Adjusting Estimates for Time Intervals

[Choven1218]

I am estimating survival and infection probabilities in a snail population. I collected snails twice a month in 2005 through November. I resumed the project in March. When setting time intervals, I pooled each month and set the interval between months as 1. For the period from November to March, I set that interval at 4. The estimates that I am receiving should be monthly estimates, but I'm wondering about the Nov-Mar estimates.

In Chapter 14 (14-18), survival rate obtained from POPAN must be corrected for the different time interval. In this example, the weekly survival rate obtained during the initial 1.5 week interval must be raised to the 1.5 power. Does the same hold true for CJS and Multi-state Models? More specifically, will I need to correct the estimates for overwintering by raising them to the 4th power?

Thanks for the help...

Choven

[gwhite]

Choven
To get the Nov-Mar interval survival, you have to take the estimate for that interval to the 4th power. All of the survival estimates are scaled to an interval of 1 (in your case, one month) so that models like S(.) are sensical. Otherwise, you would have difficulty fitting such a model.
Note that the SE of the Nov-Mar interval requires the delta method, which is simple in this case:
Var(S^4) = (4*S^3)^2*Var(S), or SE(S^4) = (4*S^3)*SE(S).

Gary

[Choven1218]

Thanks for the reply. I thought that I needed to raise my estimates to the 4th power, but I wanted confirmation before doing it.

Choven

[cooch]

Thanks for the reply. I thought that I needed to raise my estimates to the 4th power, but I wanted confirmation before doing it.

Choven

I realized after you posted your question that the issue of time intervals is not dealt with in 'the book' (other than the tangential mention in the Jolly-Seber chapter). I've added some text to a revised Chapter 4, which I'll be posting in the next day or so.