Occurrence distribution PMF values as weights in regression

[Mark Le Pla]

Hi all, 

Wanted to ask a question before going too far down a rabbit hole. 

For context: I have the "last known alive" and "potential kill site" locations of 20 animals that succumbed to predation. I was interested in using conditional logistic regression within a "used-available" paradigm to compare these locations to a suite of systematically sampled available points derived from the individual's occurrence distribution. 

I figure this is one of those occasions where an occurrence distribution is preferable over a range estimator, as conceptually I would like to compare the habitat attributes (in this case burnt/unburnt, and distance from burn edge) of all of the potential locations an animal could have been in during the sampling period to where they were just prior to being killed. 

Putting aside some potentially heroic assumptions for now (e.g. how far could they have moved from the last known alive location to where they were actually predated upon? Is where I found the collar where the animal was actually caught?), I wanted to ask a more general question about the appropriateness of using PMF values within the 95% occurrence distribution as weights for my available points within the conditional logistic regression. 

On the surface this seems appropriate, as whilst the occurrence distribution captures where the animal could have been during the sampling period, we know some of these available points were more likely to have been used relative to others. However, I'm sure there are potentially good reasons why this might not be a good thing to do, and I wanted to check that this is indeed an appropriate path forward before going ahead. 

See attached for a conceptual example of what I mean, where X = where the animal was last known alive, white dots = available points and the color gradient = the occurrence PMF for this animal during the post-fire period.

Chris, are you aware of any studies having used occurrence distribution PMF values in this way? Or is this an entirely inappropriate thing to do. Any thoughts on the matter would be much appreciated. 

Thanks,

Mark

[Christen Fleming]

Hi Mark,

I wouldn't do this, nor would I do the kind of RSFs where people make a tight buffer around the data to define the available region. This uses two different estimators - one for the available area and one for the selection - and does not propagate the uncertainty from the first estimate to the second, nor are the first set of parameters fit consistently with how the second set are fitted, and there is often sensitivity to choices made in the first fit. I think integrated SSFs and RSFs make much more sense.

If you annotate the location data with mortality, then you could consider selection like:

~ vegetation + burnt:mortality

for individuals that don't select for burnt habitat but are more likely to die there, and

~ vegetation + burnt + burnt:mortality

for individuals that select for burnt habitat and are more likely to die there, but not

~ vegetation + burnt*mortality

because this includes a mortality adjustment to the intercept term (in ctmm this term will be automatically discarded).

Best,

Chris