Known fate model fitting question

[sixtystrat]

I'm working with a student to analyze some telemetry data using the known-fate model. Quail survival was monitored for 53 intervals each of 6 years (318 intervals). The full model (318 parameters being estimated) always has the lowest AICc score (a LOT lower) even though we have tried many constrained models that SHOULD help explain things better. Many of the estimates are 1.00 so we have corrected the # parameters and the sin link produces the same result. This seems unusual to me as most of the known fate data sets that I have looked at can be simplified in one way or another. Should we simply conclude that none of the effects we have tested explain the data very well or should I suspect some sort of error? If so, any ideas on what that error might be? Just for fun, I changed c-hat to 1.5 and the model ranks changed significantly so overdispersion could affect the conclusions (but I am not sure how to estimate c-hat for known-fate data). THANKS!!!

[gwhite]

Joe:
First, there is no GOF test for known fate data unless you are willing to make some assumptions about what survival rates should be equal. You are running the saturated model with 318 parameters, and you have a deviance of zero -- absolutely no lack of fit. Of course there really is potential lack of fit, but you have no way to detect it without additional information.

Second, when you have lots of survival estimates equal to one, you have probably set up your intervals too short. An estimate of 1 has a zero SE, and hence the likelihood is pretty peaked at that estimate -- and not very happy about moving away from that estimate. I suggest that you change your interval to months instead of weeks, and then see if your covariates don't do a better job of explaining the data.

Gary

[sixtystrat]

Thanks Gary. We tried doubling up the intervals to 2 weeks and that did not help. We'll try again using 1 month and see what happens.

[gwhite]

Joe:
The issue is how many of the intervals (what proportion?) still had a survival rate estimated as 1?

Gary

[sixtystrat]

When we used the original intervals (3 days actually), the proportion with estimates of 1 was about 50%. When we changed that to 6 days using the design matrix, it was reduced to about 15%. Can the pooling be done with the design matrix or should we go back and redo the input files. Thanks again!
Joe

[gwhite]

Joe:
You could do the pooling in the design matrix, or in the PIMs for that matter. Just be sure to get your covariates laid out correctly.

Gary

[sixtystrat]

Okay that's good news. Given that the pooling can be done in the design matrix, do we simply ignore the results from the time independent models, saying that the low AIC scores are an artifact of so many 1's?

[gwhite]

Joe:

Remember that my advice is to never construct a model that you don't want to have at the top of the list! Theoretically, you're stuck with the saturated model if it is at the top.

Gary

[jlaake]

But is it at the top because all of those parameters hitting the boundary of 1 are not being counted?

[sixtystrat]

No, I went back and adjusted the number of parameters.