http://www.phidot.org/forum/viewtopic.php?t=838
http://www.phidot.org/forum/viewtopic.php?t=721
http://www.phidot.org/forum/viewtopic.php?t=537
http://www.phidot.org/forum/viewtopic.php?t=455
http://www.phidot.org/forum/viewtopic.php?t=213
The Ch 4 sidebar and thread advice indicates that changing the scale of sample intervals from monthly to annual (month to decimal years) should have no affect on the live recapture model parameters. Unfortunately, for me it results in differential survivorship.
Here is my issue-
I am estimating summer and non-summer survivorship for an endangered fish (both annual and monthly). Non-summer surv. varies with a covariate (fish length at stocking), but summer surv. is fixed.
My monthly survivorship model results in the following for the mean fish size:
Parameter Beta Standard Error Lower Upper
------------------------- -------------- -------------- -------------- --------------
1: Non-summer 1.5320809 0.1902958 1.1591010 1.9050607
2: Non-summer 1.0351014 0.1342562 0.7719594 1.2982435
3: Summer 1.4417191 0.2267902 0.9972103 1.8862280
...
I use these values to estimate monthly / seasonal survivorship for a given fish size. I then exponentiate these values to find the corresponding annual survivorship thusly: Phi(summer)^6 * Phi(non-summer)^6 = Exp. Annual
My annual survivorship model results in the following for mean fish size:
Parameter Beta Standard Error Lower Upper
------------------------- -------------- -------------- -------------- --------------
1: Non-summer -2.4290002 0.3966292 -3.2063935 -1.6516070
2: Non-summer 3.3392426 0.4082939 2.5389865 4.1394986
3: Summer -2.4589364 0.5589483 -3.5544752 -1.3633977
...
I use these values to estimate annual / seasonal survivorship for a given fish size. I then combine summer and non-summer annual survivorship for a given fish size: SQRT[Phi(summer)]*SQRT[Phi(non-summer)] = Annual
As you can see from the figure below, the resulting exponentiated monthly and annual curves are different. Results for the recapture rate estimates are nearly identical, so I assume the issue is with the survivorship.
For each model, I am standardizing individual covariates and using the alternate optimization routine.
I've tried unstandardized covariates and the regular optimization routine. No luck.
I have exhausted all my efforts for checking for simple errors- the two models are identical aside from the scale of the time interval.
All parameters are successfully estimated.
What gives? Anyone have a fresh perspective? There must be something simple that I have neglected.
Thanks for any insight.