Constrained models with dummy age coding

[steve votier]

First, this might well be a really, really stupid question, sorry if so, but having read (a fair bit) of the literature I am still a bit confused and I'm happy to take the public slagging I quite rightly deserve...

In a single state model there are issues of trap-dependence, therefore we want to apply the classic Pradel approach of using a dummy two-age class model. This seems to be just fine when adjusting the PIM's, but because I want to fit covariates to the model, I presumably need to do this in the Design Matrices. Unfortunately I have tried a number of approaches but none yields the same output as the approach using the PIM's. Can somebody help me please?

Once again apologies if I am wasting anybody's time - but I would be most grateful of any suggestions.

Cheers

Steve

[Bill Kendall]

I might be misunderstanding the question, but I know of no way to create the Pradel model with the design matrix alone. The design matrix is conditional on the PIM structure. You need to create the Pradel model with the PIM's, where the diagonal and off-diagonal survival parameters are distinct (which I believe you have already done). Use the design matrix for that model to associate covariates with the diagonal or off-diagonal parameters.

[cooch]

I might be misunderstanding the question, but I know of no way to create the Pradel model with the design matrix alone. The design matrix is conditional on the PIM structure. You need to create the Pradel model with the PIM's, where the diagonal and off-diagonal survival parameters are distinct (which I believe you have already done). Use the design matrix for that model to associate covariates with the diagonal or off-diagonal parameters.

Bill is correct (assuming I interpret your question as Bill did) - you need to remember that the PIM's define the basic parameter structure (for a trap-depdence model, or anything else). So, you start by using the PIMs to specify the basic parameter structure. Then, you build the design matrix corresponding to this structure, which you can then modify as needed to handle various constraints.

For example - take a simple CJS-type model with time-dependence in the apparent survival rate. Suppose you have one group, and 5 occasions. The PIM corresponding to phi(t) is

Code: Select all

1 2 3 4
  2 3 4
    3 4
      4


If you use the reference coding method in the DM (more generically known as the 'intercept' method), the DM corresponding to this PIM is

Code: Select all

1 1 0 0
1 0 1 0
1 0 0 1
1 0 0 0


Note: there are other ways to code this DM - this is just an example

Remember, you use the DM to constrain the estimates. The preceding DM corresponds to the PIM, so there is no constraint. You could add constraints, by modifying the DM.

I'd suggest having another go at the linear models chapter. It covers this basic idea in some detail.