time.intervals in RMark

[stellatus]

Hello,

I am using the robust design to estimate abundance and survival from six primary trapping sessions consisting of 8,7,6,8,7,7 secondary sessions (43 total occasions). The first three primary sessions are from one spring/summer season and the second are from the same season in the following year. Thus, my time.intervals look like:

0,0,0,0,0,0,0,24,0,0,0,0,0,0,30,0,0,0,0,0,288,0,0,0,0,0,0,0,35,0,0,0,0,0,0,19,0,0,0,0,0,0

However, when I check the design data for S and GammaDoublePrime, the time intervals under the "time" column are listed as: 1,25,55,342,377 and under the "Time" column as 0,24,54,342,377. The longest time interval is actually the third one but the default design data are suggesting the fourth time interval is the longest. If I use these to model S~Time, won't this be wrong?

I would like to know if survival rates differ within seasons (where I'm expecting them to be high) and between the two seasons (where I'm expecting them to be lower). To do this, I have created a couple of extra design data for S and GammaDoublePrime (and the corresponding data for GammaPrime) using (i) the time intervals I expected: 24,54,342,377,396 and (ii) a simpler representation to keep the number of parameters down: 1,1,2,1,1.

Is anyone able to tell me what's going on with the "time" and "Time" data? Perhaps I have entered the intervals incorrectly?

Annabel.

[jlaake]

The design data are correct with the intervals you specified as long as you made a typo. They should be 1,25,55,343,378. S and Gamma are what I've called interval parameters because they are defined based on an interval (eg. Survival from time t to t+1). If you read the documentation closely you'll see that I say that time design data for interval parameters is designated based on the beginning of the time interval. It appears that you used the default begin.time=1. So the first trapping session is on day 1, the second session is 24 days later on day 25, the third is 30 days later on day 55,etc. Then time is a factor variable with labels 1,25,55, etc and first survival is for day 1 to 25 (with interval 24), second is for day 25 to 55 (with interval 30), etc. So it is correct as you have specified it. For ~time, the values of time are only labels as you would get S_1^24 for first interval, S_2^30 for second interval etc and S_1,S_2 etc are separate survival rates. The design data Time is simply a numeric version with a 0 origin and logit(S_i)=a+b*TIme_i and what would be used woud be S_i^t_i where t_i is the ith time interval as shown above. In all of the above _i means it is subscripted with i. Where you are getting confused is that you are equating time design data with the time interval values (t_i) which are not in the design data. So by changing the design data for time, you were simply changing the labels or changing values for Time simply shifts the origin.

--jeff

[stellatus]

Ah I see, thanks Jeff.

So time 55 actually represents 55-343 - the longest time period which makes sense now. Sorry I missed that description in the doc.

design data are correct with the intervals you specified as long as you made a typo

Yep, that was a typo.