constraining p(t) in closed models

[Chris Jones]

I want to constrain the final capture probability in a closed population model to be equal to the preceding p (or to that from another occasion). How do I do it, please?

[abreton]

Specify the final capture probability and p mentioned in your post as the same parameter in the PIMs. Alternatively, you could structure a design matrix (based on a more general PIM) to accomplish the same end - let me know if this is the route you prefer.

[Chris Jones]

Thanks for the advice. The PIM approach worked, but I'd like to explore the design matrix approach if you have the time to explain

[abreton]

Building models in the design matrix is fairly straightforward, but if you've not done this before (or elsewhere under the generalized linear model framework), some time reading opening chapters in "A Gentle Introduction to Program MARK" will be critical to your success. Assuming you're comfortable with the Design Matrix (DM), and the relationship between the PIMs and DM, then all you need to do is apply the same submodel to get identical estimates for two parameters (such as you described in your initial post). If you're not familiar with the DM, then the following may be helpful...

Each column in the matrix represents a structural parameter (equivalent to intercept and slope coefficients in regression); and each row represents a parameter that you specified in your PIMs (note the intimate link between the PIMs and DM!). When you bring these together, you get an individual (and possibly unique) submodel for each parameter specified in the PIMs. To visualize this, imagine the top row of my design matrix looks like: 1 0 1 0 0 p1; here I'm summarizing the contents of 6 cells across the first six colmns; for simplicity, I'm going to ignore columns to the right of p1 (generally all zero's anyway; see MARK manual). Also, imagine the columns are labeled B1 B2 B3 B4 B5 PARM (these are the defalt labels in MARK). So, our submodel for p1 (recapture parameter #1 specified in the PIMs) = B1(1)+B2(0)+B3(1)+B4(0)+B5(0) which we can simplify as B1(1)+B3(1) (Bi*0 terms all drop out). So, if, e.g., you wanted p1 and p2 to be the same estimate using the DM, then you would apply the same submodel to each of these parameters. Through this short discussion, you may have detected the value and strength of the design matrix = the ability to specify a unique submodel or function for each parameter specified in the PIMs; and this translates into an enormous amount of flexibility in modeling in program MARK (For completion, I note that RMARK now offers an alternative to the DM matrix for some CMR model types - see posts on this site).

However, before you dive into the DM, as I suggested above, some homework in the MARK manual will pay off quickly and ~assure that you avoid common errors.