scaling time intervals

[tryingmybest]

All,

I want to scale to annual periods (as in 4.2.2 of the handbook) from monthly sightings ( 1112111). Should time intervals be written with the 1 in between consecutive sampling, or the scaled number?
Eg. To re-scale monthly time intervals to annual time intervals would the following 1112111 be written as (1/12=0.083) 0.083 0.083 0.083 0.16 0.083 0.083 0.083 or 111 0.16 111

Also, I've read the section in the mark handbook about this, I was just wondering why when you have consecutive sampling periods why the gaps in between the months are denoted as 1 unit of time rather than 0. Unless I've misunderstood.

Why would time intervals for sampling march-june, and then again sep-december be written as;
1112111 rather than 0002000

Cheers

[cooch]

All,

I want to scale to annual periods (as in 4.2.2 of the handbook) from monthly sightings ( 1112111). Should time intervals be written with the 1 in between consecutive sampling, or the scaled number?

With the 1. This is the MARK default -- that there is 1 'interval' (or whatever the interval length is) between sampling occasions.

Eg. To re-scale monthly time intervals to annual time intervals would the following 1112111 be written as (1/12=0.083) 0.083 0.083 0.083 0.16 0.083 0.083 0.083 or 111 0.16 111

If the '2' in '1112111' means 2 months between sampling occasions, whereas the '1' represents 1 month, then you don't actuall need to do anything more than enter '1112111'. MARK doesn't know what the interval is - *you* do. So, whatever MARK reports for (say) survival for 1 interval is just that, month survival. For the estimate over 2 monthsk, then MARK reports the square root over that 2-month interval.

Also, I've read the section in the mark handbook about this, I was just wondering why when you have consecutive sampling periods why the gaps in between the months are denoted as 1 unit of time rather than 0. Unless I've misunderstood.

You have.

Why would time intervals for sampling march-june, and then again sep-december be written as;
1112111 rather than 0002000

Cheers

Because thats how MARK does things.

Seriously -- entering a '0' for interval implies that the sampling occasions occur at the same time, which they don't. The '1' would be entered to tell MARK that there is a 1-interval separation between the occasions. (A '2' for 2-interval separation, a '3' for a 3-interval separation, and so on...).

[tryingmybest]

All,

I want to scale to annual periods (as in 4.2.2 of the handbook) from monthly sightings ( 1112111). Should time intervals be written with the 1 in between consecutive sampling, or the scaled number?

With the 1. This is the MARK default -- that there is 1 'interval' (or whatever the interval length is) between sampling occasions.

Eg. To re-scale monthly time intervals to annual time intervals would the following 1112111 be written as (1/12=0.083) 0.083 0.083 0.083 0.16 0.083 0.083 0.083 or 111 0.16 111

If the '2' in '1112111' means 2 months between sampling occasions, whereas the '1' represents 1 month, then you don't actuall need to do anything more than enter '1112111'. MARK doesn't know what the interval is - *you* do. So, whatever MARK reports for (say) survival for 1 interval is just that, month survival. For the estimate over 2 monthsk, then MARK reports the square root over that 2-month interval.

Also, I've read the section in the mark handbook about this, I was just wondering why when you have consecutive sampling periods why the gaps in between the months are denoted as 1 unit of time rather than 0. Unless I've misunderstood.

You have.

Why would time intervals for sampling march-june, and then again sep-december be written as;
1112111 rather than 0002000

Cheers

Because thats how MARK does things.

Seriously -- entering a '0' for interval implies that the sampling occasions occur at the same time, which they don't. The '1' would be entered to tell MARK that there is a 1-interval separation between the occasions. (A '2' for 2-interval separation, a '3' for a 3-interval separation, and so on...).

Amazing, all makes sense, thanks so much for the explanation!!

[tryingmybest]

All,

I want to scale to annual periods (as in 4.2.2 of the handbook) from monthly sightings ( 1112111). Should time intervals be written with the 1 in between consecutive sampling, or the scaled number?

With the 1. This is the MARK default -- that there is 1 'interval' (or whatever the interval length is) between sampling occasions.

Eg. To re-scale monthly time intervals to annual time intervals would the following 1112111 be written as (1/12=0.083) 0.083 0.083 0.083 0.16 0.083 0.083 0.083 or 111 0.16 111

Cooch, can I ask one last question following on from the scaling of time intervals? I'm a bit confused about how the output of the model relates to scaled time intervals. As in the example above I want to calculate annual survival, so have rescaled the time intervals accordingly.

The output still gives me a value for each individual capture occasion, when essentially I'm only interested in the annual overview. Do I need to tell mark beforehand to bin the output into annual survival alongside scaling the time. intervals annually.

My actual data is using 273 ch's and this was taken over the course of 4 years, so I'm sure you can imagine the massive output I'm getting of 273 values! I was hoping to reduce this to 4 annual outputs by rescaling time.intervals.

Many thanks!

[cooch]

If you have monthly sightings, then MARK reports monthly survival. If the interval between sightings is 2, MARK reports the square-root of the overall probability of survival over those 2 months, 3 month gap would be reported using cube root, and so on.

If what you really want is the estimate over the year, then the estimate is simply the product of the estimates for the months within that year. For the estimate of the variance of the product, the Delta method will suffice. In fact, the product of interval-specific survival estimates is the motivating example in the appendix which talks about the Delta method (Appendix B). If you want to simply cut to the chase, and skip the text as to why the Delta method works, skip to example (1) starting on p. 20. The addendum to the same appendix shows some other, more numerically intensive approaches to the problem.

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.