random effects for Pradel lambda

[dtempel]

I'm trying to run a random-effects model with different time trends for lambda. I'm using a Pradel model parameterized with lambda and survival and all parameters vary each year (i.e., phi(t), p(t), lambda(t)). Then I'm running the variance components under the "Output >> Specific Model Output" menu in MARK. For an 'intercept only (mean)' model, the G matrix is reported as 1.0000, and all of the S-tilde estimates are identical.

What does this mean exactly? It seems to me that MARK is unable to fit the model properly.

[cooch]

I'm trying to run a random-effects model with different time trends for lambda. I'm using a Pradel model parameterized with lambda and survival and all parameters vary each year (i.e., phi(t), p(t), lambda(t)). Then I'm running the variance components under the "Output >> Specific Model Output" menu in MARK. For an 'intercept only (mean)' model, the G matrix is reported as 1.0000, and all of the S-tilde estimates are identical.

What does this mean exactly? It seems to me that MARK is unable to fit the model properly.

How many occasions in your study? If <10 (in fact, Ken Burnham now recommends at least 15), the random effects approach will not be particularly helpful (sorry, but thats reality).

But, on the assumption you have enough occasions, then try the following:

1\ make the model you're working with phi(t)p(.)lambda(t) -- there are reasons why you might want full time-dependence for all parameters, but for the moment...

2\ run the model using simulated annealing

3\ when specifying the random effect, make sure you exclude the first and last lambda estimates. Also, make sure you're working with the reals, and not the betas.

4\ when you actually run the RE model, use starting values from the model you ran in step (2), and (again) simulated annealing.

Report back with what happens...

[dtempel]

Thanks a lot for your help and sorry for the delayed response. There were 21 occasions in my study. The phi(t), p(.), lambda(t) model runs OK, and I get the same results using either optimization method for the RE model.

1) If I try to run a RE model for phi(t), p(t), lambda(t), a Notepad window with S and S-tilde estimates immediately opens, so I assume that I just won't be able to run that RE model?

2) I've been previously told that I should exclude the first two and the last lambda estimate for a phi(t), p(t), lambda(t) model by Jim Nichols, but I don't understand why. Can you think of any reasons why I should do that instead of excluding just the first and last lambda estimate for the phi(t), p(.), lambda(t) model?

3) The phi(.), p(t), lambda(t) model actually has a much better fit than the phi(t), p(.), lambda(t) model. Are there any conceptual reasons why I shouldn't use that model for REs?

[cooch]

Thanks a lot for your help and sorry for the delayed response. There were 21 occasions in my study.

That's enough.

The phi(t), p(.), lambda(t) model runs OK, and I get the same results using either optimization method for the RE model.

Whatever "OK" means...

1) If I try to run a RE model for phi(t), p(t), lambda(t), a Notepad window with S and S-tilde estimates immediately opens, so I assume that I just won't be able to run that RE model?

No. That is normal, and happens for all VC models. If you click the RE button on the numerical estimation window, you'll then be prompted to fit the RE model. If you don't click that button, MARK will still report shrinkage estimates. See Appendix D in the MARK book -- all of this is covered there, in some detail.

2) I've been previously told that I should exclude the first two and the last lambda estimate for a phi(t), p(t), lambda(t) model by Jim Nichols, but I don't understand why. Can you think of any reasons why I should do that instead of excluding just the first and last lambda estimate for the phi(t), p(.), lambda(t) model?

The difference between 'first and last' and 'first two and last' is negligible. Basic point is that first and last are typically biased, so as long as you toss *at least* the first and last, you're probably fine. If in doubt, try both approaches, and see if the results differ.

3) The phi(.), p(t), lambda(t) model actually has a much better fit than the phi(t), p(.), lambda(t) model. Are there any conceptual reasons why I shouldn't use that model for REs?

Again, this is covered in the book -- second paragraph, section D.4.2:

Note that we use time-structure for the recovery parameter f . We do so not simply because such a
model often makes more ‘biological sense’ than a model where f is constrained (say, f.), but because
any constraint applied to f will impart (or ‘transfer’) more of the variation in the data to the survival
parameter S, such that the estimated process variance σˆ2 will be ‘inflated’, relative to the true process
variance. In general, you want to estimate variance components using a fully time-dependent model,
for all parameters, even if such a model is not the most parsimonious given the data.

In other words, applying a constraint to one parameter in a model influences the estimation of process variance for any other parameter(s).

More specifically, if a phi(.) model has lots of support, such that phi might be constant or nearly so over time, than since lambda=phi+f, then it is probably more useful to you to use the phi and f parameterization, and look at process variance in f. Lambda is estimated as a derived parameter, and you get an estimate of process variance for lambda. But, you can't fit a RE model for lambda since it is a derived parameter. See example D.4.4 in the book.

While it goes without saying, perhaps, I'll say it anyway: if you haven't worked your way through Appendix D in its entirety, you should do so before proceeding much further. A number of your questions are actually addressed there.