Model choice, AIC, Goodness of fit, and DSsim

[leob...@gmail.com]

Hi all,

I'm looking to bounce some questions off of the group mostly about model selection.

I completed a line-transect aerial helicopter distance sampling survey of wild sheep, flying a systematic, parallel transect design that had a randomized starting point.  Transects were spaced 1000 m apart.  The results were encouraging, with > 70 group sightings of sheep.  For the analysis, I had to bin distances in 50 m bins because I believe there is uncertainty for each distance measurement.   I have done some analysis and wondered if anyone could provide some input.  

I completed an AIC analysis of half normal, hazard rate, and uniform detection functions.  Half normal was the best model and showed no evidence for lack of fit, with a p-value of .8 for the goodness of fit test.  Then I added size (sheep group size) as a covariate to the half normal detection function and ran another AIC for those two models. The results show that the model with size for covariate beat the null model by ~ 130.  That is great except for when I run a goodness of fit test for the covariate model, the p-value returned was .053, just barely failing to reject.  Also, the plot of the detection function nor the q-q plot (see attached) are not all that convincing.

I wonder your thoughts for model choice here?

I was also wondering if the DSsim package might at all be useful in this context to run diagnostics on my survey design.

Thanks,

[Eric Rexstad]

Leo

Some off-the-cuff comments about your analyses, based upon your description and figures.

• Regarding goodness of fit; I don't place much weight in the size of the GOF p-value.  Anything over 0.05 (or your favourite alpha value) is adequate.
• Looking at your second detection function figure, it would seem that the majority of your sightings were of "large" groups.  The modelling suggests those groups have perfect detectability our to your truncation distance (450m?).
• you have only a few detections of non-large groups.  I speculate the two points in the 100-150m bin with detection probabilities estimated between 0.2 and 0.35 are of singletons.
• there's a second trail of detections of perhaps 5 groups, where group size is probably pairs, then a few more detections around 300m perhaps of groups of size 3?
• I'm guessing maybe 10 of the 70 detections are of non-large groups, the remainder of the detections being of groups sufficiently large that detectability is estimated to be perfect out to the truncation distance.

In summary, your design is such that the covered areas for adjacent transects abut one another; you are covering essentially 100% of your study area; lucky to have the resources to do that.  By placing the transects in that proximity, detectability of the majority of animals in the population (in groups) does not diminish perceptibly (as best I can judge by interpreting your figures).  I'm not sure what else a simulation might tell you.

I'm not inclined to suggest any alterations to your analysis.  If there were a greater number of detections of non-large groups, I might suggest treating the large groups as a strip transect (estimating abundance of individuals in big groups), then fitting detection function models to the non-large groups and producing a second abundance estimate of this remainder of the population.  However, with only ~10 detections of the small groups, you'll not produce defensible detection functions.

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Eric Rexstad
Centre for Ecological and Environmental Modelling
University of St Andrews
St Andrews is a charity registered in Scotland SC013532