Scaling time intervals vs modifying .ddl

[tryingmybest]

Hi all,

I recently posted in the MARK forum about scaling time intervals and received some great advice on how to scale them appropriately.

So, in a nutshell, take your monthly estimates, have MARK export them to a spreadsheet, derive the annual estimate simply as the product of the monthly estimates in that year, and then use the Delta method (or some other approach) to estimate the variance of the annual estimate.

I was then reading the rmark workshop notes and on page 43 it says about modifying the design data to run models with different time intervals

My occasions are monthly and I can t a time model but what I really want to t is a seasonal or annual model. How do I do that with RMark? The answer is to create a new eld in the design data that puts the parameters into appropriate bins (intervals).

My question is should I scale time intervals and then use the delta method or modify the .ddl? If I modify the .ddl do I need to use appropriately scaled time.intervals aswell?

I have monthly capture histories and want an annual overview of survival.

Cheers,

Tom

[jlaake]

Not sure what you mean by modifying the ddl. The time.intervals you designate set the times in the ddl but that is it. The time.intervals values are stored in the process.data and modifying values in the ddl doesn't affect them. The time.intervals you use should be a function of the time between your sampling occasions and not something that is manipulated. How you construct an annual rate will depend on the model you fit. If you have a constant survival model then plogis(beta) will give you the annual rate. If you have time (monthly) dependent survivals then you'll have to use the delta method. See simple example below to see if that helps your understanding.

Code: Select all

library(RMark)
data(dipper)

#analyze data assuming unit time intervals
mod1=mark(dipper)
#analyze data with half unit time intervals
mod2=mark(dipper,time.intervals=rep(.5,6))
# show results for both models; the only thing that changes
# is beta for Phi
summary(mod1)
summary(mod2)
# in mod2 survival is for a half year but the beta is for a full year
# which is 0.9025835^2

plogis(mod1$results$beta[1,1])
plogis(mod1$results$beta[1,1])^2
plogis(mod2$results$beta[1,1])




[tryingmybest]

Not sure what you mean by modifying the ddl. The time.intervals you designate set the times in the ddl but that is it. The time.intervals values are stored in the process.data and modifying values in the ddl doesn't affect them. The time.intervals you use should be a function of the time between your sampling occasions and not something that is manipulated. How you construct an annual rate will depend on the model you fit. If you have a constant survival model then plogis(beta) will give you the annual rate. If you have time (monthly) dependent survivals then you'll have to use the delta method. See simple example below to see if that helps your understanding.

Code: Select all

library(RMark)
data(dipper)

#analyze data assuming unit time intervals
mod1=mark(dipper)
#analyze data with half unit time intervals
mod2=mark(dipper,time.intervals=rep(.5,6))
# show results for both models; the only thing that changes
# is beta for Phi
summary(mod1)
summary(mod2)
# in mod2 survival is for a half year but the beta is for a full year
# which is 0.9025835^2

plogis(mod1$results$beta[1,1])
plogis(mod1$results$beta[1,1])^2
plogis(mod2$results$beta[1,1])




Jlaake,

Thanks for your reply, and the code. So I will need to use the delta method, but I'm unsure if I should scale time intervals aswell (4.2.2 in the book) so that my monthly time intervals are annually scaled similarly to the example below from the book;

As a final test,suppose that instead of monthly estimates, you were interested in estimates calculated over 6 month intervals. You could derive 6-month (i.e., half-year) survival estimates (and corresponding standard errors) by hand, but can you use MARK to do this for you directly? Sure – all you need to do is re-scale both seasonal intervals in terms of the desired season length. How? Simply by using the fact that a 7 month interval is in fact (7/6)  1.1Û6 times as long as a 6 month interval, and that a 5 month interval is (5/6)  0.8Û3 times as long as a 6 month interval. So, all you need to do is enter these re-scaled intervals into MARK.

And then use the delta method, or do I enter my time intervals monthly as they were taken (unscaled) and use the delta method without scaling time intervals?

Thanks for the guidance,

Tom