population size, SE and CI (without Delta Method)

questions concerning analysis/theory using program MARK

population size, SE and CI (without Delta Method)

Postby abadie » Tue Oct 15, 2019 3:41 pm

Hi all,

I estimated population sizes for two groups of toads (males and females) using marking-recapture data in RMark. I fitted Pollock's Robust Design to my data set, using Full Likelihood p and c model. Now, I would like to obtain the total number of adult individuals estimated in this population (males + females), as well as the standard error and confidence intervals. 
How could I access these estimates (SE and CI) without having to resort to Delta Method? Is there some alternative in Mark?

Thank you so much!
abadie
 
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Re: population size, SE and CI (without Delta Method)

Postby cooch » Tue Oct 15, 2019 4:35 pm

abadie wrote:Hi all,

I estimated population sizes for two groups of toads (males and females) using marking-recapture data in RMark. I fitted Pollock's Robust Design to my data set, using Full Likelihood p and c model. Now, I would like to obtain the total number of adult individuals estimated in this population (males + females), as well as the standard error and confidence intervals. 
How could I access these estimates (SE and CI) without having to resort to Delta Method? Is there some alternative in Mark?

Thank you so much!


The Delta method for the the variance of a 'sum' (of estimates for two groups) would take <30 seconds:

If $A=X_1+X_2$, then

$s^2_A=\mbox{var}(X_1)+\mbox{var}(X_2)+2\mbox{cov}(X_1,X_2)

But you seem to have an aversion to the Delta method, so...yes, you can use MCMC. It will take some R coding, and the like, and would be somewhat longer to implement than the Delta method (again, about 30 seconds - see above), but then you could use the term 'MCMC' in your report/paper and run with the 'cool kids'. The MCMC approach to working with derived parameters is discussed in various places in the book -- for example, addendum to chapter 14. Also in the MCMC appendix (which you'd need to study before you knew what you were doing. Probably take more than 30 seconds... ;-)
cooch
 
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Re: population size, SE and CI (without Delta Method)

Postby Bill Kendall » Tue Oct 15, 2019 5:24 pm

I thought I sent the message below before I saw Evan's response, which is a good one.

Alternatively, if you restructure your data so that sex is an individual covariate, rather than a group (assuming you have sex as an effect on at least one parameter), I believe it should generate total population size.
Bill Kendall
 
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Re: population size, SE and CI (without Delta Method)

Postby abadie » Thu Oct 24, 2019 1:18 am

Hi!!

The Delta method really took less than 30 seconds. :D

Thank you so much!
abadie
 
Posts: 2
Joined: Tue Oct 15, 2019 1:55 am


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