General model for variance components

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General model for variance components

Postby violetblue » Tue Jul 20, 2021 5:17 am

Hi, I hope someone is able to give me some guidance.

I have a 16 year dataset (2005-2020) modelled with a 2-state MSORD model.

The models I have run so far (see descriptions below);
Code: Select all
2                S(~-1 + ageclass)Psi(~-1 + to1 + to2:time)pent(~-1 + time:session:stratum)Phi(~four_a:session:stratum)p(~-1 + time:session:stratum)

3                   S(~res:time)Psi(~-1 + to1 + to2:time.c)pent(~-1 + time:session:stratum)Phi(~four_a:session:stratum)p(~-1 + time:session:stratum)

5                  S(~-1 + time)Psi(~-1 + to1 + to2:time.c)pent(~-1 + time:session:stratum)Phi(~four_a:session:stratum)p(~-1 + time:session:stratum)

4 S(~-1 + trans:time + res:time)Psi(~-1 + to1 + to2:time.c)pent(~-1 + time:session:stratum)Phi(~four_a:session:stratum)p(~-1 + time:session:stratum)

  npar     AICc  DeltaAICc weight Deviance

2  226 180046.1    0.00000      1 179591.4

3  238 180116.3   70.24379      0 179637.3

5  238 180185.4  139.38379      0 179706.5

4  252 180310.0  263.91590      0 179802.6

S(~-1 + ageclass) has 2-ageclass (transients and residents) constant survival
S(~res:time) has time-varying resident survival, constant transient survival
S(~-1 + time) has time-varying survival, no ageclasses.
S(~-1 + trans:time + res:time) has time-varying resident and time-varying transient survival
‘time.c’ indicates the final two psi are constrained so that all S can be estimated


Question 1: it really necessary (or correct) to use a model that is fully time-dependent in all parameters to estimate variance components, when not all parameters can be estimated correctly?
It seems with such highly parameterized models this could often be the case.


For example, model S(~-1 + trans:time + res:time) is the most time-dependent model above.
Several of its transient survival parameters are on the boundary (and this is even with some of the psi being constant). Should I use S(~-1 + trans:time + res:time) for the tasks below?

Task One
The most support is for the constant Survival (2-ageclass) model, but as we would like to monitor annual resident survival, I would like to fit a random effects model that could be an intermediate between S(~-1 + ageclass) and S(~res:time), using ‘S-tilde’ and RMSE as the annual estimates.

Task Two
Find the mean and variance (without sampling variation) of the first 3 resident survival estimates i.e. 2006-2007, 2007-2008, 2008-2009 (transient survival is 2005-2006).(I realise finding the mean and variance of only 3 estimates could be misleading, but it’s all the data we have).
Beta-hat being the mean, and CIs using ‘Estimate of sigma’ process variance.

Question 2: I would also like to test for a trend in abundance in the last 11 annual estimates. It looks as though I can’t compare a model with and without a trend because it is not possible to run a Random Effects ‘Linear Trend’ model on derived parameter.
Is there anything else I can do?


Thank you
violetblue
 
Posts: 23
Joined: Tue Nov 06, 2018 11:16 pm

Re: General model for variance components

Postby cooch » Tue Jul 20, 2021 8:10 am

violetblue wrote:Hi, I hope someone is able to give me some guidance.

I have a 16 year dataset (2005-2020) modelled with a 2-state MSORD model.


I've edited out the RMark-specific model syntax, since (i) this isn't the RMark sub-form, and as such (ii) the model specification will not be generally interpretable to people who don't use RMark.

S(~-1 + ageclass) has 2-ageclass (transients and residents) constant survival
S(~res:time) has time-varying resident survival, constant transient survival
S(~-1 + time) has time-varying survival, no ageclasses.
S(~-1 + trans:time + res:time) has time-varying resident and time-varying transient survival
‘time.c’ indicates the final two psi are constrained so that all S can be estimated[/size]


But, I'll leave the above in, since the 'verbal' translations are interpretable, generally.

Question 1: it really necessary (or correct) to use a model that is fully time-dependent in all parameters to estimate variance components, when not all parameters can be estimated correctly?
It seems with such highly parameterized models this could often be the case.



All parameters in a biological context vary over time. Whether or not you can detect time variation is a function of the quality of the data set. If you can't fit a time-specific model to a given set of data, then this is diagnostic of limits of the data, and by extension, limits of the inferences you can make from those data. The theory underlying the method-of-moments (MoM) approach to RE assumes mu and sigma are estimated from a model where none of the parameters are constrained. You can, of course, estimate mu and sigma in some cases from constrained models, but the validity and interpretation of those parameters is potentially problematic.


