Multi-week Constancy and pent() paramterization

[pstevens]

I am working with a fairly sparse dataset so, rather than pool across weeks within a month and lose within month recaptures, I am imposing multi-week constancy within month on my model parameters. I am using the POPAN method (need to Population estimate) and have constrained phi() and p() in the usual way using the DM. However, I am confused on constraining the pent() parameters. I can constrain them to be consistent within a given month, as I do the phi() and p() parameters, using the DM. However, the estimates still must sum to 1 (link function: Mlogit(x)). This means that for a 24 week study covering 6 months rather than getting 6 unique estimates (one per month) that sum to 1, I get 24 estimates in 6 unique groiups that sum to 1. Intuitively, this seems to leave you with a weekly rather than monthly pent() estimates since a monthly estimate must be "divided" among the 4 weeks in any given month in order to ensure that all 24 estimates sum to 1. Can I merely sum the pent() estimates within a given month (i.e. - 4 week block) by hand to get the monthly pent()? Is there a more elegant way to parametrize the DM or link function to produce a 6 truly monthly pent() estimates? Any advice/thoughts would be appreciated.

[jlaake]

The anwser you propose of summing the weekly values for the month is the only way forward. That is a consequence of the way that the mlogit is handled in MARK whereby each interval must have a separate parameter even if they are held constant. If you think about it all of your parameters are weekly parameters that are held constant across the month, however for the other parameters you can have a single real parameter for the month and for the mlogit, you need a separate real parameter for each week. I wish it didn't work that way but that is the way it is.

--jeff

[pstevens]

Thanks, Jeff. I had a sneaking suspicion that would be the case. My main concern is extracting a population estimate so I am worried about how this little artifact affects my model fit. It seems like if I am trying to compare various "constancy intervals" (e.g. - 1, 2, 3, 4 weeks) using this method, I am not really comparing apples to apples. The "base" interval (i.e. - 1 week) will not have this summing issue whereas all subsequent intervals will. Consequently, it seems like the "base" intervals always outperforms other constancy intervals (in terms of AIC/QAIC) possibly due to the pent() summing issue. Sadly, there doesn't appear to be a way around it. Thanks again.

[jlaake]

I think you are confusing issues here. The approach used in MARK is only a matter of inconvenience rather than a problem with model fitting or comparison of 1-4 week constancy. Think of it this way in regard to Phi. I could take Phi in weekly intervals for a month and use PIM of 1,2,3,4 or 1,1,1,1 and as long as I set 1=2=3=4 in the DM then the models are the same. The same goes for pent with the mlogit, with the exception that you can't do 1,1,1,1 and you are forced to do 1,2,3,4. That's it. It is just a matter of inconvenience of dealing with 4 parameters (all with the same value). You can sum the values of 1,2,3,4 but since they are all the same then you can do 4 times the value of any one of them as well, which is what you would have to do even if you could use 1,1,1,1. Now maybe you are thinking of a different model in which all entry occurs at the beginning or end of the month and it that case you would set 2-4 =0 or 1-3 =0 and have all entry in the first or last week respectively. But that would seem to be an odd thing to do.

When I say its an inconvenience it is more of an issue in that you have far more real parameters if you use an mlogit. With more real parameters you get a larger DM and a slower model run which can become a problem with large numbers of occasions and lots of groups. In RMark, I simplify PIMS to the unique real parameters but I cn't do that with any mlogit parameter due to this restriction in MARK.

--jeff