Seasonal survival estimates in live encounters data

[Andrea]

Hello,
I'm analyzing a dataset consisting of capture-recapture data collected over 16 years with a total of 66 encounter occasions taking place at the beginning of each of the 4 seasons: summer, fall, winter, & spring. Using the CSJ model, I'm interested in modeling time variation as dependent on season; therefore, in the DM I included a variable coded as 1, 2, 3, 4, 1, 2, 3, 4, and so on. However, this approach leads to seasonal survival estimates that follow an increasing trend. But my question is how do I allow for the seasonal survival estimates to vary in a non-trendy way? Do I have to add a parameter to the DM for 3 of the 4 seasons?
Thanks for any advice you can offer me,
Andrea.

[cooch]

Hello,
I'm analyzing a dataset consisting of capture-recapture data collected over 16 years with a total of 66 encounter occasions taking place at the beginning of each of the 4 seasons: summer, fall, winter, & spring. Using the CSJ model, I'm interested in modeling time variation as dependent on season; therefore, in the DM I included a variable coded as 1, 2, 3, 4, 1, 2, 3, 4, and so on. However, this approach leads to seasonal survival estimates that follow an increasing trend. But my question is how do I allow for the seasonal survival estimates to vary in a non-trendy way? Do I have to add a parameter to the DM for 3 of the 4 seasons?
Thanks for any advice you can offer me,
Andrea.

Your mixing up a continuous covariate with a discrete classification factor (i.e., mixing up a simple linear regression with a single-classification ANOVA). You want the latter, not the former. Here's your hint - you have 4 seasons, meaning you need to have...how many columns in the design matrix to code for the 4 seasons? Now, with this in mind, go back and re-read Chapter 7 - especially the examples of factorial ANOVA, of which there are many.

Also, if you want to be somewhat more elegant, you might have an a priori hypothesis that there is a particular 'pattern' among seasons - this too can be handled fairly easily. You might also consider clever ordinal constraints, using the cumulative logit link (which is also described in Chapter 7).