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 <[email protected]> Data: Mon, 19 Jan 2009 08:49:50 +0100 A: Animal Movement <[email protected]>, [email protected]
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 * _______________________________________________ AniMov mailing list [email protected] http://www.faunalia.com/cgi-bin/mailman/listinfo/animov
