Non-estimability

[Eurycea]

Thank you for your response.

Say you didn't care about N, for example, and were concerned more with testing whether p(t)=c(t) was a better model than p(t) c(t), having no prior biological information to support either model.

Then simply fit those models. At least 2 suggestions were made earlier in this thread -- either put some sort of constraint on terminal p and c, or perhaps try an additive model.

As an aside, showing some time-variation in say p or t, relative to a model where p(t)=c(t), is of marginal interest (as are time-dependent models in general). The question of interest is *why* do things vary over time -- not that they do. Of course they vary over time. They may not vary in a biologically significant way, or in a way detectable given the limits of a particular data set, but they do vary. So, suppose you find support for a temporally varying model versus a more constrained parameter reduced model. The next question would be "so what?". By itself, such a demonstration is of little value. As mentioned, it is *why* things vary over time that is of interest. So, a Huggins model with estimates constrained by relevant covariates (contrasted against other models) might be a good start to getting at the *interesting* question.

I agree and I will hopefully get to that step. At the risk of totally hijacking this topic, I'll say that in my work, a robust design is being used- I get different results for type of temporary emigration depending on how much time variation I put in the p/c models to test. I don't know why this occurs and is contrary to what I expected. However, I think it behooves me to try some different time-variance configurations of p/c if a p(t) c(t) model gives me a different result than a p(t,t) c(t,t) model... thus the interest in correctly (or most best-est way of) specifying such a model with confounded parameters is related to identifying the type of temp. emigration.

As a further aside, I'd have to work pretty hard to imagine why there would be much interest in whether or not probability of initial capture (p) differed from probability of subsequent capture, conditional on having been previous captured (c). Suppose they did (say, if individuals were trap happy following initial capture). What would you use this information for? I could see some uses in terms of modifying/improving/understanding sampling structures, but beyond that. I can't even recall a publication using closed abundance estimators where focus was in p/c, and not on N. Of course, only JDN has read all the papers, so my not having seen one should be taken with several grains of salt.

Another interest in why initial capture is different from subsequent capture relates to the method of capture. All cover objects are removed and the study site is pretty much well sifted through for an aquatic salamander. Suppose this in some way reduces capture probability, but is not reflected in just the marked individuals, but all individuals. So not necessarily conditional on having been captured, but present in the sampling area. This could have an impact on choosing another method of survey in the future, such as repeated count sampling, or presence-absence sampling, as another way to estimate detection or sampling error.

Nate

[cooch]

...a robust design is being used - I get different results for type of temporary emigration depending on how much time variation I put in the p/c models to test. I don't know why this occurs and is contrary to what I expected. However, I think it behooves me to try some different time-variance configurations of p/c if a p(t) c(t) model gives me a different result than a p(t,t) c(t,t) model...

Trying different models simply because they give you different results (regardless of whether or not they 'meet expectations') is not much more than data dredging. You specify the candidate model set, based on plausible model structures, and go from there. Running some models, looking at the results, then trying some other models, is generally a 'no-no'.

[Eurycea]

...a robust design is being used - I get different results for type of temporary emigration depending on how much time variation I put in the p/c models to test. I don't know why this occurs and is contrary to what I expected. However, I think it behooves me to try some different time-variance configurations of p/c if a p(t) c(t) model gives me a different result than a p(t,t) c(t,t) model...

Trying different models simply because they give you different results (regardless of whether or not they 'meet expectations') is not much more than data dredging. You specify the candidate model set, based on plausible model structures, and go from there. Running some models, looking at the results, then trying some other models, is generally a 'no-no'.

It's not data dredging if they were in my candidate model set, which they both were. The fact that they give different results means I need to make sure I specified them correctly, hence the initial question. But if the different time variation of p/c gives different results for other parameters that result in a different interpretation of a biological phenomenon, it seems to me that the time variation in p/c is therefore of importance, not to mention my other point. It is curious to me though, because other studies will conclude things about the type of temporary emigration with certain parts of their model constrained based on less than rock solid reasoning. What if they tried a larger model set, or used a different "model selection procedure"? Draw a different conclusion? How good is that conclusion then?

Nate