CJS phi(t) p(t) terminal phi's and p's not equal

[Urge4Sturg]

I am currently working with some simple CJS models with 4 sampling occasions. I know that the terminal phi and p are confounded and both are estimated as the product of the two paramters (as per the dipper example). however, when i run the phi(t) p(t) model using the PIM chart i am getting slightly different values for the terminal p and phi. At first i was running with encounter histories (EH's) for all individuals (15,108), and now I have re-run with summarized EH's.

When i run the phi(t) p(t) model with the individual EH's i get:


Real Function Parameters of {Phi(t)p(t)}
95% Confidence Interval
Parameter Estimate Standard Error Lower Upper
------------------------- -------------- -------------- -------------- --------------
1:Phi 0.7068693 0.1060547 0.4692966 0.8680037
2:Phi 0.5787956 0.1044254 0.3724516 0.7608556

3:Phi 0.4312749 0.0000000 0.4312749 0.4312749

4:p 0.0381389 0.0069873 0.0265722 0.0544589
5:p 0.0297242 0.0057946 0.0202445 0.0434459

6:p 0.0374741 0.0000000 0.0374741 0.0374741

Results from the summarized EH's are:

Real Function Parameters of {phi(t) p(t)}
95% Confidence Interval
Parameter Estimate Standard Error Lower Upper
------------------------- -------------- -------------- -------------- --------------
1:Phi 0.7068695 0.1060547 0.4692968 0.8680039
2:Phi 0.5787963 0.1044254 0.3724520 0.7608563

3:Phi 0.1386189 44.311411 0.8951821E-309 1.0000000

4:p 0.0381389 0.0069873 0.0265722 0.0544589
5:p 0.0297241 0.0057946 0.0202445 0.0434458

6:p 0.1165903 37.269664 0.1276252E-308 1.0000000


My questions are:

1) Am i correct in concluding that the 0 SE's for the individual EH's and the large SE's for the summarized EH's indicate the data are too sparse to estimate the product of the terminal p and phi?

2) Why are the results different for summarized versus individual EH's?

[bacollier]

My questions are:

1) Am i correct in concluding that the 0 SE's for the individual EH's and the large SE's for the summarized EH's indicate the data are too sparse to estimate the product of the terminal p and phi?

It seems so based on the information you have provided.

2) Why are the results different for summarized versus individual EH's?

Assuming the model, DM, and input data are exactly the same the results should not, in theory, be different. Are you by any chance using different link functions (e.g., sin vs. logit) or something like that? With 'enough' data for each estimable parameter I would expect you to get the same answer when using either link function, but with a really sparse dataset different link functions might cause the values where you are sparse to be different, maybe.

bret

[Urge4Sturg]

Assuming the model, DM, and input data are exactly the same the results should not, in theory, be different. Are you by any chance using different link functions (e.g., sin vs. logit) or something like that? With 'enough' data for each estimable parameter I would expect you to get the same answer when using either link function, but with a really sparse dataset different link functions might cause the values where you are sparse to be different, maybe.

The models are the same, i'm using an identity matrix for both, and the summarized EH file is summarized directly from the individual EH file. I double checked and made certain i used the logit link for both and am still getting the same results. Both ways are estimating p1&2 and phi 1&2 the same, the difference between the last p and the last phi is still puzzling. thanks for the reply, bret.


Cheers
Ben

[cooch]

I am currently working with some simple CJS models with 4 sampling occasions. I know that the terminal phi and p are confounded and both are estimated as the product of the two paramters (as per the dipper example).

Incorrect. Estimated as the square-root of the product.

however, when i run the phi(t) p(t) model using the PIM chart i am getting slightly different values for the terminal p and phi. At first i was running with encounter histories (EH's) for all individuals (15,108), and now I have re-run with summarized EH's.

The terminal phi and p values are not identifiable, and thus trying to interpret them, their product, a function of their product, is of no use. Moreover, the SE is meaningless. If you simulate phi)t)p(t), and look at the SE's of the final phi and p estimates, half the time they'll be zero, half the time they'll be astronomically large. In either case, they're meaningless. This true whether or not you have individual covariates in the .inp file.

[Urge4Sturg]

my question is not about trying to interpret these parameters, but understand why mark is giving me the results it is giving me. Why is the sqare-root of the product of the terminal p and phi, albeit useless to interpret, not returned as the same value in the results for the terminal p and phi (as per the dipper example)?