Time Variation phi: Mean estimate - Model averaging

[constant survivor]

Hello everyone,
honestly: I RTFM and searched the forum but still... a very basic question I guess.

Assume following situation:
A set of models with the top one (by AIC) being a time-dependent model.
I think I know how to calculate the mean by design matrix (from chapter 6.15, latest version). To verify: LOGIT link function parameter beta1=-1.2348471 --> mean survival is 0.225 Is this correct?

But now model averaging comes into play. Doing this I of course again have several different estimates for each time interval. From these I would like to have a mean with SE.

I think my desire must be quite common, but I could not solve my problem by searching the MARKbook or forum.
Is there a, say, connection between model averaging and calculating the mean by Design matrix? Or is it all in the delta method (which I am afraid of)?

A simple advice/solution is preferred. Although I know it doesn't exist. Please point me to specific chapters in the book. Maybe I just overlooked something or didn't account for the right chapters yet to solve my problem.

Kindest regards
Hannes

[cooch]

Hello everyone,
honestly: I RTFM and searched the forum but still... a very basic question I guess.

Assume following situation:
A set of models with the top one (by AIC) being a time-dependent model.
I think I know how to calculate the mean by design matrix (from chapter 6.15, latest version). To verify: LOGIT link function parameter beta1=-1.2348471 --> mean survival is 0.225 Is this correct?

Assuming you're using the correct 'sum contrast' DM, more or less, yes, but using the DM to estimate the mean is not the best way to proceed (because of the difficulties in generating the appropriate SE for the estimate). You are strongly advised to use a random effects approach, which is also described in the same section in chapter 6, and in much more detail in Appendix D.

But now model averaging comes into play. Doing this I of course again have several different estimates for each time interval. From these I would like to have a mean with SE.

All you'd need to do is derive an estimate of the mean and variance from each model (if you use the random effects approach, this only applies to models with time dependent variation in phi, and even then, there are some folks - named 'Ken' - who might suggest that you should do this only with full time-dependence for all parameters, since constraints on one parameter implicitly constrain other parameters as well), and then use Buckland's approach to model averaging those estimates (introduced in section 4.5 of chapter 4). If you average estimates from time-dependent models only, you might need to recalculate the AIC weights for those models only.

I think my desire must be quite common

Not really. People like to report a mean as some sort of overall description, but the utility of such a value is pretty limited. A plot of the model averaged estimates for each sampling interval is generally more informative.