Model averaging for groups in POPAN

[TimvdS89]

Hi everyone,

I need some (rather urgent) help, so I'm hoping to find some advice here. Within POPAN, I distinguished my data into 5 age classes. When running the models, there are some models that could be chosen. When model averaging those models that have a weight, I average only the N parameter of each age class - is that ok? Then I get some averaged values per age class, all with a 95% confidence interval. My main question now is:

How can I come to the total averaged N estimation? My supervisor told me it is o.k. to sum the averaged values, but I can not sum the confidence limits. How then can I obtain a C.I. for my total average population size? Is there a section in the book I completely missed on this?

I would really appreciate any help!

Kind regards, Tim

[jlaake]

Easiest thing to do is compute total N across all age classes and its variance and then model average those values. MARK doesn't give the variance for the total, so you'll have to get the v-c matrix from the menu item Output/SpecificModelOutput/VCmatrices/real estimates. The variance of total N is the sum of all the variance components. That all assumes that you are talking about the super-population size N and not N across time. If it is N across time then you need to get the v-c matrix of the derived estimates and sum the appropriate quantities. This is a simple example of the Delta Method which is covered in an Appendix of Cooch and White. If you know R, you can look at popan.derived in MARK to see how the quantities are computed.

--jeff

[TimvdS89]

Hi Jeff,

Thanks for the reply; although, admittingly, I do not really understand. Yes, I'm trying to find the confidence interval of the super population, and not for N across time. I tried following it step by step, but I believe I got stuck somewhere. As said, I averaged some models, giving me averaged values for the different age classes. For me, these are:

N1 = 26 [20 - 31]
N2 = 59 [49 - 70]
N3 = 109 [101 - 117]
N4 = 68 [64 - 72]
N5 = 56 [51 - 61]
So: Ntotal = 318 (26+59+109+68+56), with confidence interval [? -?] (am I allowed to sum these averaged values for the Ntotal this easily?)

When opening the VCMatrix for the averaged values it looks like:



I believe this VCMatrix includes the variances of all age class, which are along the diagonal?
So, if I understand correctly, adding these values (giving me a variance = 62,56307) gives me the variance of Ntotal?

I'm guessing that at this point I've already made quiet some mistakes, but if not, does that mean my Ntotal is 318 +/- 62,56307?

I'm sorry, I'm totally at a loss when it comes to computing the confidence interval for this value...
Anyway, thanks again Jeff, but I hope you can help me out one more time!

Thanks!!

[jlaake]

The variance of a sum is the sum of the variances and covariances, so you need to sum all values in the matrix and not just the diagonal values. It won't be much different than 65 but add all of the values

Assuming normal distribution, the conf int is the estimate +/- 1.96 * std error. The std error is the sqrt of the variance which will be about 8-9 so it will be roughly 302-334. Yes you can sum the model averaged N's by class and compute the variance in that way. Alternatively, you can compute total N and its variance from each model and model average those using formulas in Burnham and Anderson's Model Selection book. Should give you roughly the same answer.

--jeff

[jlaake]

You need to sum all the elements in the v-c matrix. It won't be much different.

Assuming normal distribution, it is the estimate +/- 1.96 * std error. The std error is the sqrt of the variance which will be about 8 so it will be roughly 302-334. Yes you can sum the model averaged N's by class and compute the variance in that way. Alternatively, you can compute total N and its variance from each model and model average those using formulas in Burnham and Anderson's Model Selection book. Should give you roughly the same answer.

[cooch]

Alternatively, you can compute total N and its variance from each model and model average those using formulas in Burnham and Anderson's Model Selection book. Should give you roughly the same answer.

Said formulas explained and illustrated (by example) in some detail in the last 1/3 of Chapter 14.

[TimvdS89]

Thanks guys, this is a massive help!

One final question: when I'm not averaging the models, and still would like to compute Ntotal with confidence interval for a single model, can I follow the path: Output -> Specific Model Output -> Variance components -> Real Parameter Estimates -> select the 5 N's? Doing this gives me a single variance value.

Thanks a bunch!

Tim