Confounded parameters

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Confounded parameters

Postby amela22 » Tue Apr 24, 2018 10:47 pm

Hi all,

My capture-recapture data consists of 25 sampling occasions (monthly intervals) across 5 strata. I am fitting a multistate mark-recapture model in RMark that estimates p as a function of season*year and S as a function of season, where season was defined in the design data as intervals 1,2,3 for 'Fall', 4,5,6 for 'Winter', etc.

My question has to do with the p and S parameter being confounded (jointly estimated) in the final interval. I would like to fix/constrain p in the final interval so that the independent S value will be output. I am a little confused though by the fact that the input data is across 25 monthly encounter occasions, but I am modeling p and S with season, which is an aggregate of 3 monthly time intervals.

My question is, if I have a model p(~season+stratum) S(~season+L+stratum) Psi(-1+stratum:tostratum), is the last interval (time=25) or the last season (season=4) confounded?

Thanks in advance for the help,
amela22
 
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Re: Confounded parameters

Postby jlaake » Tue Apr 24, 2018 11:53 pm

It would be 25 and since you aren't estimating a separate p and Phi for time=25 they shouldn't be confounded.
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Re: Confounded parameters

Postby amela22 » Fri Apr 27, 2018 12:10 pm

Thanks for your quick reply Jeff. I have been in the field so I apologize for my delayed response.

So there is no need to fix p at time=25 to estimate survival independently? I think this makes sense because I am not using time as a covariate of p and S. Instead I am using season, where p in all seasons are estimable because the monthly time intervals provide adequate information since they are aggeregated. On the other hand, if my sampling intervals were every 3 months (seasonally) then p and S in the final season would be confounded since there is no information past season 4 to inform the estimate of S.

Am I on the right track with this?
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Re: Confounded parameters

Postby jlaake » Fri Apr 27, 2018 12:26 pm

It doesn't have anything to do with seasons. You have 25 occasions so your capture history has 25 values. If you were to have p and S vary by time (1-25), then for the last occasion (25) there are no observations after it so you don't know if it is 0 because it wasn't seen or it is dead. But in your case, by using seasons, you are effectively binning the intervals which constrains them to be equal. This would be like setting p_24 = p_25, in which case the last S would be estimable.

--jeff
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