - P-value or AIC). You coul, if you choose, estimate c-hat, and simply apply it, and not worry about why your model has some lack of fit. This is quite commonly done.

Using RELEASE (or the equivalent) can generate an estimate of c-hat (often involving some algebraic gymnastics of this test minus that test and so forth), and as such, may not be the most efficient way to generate an estimate of c-hat.

However, things like the bootstrap, or the median c-hat, only provide an estimate - nothing more. The main utility of RELEASE (in my opinion) is that it allows you to look at your data in detail. It (and U-CARE, which is really an extension to RELEASE) provides LOTS of details on why there is lack of fit, and where it is occuring. The standard diagnostics for transience, for example, can be done in terms of looking at the cohort-specific contingency tables that RELEASE or U-CARE both generate.

Again, all of this is covered in Chapter 5. And, again, I commend you to read it through. The fact that you mentioned the 'help file' as a starting point suggests that you perhaps haven't read the documentation.