Spatial dependence in detection

[Mike.Meredith]

(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.

[darryl]

Haven't thought about the equivalency of different detection histories because I haven't dealt with this model very much myself, but on the other stuff...

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 interpretation of theta is something slightly different. It's not so much that tracks ARE on the trial in that segment, but some chance of tracks being in that segment. p is then a combination of other stuff (probability track are actually left in segment, probability of finding the tracks, etc). Jim Hines might correct me on this, but I think of this model as a way to account for potential violation of the closure assumption and/or independence of surveys. The theta's (or sspsi's) are 'availability' probabilities, ie, in some segments the species is unavailable (no chance of detection, p=0), and available in others (p >0). Note there are 2 thetas as you can allow the probability of availability to be different depending on whether species was available or not in the previous segment.

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.

Depends what model you're fitting. I'm guessing that making both theta and p segment specific is going to cause problems. Did you get any warnings about convergence or the variance-covariance matrix? I think you might need to have at least one of the parameters constant.

Note most of the information about the thetas comes from having a lot of you sites with detection histories where you have runs of 1's or 0's, eg, 001111010000, or 1110000110100

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.

As you don't know whether the species was available or not in the segment before the first one you surveyed, this option is kind of averaging across both possibilities. I think in the first version of the model it was assumed the species was not available prior to first segment.

BTW when p is fixed and only 3 parameters are estimated from the data, the AIC reported is still based on 4 parameters.

Did you delete out the column for p in the design matrix? The parameter count comes from total number of columns specified in the design matrices.


Cheers
Darryl

[Mike.Meredith]

Thanks, Darryl.

My interpretation of theta is something slightly different. It's not so much that tracks ARE on the trial in that segment, but some chance of tracks being in that segment.

Ok, so if you surveyed the trail many, many times over a long period, theta would be the proportion of times you saw tracks (let p=1 for the moment!) on each sement, which would differ among segments.

My idea was that that would be (approx) the same proportion for all segments, a consequence/extension of the closure assumption. My theta is a result of animals leaving lots of tracks together, spilling over the boundaries between segments. So if today I spot tracks on segment k, I say "Aha, the probability* there are tracks on segment k+1 is theta1!" And if next week there are no tracks on segment k, prob of tracks on segment k+1 = theta0 (theta0 < theta1).

(* Don't shoot! I'm a Bayesian!!)

Of course, p < 0, so there's the complication of tracks being on segment k but not detected. Which is why we need software!

Did you get any warnings about convergence or the variance-covariance matrix?

**** Numerical convergence may not have been reached.
Parameter estimates converged to approximately
5.24 significant digits.
5+ sig figs seems adequate!

BTW when p is fixed and only 3 parameters are estimated from the data, the AIC reported is still based on 4 parameters.

Did you delete out the column for p in the design matrix?

Ok, that works...with a couple of little glitches:
(a) The output gives estimates for the first 3 p's, but in fact the values are identical to psi, theta0 and theta1, so it's just a print-out problem.
(b) if you retrieve a model with no p column it has no detection matrix and crashes if you try to run it (the MS "...needs to close..." box pops up).

Cheers,
Mike.