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Hi André,<br>
<br>
Good questions. Your diagnosis shows that you understand what's
going on. You're quite right that selecting a value for 'a' is not
intuitive, in part because it represents a cumulative distance of
each point to several of its nearest neighbors, and in the case
where time is incorporated in the selection of nearest neighbors
(s>0), the distance is not a physical distance. <br>
<br>
The auto.a() function provides a starting point that has proven
useful for many datasets, but it really is just that - a starting
point to narrow down the range of 'a' values that provide a
reasonable balance between over-estimation and under-estimation. The
ultimate selection of 'a' should be based on your (admittedly
subjective) assessment of minimizing spurious holes in the
utilization distribution, and spurious cross-overs. Part of the
subjectivity in selecting a parameter value (for any home range
estimation method really) involves reflecting upon whether your
research question requires better fidelity to the core area or
overall 'home range'. In other words, there is no recommended 'a'
value. There are only recommended principles for selecting 'a' or
'k' (see appendix I of Lyons et al 2013), along with some tools
(plots) to help you select a value. All of which is less convenient
to be sure than a one-click solution, but hopefully keeps you close
to your data and pushes you to think about what you want from your
space use model. <br>
<br>
As to why the upper and lower ranges returned by the 'auto.a()'
function did a poor job for your dataset is hard to say, but it
could be related to the geometry of the points or the sampling
frequency. Remember that <tt>auto.a(ptp = 0.98, nnn = 2)</tt>
returns the value of 'a' such that 98% of points have at least two
nearest neighbors. If the distribution of points is wide ranging,
this could result in a large "lower bound" that blows up the core
areas. The suggestion to let <span lang="EN-US">k =
sqrt(numberOfPoints)</span> is likewise a a starting point and not
meant to be a recommended value. <br>
<br>
There is alternative function called <tt>lxy.amin.add()</tt> to
help identify upper and lower bounds for 'a'. But it is more of a
convenience function and it operates on similar principles as
auto.a(). There is also a relatively new function in tlocoh.dev that
opens a GUI (Shinyapp) which is designed to help select parameter
values. It isn't documented yet but see some sample code below.<br>
<br>
Hope this helps.<br>
<br>
Andy<br>
<br>
<br>
<tt>if (!require(tlocoh.dev)) stop("Please install tlocoh.dev")</tt><tt><br>
</tt><tt>## Loading required package: tlocoh.dev</tt><tt><br>
</tt><tt>if (packageVersion("tlocoh.dev") < "1.2.02")
stop("Please update your tlocoh.dev package")</tt><tt><br>
</tt><tt><br>
</tt><tt>## Load suggested packages</tt><tt><br>
</tt><tt>pkgs <- c("rgdal", "raster", "shiny", "dismo")</tt><tt><br>
</tt><tt>not.installed <- pkgs[!sapply(pkgs, function(p)
require(p, character.only=T))]</tt><tt><br>
</tt><tt><br>
</tt><tt>## Create a hullset with evenly spaced parameter values (in
this case k=4:20,</tt><tt><br>
</tt><tt>## (could also be evenly spaced 'a' values, use something
like a=seq(from=1000, to=15000, by=1000)</tt><tt><br>
</tt><tt><br>
</tt><tt>raccoon.lhs <- lxy.lhs(raccoon.lxy, s=0.05, k=4:20,
iso.add=TRUE, status=FALSE)</tt><tt><br>
</tt><tt><br>
</tt><tt>## Download a background image</tt><tt> for display<br>
</tt><tt>raccoon.gmap <- lhs.gmap(raccoon.lhs, gmap="hybrid")</tt><tt><br>
</tt><tt></tt><tt><br>
</tt><tt>## Graphically select one of the parameter values by
examining the isopleths, EAR plot, and ISO area plot</tt><tt><br>
</tt><tt>raccoon.sel <- lhs.selection(raccoon.lhs)</tt><tt><br>
</tt><tt>raccoon.sel <- lhs.shiny.select(raccoon.lhs,
selection=raccoon.sel, gmap=raccoon.gmap)</tt><tt><br>
</tt><tt><br>
</tt><tt>## Apply selection</tt><tt><br>
</tt><tt>raccoon.lhs <- lhs.select(racoon.lhs,
selection=raccoon.sel)</tt><tt><br>
</tt><br>
<br>
<br>
<div class="moz-cite-prefix">On 5/18/2015 10:38 AM, André Zehnder
wrote:<br>
</div>
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<p class="MsoNormal"><span lang="EN-US">Hi all,<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US">I am performing a home
range analysis with GPS data of some leopards and lions. The
input data has a highly variable point density and result in
quite large areas (roughly a magnitude of 500 to 1’000 km2
for the 95% isopleth). In agreement with the tutorial, I
begin with selecting the value for the temporal parameter s
and then select suitable k values. As an orientation for
that I use the rule of thumb ( k = sqrt(numberOfPoints)) and
the plots. When a k-value has been chosen, the tutorial
recommends to use the auto.a() function
(lxy.nn.add(toni.lxy, s=0.003, a=auto.a(nnn=15, ptp=0.98))).<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US">However, the recommended
a-value is massively too high and results in a oversmoothed
home range that lacks any details. The higher the s-value,
the more severe is this issue. While the result of the
suggested a-value still shows a few weak spatial details for
s=0, almost circular home ranges result for all isopleths
with s>0. I checked whether this issue occurs only for
one dataset, but it is the same for all 5 datasets I have
checked. I attached two images that present the result when
using the recommended a-value (auto_) and one that presents
a manually selected a-value (manually_). For example, for
s=0.005, I would rather take an a-value between 150’000 and
190’000 than the recommended value of 1’150’000. The
auto.a() function should thereby include at least k points
for 90% of all hulls.<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US">Therefore the question:
Has anyone experienced the same issue or is it even a known
technical problem with the package? My datasets contain
5’000 to 30’000 fixes, have some gaps and includes sometimes
different sampling intervals. May the auto.a() function have
severe problems due to that? The choice of an a-value is
rather subjective and not really intuitive, especially when
s>0. But when the auto.a() function can’t be used to get
an approximate reference, what other measures are available
to be able to justify your choice of the a-value?<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US">PS: I use T-LoCoH
version 1.34.00 with RStudio 0.98.1103.<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US">Best regards,<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US">André Zehnder<o:p></o:p></span></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
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