Robust design, time between sessions varying between sites

questions concerning analysis/theory using program MARK

Robust design, time between sessions varying between sites

Postby Tom.B » Wed Sep 04, 2013 1:17 pm

Hi all,

I'm working with Pradel RD models and have data from 12 primary sessions and three sites. I want to examine differences in fecundity and survival between sites. Sites were trapped sequentially in a random order each session, meaning that time between sessions can vary by up to about 50% for a particular 'open' interval.

If I combine the data from all three sites and specify, say, the mean time between sites or the time between finishing the last site and starting the first one in the next session as my open time period lengths, can I then correct for the differences in time lengths simply by multiplying the monthly Phi and f values and associated CIs for each site by the appropriate differences?

ie, if the time between two sessions is 1.5 time greater for one site than the time specified when processing the data, can I just multiply the Phi and f values and CIs by 1.5?

Thanks,
Tom
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Re: Robust design, time between sessions varying between sit

Postby jlaake » Wed Sep 04, 2013 1:31 pm

Tom-

Not sure about your suggestion. One way to handle this is to extend your capture histories such that each section of the capture history is for a particular site and then constrain parameters for the dummy portions of the capture history. For example, with 3 sites for a CJS style with 4 primary occasions it might be as follows for site 1,2,3

100100000000
000011010000
000000000111

For each capture history only 4 occasions are data and the rest are dummy data for which you would have to constrain parameters. But this approach would let you set the time intervals for each site differently.

Another approach is to use unit time intervals but use the actual time interval as a covariate with a log-link. That can have issues with survival > 1 so you might want to use annual time intervals to lower S and get it away from the boundary even further.

--jeff
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Re: Robust design, time between sessions varying between sit

Postby Tom.B » Wed Sep 04, 2013 1:50 pm

Thanks very much Jeff, that makes sense. With your first suggestion I'm struggling to envisage how I'd constrain different sections of the CH for different sites - any suggestions? (using RMark).
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Re: Robust design, time between sessions varying between sit

Postby jlaake » Wed Sep 04, 2013 2:08 pm

You'll have to think about that carefully. For CJS, you would set Phi=1 and p=0 for the dummy occasions. Gets a little messier with a Robust Design and there may be several ways to do it. Essentially you want to set the parameters in such a way that there is no information in the dummy portion of the data and you want it so that it doesn't influence the parameters you are estimating. One way to constrain parameters with RMark is to create a dummy 0/1 variable and use it as an interaction with all of the parameters that are being estimated. It would be 0 where there was dummy data and 1 where there is real data and that could vary by time for the various sites.

With the newest version of RMark on CRAN you can now set fixed parameters by creating a field called fix in the design data and add the real value for those you want to fix and NA for those that are estimated. For example with my dummy CJS example with 12 occasions and 3 sites, if I used site as a group factor, then I could do something like the following after ddl=make.design.data(...) with begin.time=1

ddl$Phi$fix=NA
ddl$Phi$fix[ddl$Phi$site==1 & ddl$Phi$time%in%4:11]=1
ddl$Phi$fix[ddl$Phi$site==2 & ddl$Phi$time%in%c(1:4,8:11)]=1
ddl$Phi$fix[ddl$Phi$site==3 & ddl$Phi$time%in%1:8]=1

ddl$p$fix=NA
ddl$p$fix[ddl$Phi$site==1 & ddl$Phi$time%in%5:12]=0
ddl$p$fix[ddl$Phi$site==2 & ddl$Phi$time%in%c(1:5,9:12)]=0
ddl$p$fix[ddl$Phi$site==3 & ddl$Phi$time%in%1:9]=0

It would be different for Pradel because it estimates p for the first occasion where CJS does not.

