Additive or Independent model for survival

[msrentz]

Hello all: I hope this is in the right place. I am doing my analysis in RMark, but my question is a bit more global.

I have a set of data with mark-recapture of small mammals across 3 years, with collection May-November. I am doing a Robust design, and in general the Robust models with heterogeneity give good, reasonable estimates. I have 3 locations, each of which is divided into 3 treatments. The goal is to compare survival rates and population between the treatments over time (as they are treated).

I have run basically the same model with S ~treatment * t.gap (primary period) and S ~treatment + t.gap and get similar but differing (in a very meaningful way) results. In general the additive model makes good biological sense, but does it still allow me to compare survival between the treatments? In general, I think survival will be a function of treatment and time of the year, I am just not sure if that means "treatment + time of year" or "treatment * time of year".

I hope this question is not too basic, I have just tied myself in knots and am looking for more opinions.

Mike.

[msrentz]

All: I was able to get some help with this off-line. Please consider it closed. Main finding: do not constrain parameters if thou art comparing them between treatments, and + was so constraining.

Mike.

[jlaake]

I interacted with Mike offline because I was concerned that his last message might leave some with the wrong impression. An additive model can be used to evaluate treatment effects but you should always consider the possibility of interactions as well. As additive model does constrain the parameters but that may be quite reasonable depending on the situation. In his case with a BACI design it was the interaction of the treatment across year that is of interest but even then there are several formula that can be evaluated.

[msrentz]

Revisiting this as I am still having issues: Both additive and independent models come up with very similar estimates of N, but very different estimates of S. This concerns me as they differ enough to differ in which hypotheses they support. Of primary concern at least logically, is that additive models will produce an estimate of S even for periods in which the first session has an estimated population of 0 (or as RMark tells me X to the negative large number).

Independent models generally allow for greater variability in S, including values with very low numbers (10 to the negative 6) when the beginning session has no animals.

Generally, the models seem to have similar deviance scores, leading to the less parameterized additive models to win out for AIC. The working advice is to allow AIC to choose the better model between additive and independent, but again, my concerns above.

Perhaps more importantly, I am also having considerable trouble getting models to converge, so I may have more global issues as well, which could in part be helped as soon as I learn how to fix N for some time/group combinations. But that is for another line of questions.

[cooch]

...which could in part be helped as soon as I learn how to fix N for some time/group combinations. But that is for another line of questions.

Well, I can 'stop you here' before you go too far down that road. There is no way in MARK that you can put a logical constraint on population size (say, equality of N over treatments). There is a relatively simple reason. From p. 7 of Chapter 14 of 'the book' *closed population abundance chapter):

You need to think carefully before applying constraints to N, since in fact, N isn't in the likelihood - MARK uses f(0), and N is estimated as a derived parameter. As such, despite what you might think, if you try to constrain N, you're really constraining f(0), which may not make good sense. Consider two locations, and you think you're building a constrained model where you set N_1=N_2 in the DM. Unfortunately, what you're really doing is setting f_(0,1)=f_(0,2). Does it really make sense to say that the number never caught (f(0)) is the same in the 2 locations?

In other words, applying a constraint to N in fact means you're applying a constraint to f(0), which generally (almost always?) makes no biological sense. Meaning, in effect, you can't apply a constraint to N. As for why MARK uses F(0) and not N in the likelihood, consult Chapter 14.

[msrentz]

Well, as the kids say these days <head-desk> Thanks for the warning/reminder. I got so buried in naming individual trees I forgot the forest, including the issue you point out. Given that I was trying to constrain the population to 0 to reflect an utter lack of captures of that species it seems reasonable on the surface, but I understand the issue. Thanks again for stopping me