survival analysis with territory as random effect

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survival analysis with territory as random effect

Postby dtempel » Thu Dec 14, 2017 3:41 pm

I'm interested in analyzing a long-term data set (spotted owl) with two goals:

(1) perform a variance components analysis with a spatial component (i.e., territory) so that the relative contribution of spatial variation to process variance can be estimated;
(2) obtain territory-specific survival estimates where territory is treated as a random effect (i.e., territory-specific shrinkage estimates).

I'm familiar with using MARK to conduct variance components analyses to estimate process variation, but I would further like to know how much spatial variation contributes to the process variation. Can territory be treated as a random effect in MARK to do this? If not, is there an alternative approach or software that might be used? I'm less familiar with Bayesian analysis, but it seems like the problem might be more tractable using MCMC (e.g., WinBUGS). Any suggestions or help would be greatly appreciated!
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Re: survival analysis with territory as random effect

Postby cooch » Thu Dec 14, 2017 5:47 pm

dtempel wrote:I'm interested in analyzing a long-term data set (spotted owl) with two goals:

(1) perform a variance components analysis with a spatial component (i.e., territory) so that the relative contribution of spatial variation to process variance can be estimated;
(2) obtain territory-specific survival estimates where territory is treated as a random effect (i.e., territory-specific shrinkage estimates).

I'm familiar with using MARK to conduct variance components analyses to estimate process variation, but I would further like to know how much spatial variation contributes to the process variation. Can territory be treated as a random effect in MARK to do this? If not, is there an alternative approach or software that might be used? I'm less familiar with Bayesian analysis, but it seems like the problem might be more tractable using MCMC (e.g., WinBUGS). Any suggestions or help would be greatly appreciated!


Go Bayesian. Not doable in MARK. MARK's routines decompose temporal variation. If you have spatiotemporal interests, you need to go elsewhere.
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Re: survival analysis with territory as random effect

Postby gwhite » Thu Dec 14, 2017 8:27 pm

If you enter each territory as a separate group, you will get territory-specific estimates. These could be used in the random effects/variance components analysis, but likely many of the territories will have survival estimates of 1 with SE=0, this approach will not work.

Thus I would use the MCMC algorithm in MARK and put a hyperdistribution on the survival estimates to estimate the sigma of the distribution, and hence the process variation across territories.

Gary
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Re: survival analysis with territory as random effect

Postby cooch » Thu Dec 14, 2017 10:25 pm

I thought of that at first, but it wasn't obvious how to partition total process variance into a spatial and temporal component, separately. Easy enough to create a territory-specific mu and sigma structure using MCMC, but it wasn't (and still isn't) obvious how you could set it up to do what I think is the intent in the original question -- which, if I interpret correctly, is to come up with an overall assessment of the relative contributions of time x territory on survival.

Further, setting up a territory as a group is basically setting it up as a fixed effect, which seems counter to the intent.

Its late, so maybe I'm missing something, but...
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Re: survival analysis with territory as random effect

Postby gwhite » Fri Dec 15, 2017 3:25 pm

Putting each territory in a separate group is a fixed effects model, but what the random effects analysis does is pull apart the sampling variance from the process variance of territory. Doing groups is no different than doing time-specific estimates -- same deal. But like I said previously, I'm betting most territories have estimates of 1, and so will not work well. Hence the need for a hyperdistribution in the MCMC module.

Note that you will likely not be able to fit both spatial and temporal distribution simultaneously because of the sparseness of the data within each territory. You might be able to fit a hyperdistribution model with time and space as additive effects, but not crossed.

Gary
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Re: survival analysis with territory as random effect

Postby cooch » Fri Dec 15, 2017 3:41 pm

gwhite wrote:Putting each territory in a separate group is a fixed effects model, but what the random effects analysis does is pull apart the sampling variance from the process variance of territory. Doing groups is no different than doing time-specific estimates -- same deal. But like I said previously, I'm betting most territories have estimates of 1, and so will not work well. Hence the need for a hyperdistribution in the MCMC module.

Note that you will likely not be able to fit both spatial and temporal distribution simultaneously because of the sparseness of the data within each territory. You might be able to fit a hyperdistribution model with time and space as additive effects, but not crossed.

Gary


So, I'm not sure how you would set it up to get \mu and \sigma over groups? Meaing, if you want a \mu over groups, and \sigma over groups. I'll have to give it some thought.
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Re: survival analysis with territory as random effect

Postby gwhite » Fri Dec 15, 2017 3:48 pm

Each group (territory) has its own survival estimate, probably either one or zero. So the hyperdistribution will be the mean and sigma of these estimates.
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Re: survival analysis with territory as random effect

Postby cooch » Fri Dec 15, 2017 4:00 pm

gwhite wrote:Each group (territory) has its own survival estimate, probably either one or zero. So the hyperdistribution will be the mean and sigma of these estimates.


I can see if fit a phi(territory) model (no temporal variation), then its easy to generate \mu and \sigma over territories (since without time variation, each territory gets its own phi parameter), but where I'm stuck is how to do a phi(territory + time) model. In your earlier post, you suggested it 'might' be possible. If so, I'm strggling to see how. But, since I'm home with a sick kid, something to muddle over...
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Re: survival analysis with territory as random effect

Postby cooch » Fri Dec 15, 2017 6:04 pm

Gary reminded me of an approach based on the DM as implemented in both the MCMC and method of moments RE technologies implemented in MARK. Silly me forgot that it was documented in a certain book on using program MARK. :oops:

However, I'm now prompted to add a more fully worked example, which demonstrates calculating mean/variance over groups (and, in the process, how you could handle group + time models, generating a separate mean and variance for each effect).

Sometime in the next few days.
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