Model Averaging with Nest Survival

[zugunruhe1]

Hi MARKers, I understand that model averaging is the generally preferred way to report model estimates (and that it is necessary to get the unconditional SE). I was referring to the example on page 4-43 to obtain average daily survival values for each year of a 2-year nest survival study, but since the nest survival PIM is structured pretty differently than survival/recapture PIMs I wanted to check I was doing it right. To compare survival as a function of year alone, I would want years to have the same values within years but different values between years; when I select model averaging in MARK the default is to make each day of the nesting season both within and between years a different value (i.e. 1-117 for year 1 and 118-236 for the 2nd year). Would selecting only the first box in the PIM for each year be an effective way to get model-averaged nest survival estimates for each year?

(I'm also unsure where the CI that the example reports for parameter 57- [0.5211, 0.9803] - came from- the only one I see is 0.49997 to 0.9819 right under the unconditional SE. This is reported on page 4-48.)

Bonus question If I wanted to plot how nest age influenced survival across the nesting season, would simply plotting the estimates of the real parameters of survival on each day of the nesting season be adequate or would it also be recommended to involve model averaging for that?

Thank you!

[cooch]

Hi MARKers, I understand that model averaging is the generally preferred way to report model estimates (and that it is necessary to get the unconditional SE). I was referring to the example on page 4-43 to obtain average daily survival values for each year of a 2-year nest survival study, but since the nest survival PIM is structured pretty differently than survival/recapture PIMs I wanted to check I was doing it right.

You'll have a better idea (and level of understanding) of the 'PIM' presented in the model averaging functions in MARK if/when you've worked through Chapter 7. The default structure in the model average is the full age x time x cohort specification. From that, you select the appropriate indices corresponding to*your* PIM structure.

To compare survival as a function of year alone, I would want years to have the same values within years but different values between years; when I select model averaging in MARK the default is to make each day of the nesting season both within and between years a different value (i.e. 1-117 for year 1 and 118-236 for the 2nd year). Would selecting only the first box in the PIM for each year be an effective way to get model-averaged nest survival estimates for each year?

If your PIM is fully time specific (no age or cohort structure), then yes -- pick the first row is sufficient.

(I'm also unsure where the CI that the example reports for parameter 57- [0.5211, 0.9803] - came from- the only one I see is 0.49997 to 0.9819 right under the unconditional SE. This is reported on page 4-48.)

Typo, I believe. t should be [0.500,0.982], which is what is reported by MARK.

Bonus question If I wanted to plot how nest age influenced survival across the nesting season, would simply plotting the estimates of the real parameters of survival on each day of the nesting season be adequate or would it also be recommended to involve model averaging for that?

In general, you want to plot the model-averaged values, since they're arguably the most defensible -- since they count for the model specification uncertainty in your candidate model set.

[zugunruhe1]

Thank you! Yes the PIM (at least the one I want to get for year) has no age or cohort structure. I did the model averaging by just choosing the first box in the PIM for each year and the estimate for the first year indicates that the Percent of Variation Attributable to Model Variation is 90.95%; is that high a percentage "normal"? (For year 2 this percentage is 63.74)

I appreciate the reminder on Chapter 7- I did read through Chapters 1-7 before tackling the nest survival chapter and I get that the default model averaging structure is the "full" specification, just want to make sure I'm interpreting how to manipulate them for nest survival correctly. I did go back and look at the model averaging example for age/cohort models in Chapter 7 but it didn't clear things up much since it's for a pretty different situation.

So to get model-averaged values for nest age alone without including year as a factor... since nest age is the sum of the age and (day of nesting season -1) would it be correct to check all boxes except the first box and last box in one of the year PIMs? I guess my main struggle with that is how to incorporate the nest age "formula" with the PIMs.

[cooch]

Thank you! Yes the PIM (at least the one I want to get for year) has no age or cohort structure. I did the model averaging by just choosing the first box in the PIM for each year and the estimate for the first year indicates that the Percent of Variation Attributable to Model Variation is 90.95%; is that high a percentage "normal"? (For year 2 this percentage is 63.74)

Somewhat high, but largely a secondary issue at this point.

So to get model-averaged values for nest age alone without including year as a factor... since nest age is the sum of the age and (day of nesting season -1) would it be correct to check all boxes except the first box and last box in one of the year PIMs? I guess my main struggle with that is how to incorporate the nest age "formula" with the PIMs.

You'll need to post a lot more details about the analytical structure(s) you're working with -- at the least, the PIMs. It sounds as if you're doing nest survival analysis in different years, such that each year is (in effect) a different level of a 'factor', which just happens to be calendar year. Correct?

No idea what you refer to when you say 'year PIMs'.

[zugunruhe1]

Sorry, didn't mean to be vague there. I entered my nest survival data with 2 groups (one for each year) and 8 covariates (nest age being one of these covariates). So the PIMs for each group (year) that come up for model averaging are numbered 1-117 and 118-236, respectively, in an even grid (since there are no cohorts). I'd like to know how to manipulate the PIMs get model averaged values for nest age regardless of year. Thanks!

[cooch]

Sorry, didn't mean to be vague there. I entered my nest survival data with 2 groups (one for each year) and 8 covariates (nest age being one of these covariates). So the PIMs for each group (year) that come up for model averaging are numbered 1-117 and 118-236, respectively, in an even grid (since there are no cohorts). I'd like to know how to manipulate the PIMs get model averaged values for nest age regardless of year. Thanks!

So year as a 'grouping' (factor, classification variable), and you want time-specific estimates effectively pooling between years.

Unfortunately (for you), this is not something you can do from within the model averaging structure withing MARK, at least, not without a bit of work. You can either (i) simply calculate the average between groups for each time interval, using the Delta method (Appendix B) to derive the variance estimate for that average, or (ii) recode everything using individual covariates, where 'year' (group) is coded as a covariate - your model would include year, time, and a year.time interaction, in addition to anything else. It is somewhat complicated, but doable. See Chapter 11.

My suspicion is that option (1) would be the fastest -- once you have your head wrapped around the Delta method, you could code things up as an Excel macro to handle the time-specific calculations -- this part would take very little time, even for someone (like me) who isn't an Excel wizard.

[cooch]

Another approach which I forgot to mention which uses a rather different 'conceptual' approach is to use a random effects model (Appendix D). See especially section D.5. Especially text beginning with 'In one sense, a random effects model is a model which is...'. The point of said text being that a RE model can be constructed to generate estimates which are largely equivalent to model averaged values. A fair bit of theory to wade through to really understand how RE models work, but -- the upside is that it is trivial to build a random effects model which 'averages over groups'.

[zugunruhe1]

OK. Thanks very much for all the suggestions!