Task Two
Find the mean and variance (without sampling variation) of the first 3 resident survival estimates i.e. 2006-2007, 2007-2008, 2008-2009 (transient survival is 2005-2006).(I realise finding the mean and variance of only 3 estimates could be misleading, but it’s all the data we have).


Substitute 'meaningless' for 'misleading'. At minimum, you need 8-10 values for MoM to yield reliable estimates of mu and sigma (I believe Ken Burnham is now actually advocating something closer to 15). It may be all the data you have, but that is not justification for trying to squeeze blood out of a turnip.

Question 2: I would also like to test for a trend in abundance in the last 11 annual estimates. It looks as though I can’t compare a model with and without a trend because it is not possible to run a Random Effects ‘Linear Trend’ model on derived parameter?


Sure you can -- you can run a VC analysis of betas, reals, or derived parameters. And, one of the 'hard-coded' options for the VC RE modeling is 'trend'.
cooch
 
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Re: General model for variance components

Postby violetblue » Wed Jul 21, 2021 9:16 pm

Thank you very much for your clarification and for the amendments to my post.

It sounds as though since I can't get a fully time-varying RE model, I won't be able to estimate time-varying survival without sampling covariance. Additionally, I cannot find a mean and variance of 3 resident survival estimates because the MoM approach is illogical for this.

Do you think MCMC instead is potentially a good approach, or should I abandon the whole idea of finding a mean of 3 values?

It also still seems to me I still can't do a VC analysis to find a linear trend in abundance because
I don't have a fully time-varying model. Even if I did, the 'Random Effects Model' option is greyed out for derived parameters so I couldn't compare to a model without a trend in abundance.
But you seem to be saying I can? I think I'm missing something here. Can you please point me in the right direction?

Thanks
violetblue
 
Posts: 23
Joined: Tue Nov 06, 2018 11:16 pm

Re: General model for variance components

Postby cooch » Thu Jul 22, 2021 8:28 am

Do you think MCMC instead is potentially a good approach, or should I abandon the whole idea of finding a mean of 3 values?


No -- regardless of whether or not you use MoM, MCMC, or any other estimation technology, estimates based on a sample of only 3 won't be worth much.

"The combination of some data and an aching desire for an answer does not ensure that a reasonable answer can be extracted from a given body of data". — John Tukey

It also still seems to me I still can't do a VC analysis to find a linear trend in abundance because
I don't have a fully time-varying model. Even if I did, the 'Random Effects Model' option is greyed out for derived parameters so I couldn't compare to a model without a trend in abundance.
But you seem to be saying I can? I think I'm missing something here. Can you please point me in the right direction?

Thanks


No -- it applies only to time-varying models. If you have a time-invariant model, then by definition, there is no trend. A 'trend' is a structural constaint applied to a model where estimates can potentially vary over sampling occasions.
cooch
 
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Location: Cornell University

Re: General model for variance components

Postby violetblue » Thu Jul 22, 2021 7:21 pm

I really appreciate your advice, thank you.

Can you please just confirm my understanding?

1. My fully time-dependent model has some Betas on the boundary so I can't use it to find a trend in the derived parameter abundance, and

2. I also can't use a model with constant survival but other Betas time-varying (no parameters on the boundary) to find a trend in derived abundance because this is not a fully time-dependent model.

Kind regards
violetblue
 
Posts: 23
Joined: Tue Nov 06, 2018 11:16 pm

Re: General model for variance components

Postby cooch » Thu Jul 22, 2021 8:16 pm

violetblue wrote:1. My fully time-dependent model has some Betas on the boundary so I can't use it to find a trend in the derived parameter abundance, and


You mean, reals on the boundary. The question for boundary estimates can be evaluated further using data cloning -- appendix F.

2. I also can't use a model with constant survival but other Betas time-varying (no parameters on the boundary) to find a trend in derived abundance because this is not a fully time-dependent model.

Kind regards


You can do whatever you want, but the interpretation from any model is conditional on the constraints you apply to the model. Think of 'mean survival' for a data type with (say) 3 parameters. Your estimate of the mean will differ if the other 2 parameters are time-dependent, or are constant, or combinations of the two. And so one, and so on.

Best you can hope for is (i) make whatever constraints you need to make to 'less important parameters' to allow you to estimate things you're interested in, and then (ii) spend a bunch of text pointing out that the estimates of things you might be interested are influenced by the constraint assumptions you made.

And, remember that a mean based on a sample of 3 is not worth the effort.
cooch
 
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Location: Cornell University


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