Calculate mean from weighted average estimates

[constant survivor]

Hello again,
I have 29 weighted average estimates from model averaging (29 year-to-year intervals).
I want to calculate a mean out of these estimates with corresponding SE and CI.

How can I do that?

If you need more information on the background please just tell me.

Thanks and kind regards
Hannes

[cooch]

Appendix D - random effects. There is a demonstration of the basic idea in Chapter 6. Full details in Appendix D.

[cooch]

Section 6.15 in Chapter 6 shows an example of calculating the mean over time intervals. While it is possible, in theory, to derive a mean over the model averaged values, you don't want to. The model averaged estimates are analogous to shrinkage estimates, the the random effects approach described in 6.15 shows you the best way to get an average over those estimates.

[constant survivor]

Hi cooch,
thanks for reply. Your written lines are a little bit confusing but if I got it right, then the 'design matrix approach' from section 6.15 is not the right thing here. Instead I should go with the random effects approach described in Appendix D, right? Too bad, because this seems horribly complicated at first glance...

Best
Hannes

[cooch]

Hi cooch,
thanks for reply. Your written lines are a little bit confusing but if I got it right, then the 'design matrix approach' from section 6.15 is not the right thing here.

Correct.

Instead I should go with the random effects approach described in Appendix D, right? Too bad, because this seems horribly complicated at first glance...

As compared to the Delta method approach which is your alternative? Not really. For what you want, its actually pretty simple. If you simply apply the example steps from Chapter 6 to your problem, its pretty easy. If you want to *understand* what you're doing, Appendix D.

[constant survivor]

As compared to the Delta method approach which is your alternative? Not really. For what you want, its actually pretty simple. If you simply apply the example steps from Chapter 6 to your problem, its pretty easy. If you want to *understand* what you're doing, Appendix D.

Which 'example steps' do you mean? are we talking about the same thing: section 6.15 "A final example: mean values" ??

This is what I referred to as 'design matrix approach'. And you said, it's not the way to go. I'm confused.

Or should it be a combination of 6.15 and random effects models?

[constant survivor]

ok, sorry! I should've read the side bar in section 6.15 right?!

[cooch]

ok, sorry! I should've read the side bar in section 6.15 right?!

Section 6.15 contains the -sidebar-, so..yes. Starting near the top of p. 100.

[constant survivor]

As expected this raised some questions for me.

Maybe some general info about my data first:
31 occasions (year-to-year); two groups (male/female); estimation of apparent survival rates for adult breeding birds of seven species; live recaptures; all of my 'best' models are TSM models; most of the 'candidate model lists' for each species include a trend model and additionally sex as factor for phi -> when I am model averaging, this leads to 29 different estimates for TSM class 2+ for each sex; it is these different estimates that I want to 'summarize' into a mean estimate...

1.) Maybe not that important here, just for info: when running the calc_mean.inp dataset (exercise data), I got slightly different estimates as written in the book. My book version is the 19th edition...

2.) If I got it right, I should use the variance components approach as described in the side bar of section 6.15. Which model should I use (i.e. retrieve before doing the variance component estimation) ? Should it always be phi(t)p(.)? Because obviously the outcome differs when for example phi(t)p(t) is used.
I think phi(t) is fixed in this regard (?) but what about p?

3.) How to obtain mean values for males and females separately?


Maybe so far
Thank you so much
Hannes

[cooch]

1.) Maybe not that important here, just for info: when running the calc_mean.inp dataset (exercise data), I got slightly different estimates as written in the book. My book version is the 19th edition...

I believe that was corrected in the 20th edition (you should always check against the online version of a chapter, since it is always more recent than a printed version).

2.) If I got it right, I should use the variance components approach as described in the side bar of section 6.15. Which model should I use (i.e. retrieve before doing the variance component estimation) ? Should it always be phi(t)p(.)? Because obviously the outcome differs when for example phi(t)p(t) is used.
I think phi(t) is fixed in this regard (?) but what about p?

In general, you should use phi(t)p(t). Applying a constraint to (say) p (say, p(.)) also implicitly constrains the phi(t) shrinkage estimates, biasing them slightly relative to 'truth'.

3.) How to obtain mean values for males and females separately?

Time to start reading Appendix D. Example described in section D.4.3 is largely equivalent. It does presume some familiarity with the design matrix, though.