It would be nice if MARK allowed different time intervals for each group and then you could make each site a group, but I don't believe that is possible.
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Re: Robust design, time between sessions varying between sit

Postby cooch » Wed Sep 04, 2013 2:13 pm

Another critical issue is that gamma parameters aren't interpretable -- at least, not without *strong* assumptions, and great care -- if the intervals between primary occasions vary. See, for example, section 15.9 in the RD chapter.

http://www.phidot.org/software/mark/doc ... chap15.pdf
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Re: Robust design, time between sessions varying between sit

Postby Tom.B » Wed Sep 04, 2013 2:41 pm

cooch wrote:Another critical issue is that gamma parameters aren't interpretable -- at least, not without *strong* assumptions, and great care -- if the intervals between primary occasions vary. See, for example, section 15.9 in the RD chapter.

http://www.phidot.org/software/mark/doc ... chap15.pdf


Hi Evan, thanks for weighing in.

I'm using "Robust Design Pradel Recruitment Huggins' Closed Populations" (RDPdfHuggins) models, having re-read 15.9 am I correct in thinking that the Phi's will have been time corrected, but not the f's?
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Re: Robust design, time between sessions varying between sit

Postby Tom.B » Thu Sep 05, 2013 9:34 am

jlaake wrote:With the newest version of RMark on CRAN you can now set fixed parameters by creating a field called fix in the design data and add the real value for those you want to fix and NA for those that are estimated.


Brilliant, that did it. I struggled a little to get your code working for my data then decided to kept it simple and just coded everything according to parameter index values and it seems to have worked.

I'm still rather concerned about whether or not Evan's comment about interpretability applies to fs in RDPdfHuggins models.
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Re: Robust design, time between sessions varying between sit

Postby Tom.B » Fri Sep 06, 2013 8:18 am

Right, what I hope will be a last question;

I'm really struggling to figure out which parameters I need to constrain in order to fit time dependent models to more than one parameter. Phi~time.f~dot and Phi~dot.f~time models both run fine, but I can't get Phi~time.f~time to produce anything sensible. Similarly, models with time + group effects on a single parameter aren't working either.

I tried using constant p=c detection parameters as per the (non-Robust) example in 13.4 but that didn't work either.

Is it the first p and first f which are confounded? Do I need to set them equal to the second session using bins?

EDIT - I fixed first two fs and last two Phis and it seems to work for Phi~time.f~time model, although time+group effects still aren't working.

EDIT 2 - just realised that the time models already include site effects because of the way times are coded with the dummy capture occasions. D'oh! So now I need to figure out how to constrain different bins to be the same to test for a site effect (thinking out loud is really embarrassing).
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Re: Robust design, time between sessions varying between sit

Postby cooch » Fri Mar 16, 2018 4:04 pm

jlaake wrote:Another approach is to use unit time intervals but use the actual time interval as a covariate with a log-link. That can have issues with survival > 1 so you might want to use annual time intervals to lower S and get it away from the boundary even further.


I just remembered that the log link and its possible use in handling missing/unequal intervals is in 'the book' -- chapter 4 (section on unequal intervals/missing occasions). But, I didn't deal with (because I hadn't thought of it) the issue that Jeff brings up (my 'examples' were based only on the simple case of - say - a single missing occasion, amounting to an single 'unequal' interval out of a time series.)
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Re: Robust design, time between sessions varying between sit

Postby jlaake » Fri Mar 16, 2018 4:48 pm

Just happen to be working with someone on this type of problem with someone. The log-link works great as long as you construct the design matrix correctly. In RMark lingo, you need to exclude the intercept and interact the interval covariate with each other variable you are including for survival. The reason the log link works is because of the following:

$exp(beta*interval)=exp(beta)^{interval}=S^{interval}$

The above is equivalent to formula=~-1+interval in RMark. But if you want to say have a sex effect you would need to use a formula=~-1+sex:interval which would create an algebraic relationship like

For females
$exp(betaf*interval)=exp(betaf)^{interval}=S^{interval}$

For males
$exp(betam*interval)=exp(betam)^{interval}=S^{interval}$

Or if you specified as intercept + male effect it would be formula=~-1+interval+male:interval which would be

For females
$exp(beta0*interval)=exp(beta0)^{interval}=S^{interval}$

For males
$exp(beta0*interval+betam*interval)$=exp(beta0+betam)^{interval}=S^{interval}

Either works but the key is that there isn't a beta that isn't multiplied by interval. If that was allowed to happen then the algebra above doesn't work.

Hopefully I just didn't repeat what you had in ch 4.

--jeff
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