Calculate mean from weighted average estimates

questions concerning analysis/theory using program MARK

Re: Calculate mean from weighted average estimates

Postby constant survivor » Thu Oct 15, 2020 2:30 pm

ok. After I read Appendix D.4.3.
Here is what I tried to separately calculate mean for each sex (sex is coded in inp file as '1 0' and '0 1'):

1. build model phi(s+t)p(t) (with Design matrix)
2. select variance components real paramter estimates
3. parameter indices selected: 1 to 60
4. Design matrix specifications: user specified
5. for design matrix two columns: one for intercept (phi1-60='1', one for sex (phi1-30='1'; phi31-60='0')
6. ok

The numerical output says:

beta-hat
-----------
0.129
0.065

My conclusion: mean survival of females is 0.129. Mean survival of males is 0.065 higher.


This must be wrong. Please give me a hint.

Hannes
constant survivor
 
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Re: Calculate mean from weighted average estimates

Postby cooch » Thu Oct 15, 2020 3:28 pm

constant survivor wrote:ok. After I read Appendix D.4.3.
Here is what I tried to separately calculate mean for each sex (sex is coded in inp file as '1 0' and '0 1'):

1. build model phi(s+t)p(t) (with Design matrix)


Why that model? Should be phi(s*t)p(s*t) (you use the fully specifid model, not the most parsimonious). This model at is the default PIM-based model, which is all you need.

3. parameter indices selected: 1 to 60


Probabgly wrong, since you should (i) only include the survival parameters that (ii) aren't confounded.

4. Design matrix specifications: user specified


Correct...

5. for design matrix two columns: one for intercept (phi1-60='1', one for sex (phi1-30='1'; phi31-60='0')


This will work, but you need to correctly backtransform from the offset-coded linear model to the real paramter scale.

Far easier to simply have (i) a 2-column DM, (ii) first N rows (say 390, but I suspect thats wrong), make '1 0', and (iii) second N rows make '0 1'. This way, each column corresponds to the group, rather than and intercept and offset.

There is a discussion of this in Appendix E (the MCMC appendix) - starting at the bottom of p. 34. The idea applies equally well to variance components.


6. ok

The numerical output says:

beta-hat
-----------
0.129
0.065

My conclusion: mean survival of females is 0.129. Mean survival of males is 0.065 higher.


On the logit or sin scale, depending on your choice of link functions. You'd need to back-transform.

Please give me a hint.


Before you start messing with variance components, or MCMC, the assumption (which I pointed out) is that you're expert in design matrices, and have fully worked through Chapter 6. At which point, some of the above would be fairly obvious.
cooch
 
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Re: Calculate mean from weighted average estimates

Postby constant survivor » Fri Oct 16, 2020 4:31 am

Hi cooch,
I tried again considering your suggestions

1. build model phi(s*t)p(s*t) (with PIM)
2. select variance components real paramter estimates
3. parameter indices selected: 1-29 (males) and 31-59 (females)
4. Design matrix specifications: user specified
5. for design matrix two columns: phi1-29 = '1 0' , phi31-59 = '0 1'
6. ok

The numerical output says:
beta-hat SE(beta-hat)
-------------------------------------
0.255 0.056
0.392 0.060

At least 'more correct'?

Three general questions to me at this point:

1. Does it matter if I build the full model with PIM or with design matrix? Because obviously the outcome of VC estimation differs.

2. I am unsure about parameter indices selection for VC estimation. I know that confounded parameters should be rejected. I know about 'Addendum: counting parameters' in the book bot don't know if I got it right? I rejected phi30 (for males) and phi60 (for females) because of my assumption of them being confounded.

3. Is it correct to derive 95% CI from SE(beta-hat) of VC output?
constant survivor
 
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Re: Calculate mean from weighted average estimates

Postby cooch » Fri Oct 16, 2020 9:15 am

constant survivor wrote:

1. build model phi(s*t)p(s*t) (with PIM)
2. select variance components real paramter estimates
3. parameter indices selected: 1-29 (males) and 31-59 (females)
4. Design matrix specifications: user specified
5. for design matrix two columns: phi1-29 = '1 0' , phi31-59 = '0 1'
6. ok

The numerical output says:
beta-hat SE(beta-hat)
-------------------------------------
0.255 0.056
0.392 0.060

At least 'more correct'?

