Delta Method and weighted variances?

[JDJC]

Hi folks, I have a couple of disjoint questions. I'm working with a series of (9) spatially replicated closed capture-recapture samples, and have been using spatially explicit models to estimate population size over a larger region using covariate influence on density. R can integrate models using null (distance only) or finite mixture detection sub-models over the entire region of inference, but it can't (or can't allocate vector of size x, etc) accommodate models incorporating trap covariates. I've broken the 9 arrays into 2 separate subunits--and these trap covariate models invariably provide better fit--and am hoping to integrate the estimates from the subunits as estimates over the entire sample using the delta method. These subunits have different #'s of arrays and individuals/effective sample size: could (should?) I weight the means or variances to approximate model estimation over the entire sample? Also, I'm interested in comparing total-sample fit: I multiplied the subunit-specific likelihoods for total-sample comparison, but was told this was not an appropriate approach...is there some mysterious method for adding likelihoods or averaging independent AIC weights I'm completely unaware of?


Thanks (and I apologize: the stats department here is awol post-May...and pre-May as well, I suppose),

John

[murray.efford]

Hi John

Are you using 'secr'? It sounds like you have hit one of the design limits in 'secr': it demands space in proportion to the number of levels in covariates times the number of animals etc., so continuous covariates sometimes break it. Rather than go to all the trouble you have, I would suggest discretising your trap covariates as a small number of levels - you will lose almost nothing and the software should cope!

Partly answering your question: if your subunits are quite separate you have two independent datasets so the log likelihood for the whole is literally the sum of the parts. The catch is that you have estimated parameters separately for each subunit so the result is messy. Have you tried treating spatial subunits as 'sessions'? Sessions are simply independent units - they can be temporal, spatial or a combination of the two, and layouts, number of occasions etc. may differ between sessions. I think by using the 'session' construct you get a lot more control than with the ad hoc procedure you are proposing (secr maximises the log likelihood summed across 'sessions').

Murray

[JDJC]

Hi Murray,

Yep, I am using 'secr', and you nailed it: continuous habitat covariates. Thanks (and further thanks for the probability lesson)!

John