# [AniMov] BBMM questions: Sig2 and missing locations

Paolo Cavallini cavallini at faunalia.it
Mon Jan 19 08:59:42 CET 2009

```I forward this email from Clément. I had to remove the attachment, who
can however be found at:
http://www.faunalia.it/animove/docs/Bullard1991.pdf
All the best.
pc
====================
Oggetto:
Re: [AniMov] BBMM questions: Sig2 and missing locations
Da:
Clément Calenge <clement.calenge at oncfs.gouv.fr>
Data:
Mon, 19 Jan 2009 08:49:50 +0100
A:
Animal Movement <animov at faunalia.com>, andrea.maxie at gmail.com

Hello,

> 1)  As I understand from Horne et al. 2007, Sig2 is the standard deviation
> of location error.  However, I have used data from stationary collars to
> estimate location error and find that the data conforms to a bivariate
> distribution (either by normal or Laplace distributions, see McKenzie
et al.
> 2008, Environ Ecol Stat [Online]), rather than a simple normal
distribution. By log-transforming the data, it is possible to normalize
this distribution
> and obtain sd values, but I wanted to verify that that is an appropriate
> method for obtaining the required standard devitation value for the BBMM.
>

I do not actually understand the approach that you propose (you did not
provide enough information): as I understand it, you considered the true
location of your stationary collars to be at the coordinates (0,0) and
the relocations to be (error_x, error_y), i.e. the x and y components of
the errors. In this way, you have estimated a bivariate distribution of
your error.

Estimating the sig2 parameter could imply for example to (i) verify that
the location error is circular normal (same sd in X and Y direction, no
correlation between the two directions), (ii) estimating the sd in the x
and y direction, (iii) averaging the two SD. It seems from the elements
that you gave that the point (i) is not a reasonable one (but see
below). However, I do not understand why or how you wished to circumvent
this problem (if it is actually a problem).

Is it that your error is bivariate normal? or that it is highly
asymmetric? What do you want to log-transform? Maybe you want to
transform an asymmetric distribution of the distances between the
relocations and the true location of the stationnary collar, with a
log-transformation to make it normal (but the distribution of these
distances are not expected to be normal, even under the assumed model
for the BBMM: if the location error in X and Y is circular normal
(Bullard, 1991, p. 18), the squared distances between the relocation and
the true location are expected to follow a chi-square distribution, i.e.
asymetric, so there is no reason to log-transform the distances)... Or,
maybe you want to log-transform the coordinates (error_x, error_y)
themselves? but because these location errors may be negative, I do not
understand how you can compute the log? Some precisions would be useful
there.

Now some words about the problem of choosing a value for this smoothing
parameter; it is a difficult problem, similar to the problem of the
estimation of the smoothing parameter h in the classical kernel
estimation. In my opinion, if your data had been collected with a
perfect precision, it would still make sense to use a parameter sig2
different from 0, at least for exploration purposes. Indeed, a parameter
sig2 equal to 0 would correspond to an infinite density over the points
where the animals have been relocated (see the report of Bullard as an
attached file, and especially his fig. 10). Adding a noise with a
circular normal distribution was a trick used by Bullard (1991) to
"blur" these peaks, and he used the location error as a justification
for this trick (see his thesis p. 18). Using a sig2 different from 0 in
this case, would still allow to blur these peaks and allow data
exploration (but this would imply a subjective choice of sig2, based on
a visual examination of the estimated UD).

In your case, even if the location errors are not perfectly circular
normal, and if your aim is exploration of animals space use, you may
also estimate sig2 using the approach described above as a first
approximation (i.e. steps (ii) and (iii)), and then adjust sig2 based on
a visual exploration of the resulting UD by varying the value of this
parameter close to this first approximation (there is a great deal of
subjectivity here, but exploratory data analysis strongly relies on
subjective choices).

If your aim is not exploration, but confirmation of a statistical
hypothesis, you should be more precise concerning what you want exactly
(and why you use BBMM rather than other existing methods). Note however
that there is no theoretical reason to use a circular normal
distribution as a model for the error in the BBMM. Any other
distribution could be used but this would require some mathematical
developments (actually, for classical kernel estimation, the use of a
matrix containing smoothing parameters with a covariance between the x
and y direction already exists, see Wand and Jones, 1995). And other
error models are not currently implemented in kernelbb.

> 2)  I am hoping to get some clarification regarding the ltraj function and
> inclusion of missed fixes in the data set for the purpose of using the
BBMM. More specifically, will the home range and UD estimation be
affected by the
> ommission of missed fixes from the dataset.  Before deciding on using the
> BBMM, I had removed missed fixes from my data set, and so I did some
initial
> coarse-scale comparisons against data that included the missed
locations.  I
> didn't find noticeable differences in the UDs, and continued with
analysis,
> but perhaps I made this decision with haste.  I am wondering if it is
> necessary to reinsert the missed locations in the data set and redo the
> analysis.
>

Concerning the special case of the function kernelbb, it does not make
any difference whether you remove or let the missing values in the data
prior to estimation (they are removed anyway before the estimation by
the function). This may not be the case for other functions of
adehabitat dealing with the class "ltraj".
HTH,

Clément Calenge

--
Clément CALENGE
Office national de la chasse et de la faune sauvage
Saint Benoist - 78610 Auffargis
tel. (33) 01.30.46.54.14

--
Paolo Cavallini, see: * http://www.faunalia.it/pc *
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