(This relates to the thread "ssPsi0 and ssPsi1", but I think these parameter names have been changed.)
I'm looking out for Jim's paper on this, but in the meantime I'm trying to use the option with the "Spatial dependence..." section of the Help file in PRESENCE.
The 472 sites are 3.25km2 cells; in each cell, the trail is divided into 8 * 600m segments and we record detection/nondetection of ungulate tracks in each segment. The spatially dependent model would seem to be appropriate for this...except that we wouldn't expect the direction of walking the trail to make any difference. From the help file, it seems that a detection history of 11010 would have a different likelihood than 01011; is this the case?
Am I right in interpreting the parameters as follows?
psi = probability that the cell is occupied;
theta = probability that tracks are present on a segment given that the cell is occupied;
p = probability that tracks are detected given that tracks are present;
(so the usual p(detection of tracks) = theta * p).
My concern is, is it possible to separate out theta and p without multiple observations of each segment? Initial analyses of data suggest not: p has a confidence interval ranging from near 0 to 1.
This seems to be resolved if I use "Initial theta0 = theta0/(theta0+(1-theta1))", but I don't see why using an 'average' theta for the first segment should make a difference.
If they can't be separated, can we just estimate (theta1*p) and (theta2*p), assuming that p does not depend on what happens in adjacent segments? I tried this by using the "Fix Parameters" button and setting the p's = 1, and got sensible results.
BTW when p is fixed and only 3 parameters are estimated from the data, the AIC reported is still based on 4 parameters.
Thanks for comments/suggestions.
Mike.