Three general questions to me at this point:

1. Does it matter if I build the full model with PIM or with design matrix? Because obviously the outcome of VC estimation differs.


The PIM-based model for phi(g*t)p(g*t) is based by default on an underlying identity design matrix, which, given your objective, is what you want. The default DM you would build using the menu option 'Design | Full' is based on the intercept-offset coding scheming, which is not what you want. This is explained in fair detail in Chapter 6.

2. I am unsure about parameter indices selection for VC estimation. I know that confounded parameters should be rejected. I know about 'Addendum: counting parameters' in the book bot don't know if I got it right? I rejected phi30 (for males) and phi60 (for females) because of my assumption of them being confounded.


At the risk of being blunt, if you don't know which parameters are confounded in a phi(g*t)[(g*t) model, then you are strongly advised to do a significant amount of remedial reading of the book before going a lot further. Specifically, chapters 3 -> 6 in their entirety.

3. Is it correct to derive 95% CI from SE(beta-hat) of VC output?


Not quite -- the SE values you're looking at at the top of the output are the SE values which including both process and sampling variation. For process variation only (which is presumably what you want), that's at the bottom. If you read Appendix D, you'll get a full introduction to this.

The problem is that the method of moments (MOM) approach being used here doesn't allow you to get a separate estimate of process variation for each mean. So, you're left with 2 alternatives: (1) use the SE estimated that included both process and sampling, accepting that they are inflated relative to process alone), or (2) use the MCMC capabilities in MARK to do what you need (appendix E).

Or, simply run males and females separately, as seaparate MARK analyses, at which point you can use MOM, and not have a DM to worry about at all. The estimates will differ a bit relative to the values you get from the joint analysis of males and females, but not by much (in my experience).
cooch
 
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Re: Calculate mean from weighted average estimates

Postby constant survivor » Sun Oct 18, 2020 6:01 am

Or, simply run males and females separately, as seaparate MARK analyses, at which point you can use MOM, and not have a DM to worry about at all. The estimates will differ a bit relative to the values you get from the joint analysis of males and females, but not by much (in my experience).


Ok thats also an option for me.

If you allow for one more question:
When doing a 'simple' VC estimation from model phi(t)p(t) with 'Intercept only' as DM spec. I get a way too low mean estimate compared to the estimates from a TSM model with a linear trend defined for TSM 2+ for the same species dataset.
I guess this is because of the 'low survival' of the transients which is not considered in phi(t)p(t)?

Shouldn't it be more plausible to build model phi(t/t)p(t) and then do the VC estimation from this model?
constant survivor
 
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Re: Calculate mean from weighted average estimates

Postby cooch » Sun Oct 18, 2020 10:04 am

Then do it for the TSM model -- whatever works for you. You simply need to keep track of the appropriate indexing (diagonal, off-diagonal) for the TSM models.
cooch
 
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Location: Cornell University

Re: Calculate mean from weighted average estimates

Postby constant survivor » Tue Nov 10, 2020 9:50 am

Hi cooch and everybody else,
I did not wanted to open a new thread for this, thats why I post this here:

Following cooch's proposal, I wanted to do a separate estimation of mean survival for males and females via the Methods of Moments (MOM) approach.
So I made a new .inp file for males only. 31 occasions.
I then built TSM-model phi(t/t)p(t).

When I try to do the VC estimation I get a message:

"WARN -- No function convergence fo upper 95% CI:365110.73"
~ I click ok ~
"WARN -- No function convergence fo lower 95% CI:816404.96"
~ I click ok ~
"ERROR -- MAtrix D was found to be not positive definite. sigma2=590756.21 (816404.96 to 365110.73)"
~ I click ok ~
"Variance components failed"


What is the problem? Sparse data? Then which alternatives do I have, because this was the way I wanted to go for calculating a mean estimate of phi.

Thanks
Hannes
constant survivor
 
Posts: 36
Joined: Wed Dec 11, 2019 12:20 pm

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