data truncation??

[Craig Farquhar]

Greetings, I have a dataset collected from Mexico on a small, insectivorous
bird. Data were collected from points laid out at least 250 m from one
another in a systematic grid across relatively homogeneous habitat. Fifty
points were surveyed yielding 142 registrations. Actual distances were
recorded using a laser rangefinder. Distances recorded ranged from 1 to 100
m, the latter record being the sole observation beyond 60 m. Every effort
was made to record data at, or near, the point (r=0) in each case. However,
upon inspecting a histogram of the data it is clear that much heaping occurs
around the 40 m mark, with none at the points (r=0) and very few within
about r=20 m. I have been attempting several truncation approaches to
minimize bias, including:

right-truncate beyond 60, no left truncation
right-truncate the greatest 10% (as suggested by Buckland et al. 2001:151),
no left truncation
right-truncate beyond 60, left truncate within 20 m (chosen more or less
arbitrarily but in light of the fact that very few records exist in that
group)
right-truncate the greatest 10%, left truncate within 20 m

AIC values (587-507) seem to go down with increasing truncation effort, but
density (3.7-4.5) and cv (9.8%-11.6%) increase slightly. I am wondering how
significant these truncation efforts are in yielding the most robust model
estimates of density. Additionally, I have tried several types of cutpoint
intervals, but all around 10 groupings each with little change in AIC,
density and cv values.

Is there anything else I should try?

Craig Farquhar, PhD
Avian Ecologist
Wildlife Diversity Branch
Texas Parks and Wildlife Department
3000 S IH-35, Ste. 100
Austin, Texas 78704
work tel: 512-912-7018
work fax: 512-912-7058
email: <mailto:craig.f...@tpwd.state.tx.us>
craig.f...@tpwd.state.tx.us

[Steve Buckland]

> > AIC values (587-507) seem to go down with increasing truncation effort, but
> > density (3.7-4.5) and cv (9.8%-11.6%) increase slightly. I am wondering how
> > significant these truncation efforts are in yielding the most robust model
> > estimates of density. Additionally, I have tried several types of cutpoint
> > intervals, but all around 10 groupings each with little change in AIC,
> > density and cv values.

Craig, as noted in the 1993 and 2001 books, 'AIC can only be used to
compare models fitted to exactly the same data. It cannot therefore be
used to select a truncation distance w, or to compare models if different
truncation distances have been used, or to assess whether, or how, to
group distance data.' (p 111 of the 2001 book.)

If you're using a laser rangefinder, it seems unlikely that you have any
significant heaping, and more likely that you are mis-interpreting your
data. For point transect sampling, there is almost no area within say 2
metres of a point, so you expect no, or almost no, detections. There is
much more area between say 39m and 41m (40 times as much area), so
you get more detections at around 40m. At greater distances, you fail to
detect many birds, so numbers fall again. Hence your histogram should
increase then decrease. If you select the point transect option in
Distance, its fits will also have this property. If goodness-of-fit
suggests you still have too few detections near the point and too many at
40m, this may be because birds are moving away from the observer before
being detected.

Right-truncation at around 60m would probably be OK for your data. I
would not left-truncate unless I was convinced there really was a serious
problem with the reliability of small distances.

Steve Buckland
_________________________________________________________________________
Stephen T. Buckland
Director, Centre for Research into Ecological and Environmental Modelling
The Observatory, Buchanan Gardens, St Andrews KY16 9LZ, Scotland
Tel. +44-(0)1334-461841 Secretary +44-(0)1334-461829
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_________________________________________________________________________

[Len Thomas]

Hi Craig, List,

The pattern you describe (very little data close to the point, a hump at some
distance out and then little data at greater distances) is exactly what one
expects for point transect data -- see, for example Buckland et al 2001 figures
5.1 and 5.2. This is because two things are going on at once: the detection
probability decreases as you move away from the point in a non-linear fashion,
but the area surveyed (see figure 2.3) increases linearly. I put an overhead
from our introductory workshop on the web which will hopefully make this clear -
see http://www.ruwpa.st-and.ac.uk/distance/points.pdf

It's hard to give specific advice about truncation without seeing the data, and
I'm wary of cookbook recipes -- but truncation of around 10% of point transect
data is a good starting point. The aim is to remove "outliers" -- that is the
odd observation at large distances that can cause Distance to add an extra
adjustment term when it doesn't affect the fit at 0 distance and only decreases
precision. As a rough gude, and assuming "good" data, try fitting any old
detection function and truncating 10%; if there are one or more adjustment terms
fit, try a slightly greater truncation and see if you can get it to drop one of
the adjustment terms, and if it does, see if it makes the estimate of h(0) more
precise. Not something to get hung up about though -- with "good" data it
should make little difference for truncations of about this much -- i.e., the
density estimate should not move much relative to its standard error, and the CV
should not change greatly.

Note that you cannot compare AIC amoung analyses with different truncations (or
cutpoints, when intervals are specified in the Data Filter). AIC is only a
valid comparison when you're comparing analyses using exactly the same input
data, and truncation changes the data.

I would avoid left truncation, especially for point transect data where the
observations made close to the point are especially important in determining the
slope of f(x) at 0 distance -- which is the h(0) in equation 3.14 of the book.
You can use the goodness-of-fit tests to check whether there really is a serious
lack of fit of the data close to the point.

I would also avoid putting the data into intervals for the analysis, especially
since you collected exact distances with a laser rangefinder. When the data are
"good" all you do by putting data into intervals is loose some precision --
although it usually makes little difference in practice when you get about 7 or
more intervals. I *would* recommend specifying your own cutpoints for the
diagnostic goodness-of-fit tests (under Model Definition | Detection function |
Diagnostics) but this is only for the gof tests and not for fitting the
detection function, so makes no difference to the acutal fit (there's lots more
about this point in the online manual).

Hope this helps,

- Len



--
Len Thomas l...@mcs.st-and.ac.uk http://www.creem.st-and.ac.uk

Centre for Research into Ecological and Environmental Modelling

The Observatory, University of St Andrews, Scotland KY16 9LZ
Tel. (0)1334-461801 Fax. (0)1334-461800 Secretary (0)1334-461829