Nest Survival: Delta method from nest age values

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Nest Survival: Delta method from nest age values

Postby rjfriendly2 » Tue Jun 28, 2022 11:40 pm

Hello,

Background information of my study design. In my process.data function I have nocc = 75, model = "Nest", groups = c("Year","Site"). I have 2 sites: 1 site has 24 years of data and other has 10 years of data.

The best supported model is DSR ~ -1 + cinit + NestAge + Site:Year.
cinit - is the initiation date and is centered.

I followed the mallard example to extract the values of interest, where I want DSR of nest ages 1-24. I used the find.covariates function and assigned 1-24 for each site and each year. the reminaing 51 values are there.

Then I created a design matrix using fill.covariates, where I ended up having a very large matrix. To get my survival estimates, I used the compute.real function and it looks something like this
topmodel.survival <- compute.real(final_top_model, design = design)[c(1:24, 75:98, 149:172.... so on)]
I did this to get the DSR for each nest age for each site and year.

Now, to get the cumulative nest success, a nest will surivive the 24 day incubation period, it is easy enough to get that product for each year and site. The problem I am having is getting the sampling variance or se for that product. I have read the sections that covers delta method in the mark book and looked at other threads on this forum. I found them to be helpful, but I'm afraid of messing things up since for nest survival models can use nestage.

When I use the compute.real, do I need to exclude the [c(1:24).. ] part to get all of the 75 estimates for each year and set vcv = true? Will this allow me to have those values to use the deltamethod.special function? I ultimately want to get the 24 day nesting success with a se or 95% CI around those points for each site and year.

I will appreciate any guidance or help!!!
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Re: Nest Survival: Delta method from nest age values

Postby jlaake » Wed Jun 29, 2022 6:35 pm

I suggest to simplify this by only computing them for each for one and site and year at a time and then computing the total survival for 24 days or the cumulative survival from 1 to 24. It gets messier if you try to do all of the years and sites at once. The only reason to do the latter is if you want to get estimation covariance bt sites/years. Try it for one site/year and compute results by hand and once you are confident it is working then you should be able to use it as a template. If you want your hand calculated example to be simpler, use just the first 5 days maybe.

Jeff
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Re: Nest Survival: Delta method from nest age values

Postby rjfriendly2 » Wed Jun 29, 2022 10:46 pm

Thanks @jlaake. I never really thought about doing them separately. I think I was thinking too hard about it. Since 5 estimates a little too much by hand I did by 3 estimates. I used the real estimates and the 3x3 of vcv matrix. The deltamethod.special resulted in having the need to square the value to get the variance. As when I did by hand calculation it resulted in the variance.
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