PS: do you have any suggested readings or references regarding this quote from the animove website: "Finally the last method (which I prefer, personally), is to specify a value for the smoothing parameter (the same for all animals), based on some visual exploration of the data." Thanks.
Silverman (1986, Density estimation for statistics and data analysis. Chapman & Hall, p. 43) indicates: "It should never be forgotten that the appropriate choice of smoothing parameter will always be influenced by the purpose for which the density estimate is to be used. If the purpose of density estimation is to explore the data in order to suggest possible models and hypotheses, then it will probably be quite sufficient, and indeed desirable to choose the smoothing parameter subjectively". Silverman then indicates that if the aim is to compare results with other studies, an automated method may be preferable. In theory, I agree with this argument. However, as you may have noted on the animove website (and in particular in the thread where you found this quote), the algorithms used by different software often return different results. The situation is even more dramatical when the LSCV does not converge... Therefore comparison between studies may be difficult, and an argumented subjective choice seems better to me than an automated choice that does not rely on sound bases (e.g. using the ad-hoc method for smoothing when LSCV does not converge relies on the hypothesis of a bivariate normal UD, which often results in strongly oversmoothed UD). As Silverman (1986) notes: "In this discussion I have deliberately used the word /automatic/ rather than /objective/ for methods that do not require explicit specification of control parameters. Behind the process of automating statistical procedures completely always lies the danger of encouraging the user not to give enough consideration to prior assumption (...)". Of course, automated method may be a starting point to the further refinement of the smoothing parameter. Silverman (1986), section 3.4.1 and following gives further details.
Also, have a look at Wand & Jones (1995, Kernel smoothing, Chapman & Hall), chapter 3 (p. 58): "There are many situations where it is satisfactory to choose the bandwidth subjectively by eye. This would involve looking at several density estimates over a range of bandwidth and to decrease the amount of smoothing until fluctuations that are more 'random' than 'structural' start to appear". Wand & Jones then indicate that this strategy may be time consuming, and that it is more viable when the user has a reason to suppose the existence of a certain structure in the data.
Of course, it is impossible, in data analysis, to recommend a given approach for all cases. However, in most cases, when I need kernel smoothing, I indeed prefer to explore the patterns in the data using subjective choices for the smoothing parameters.
Best regards, Clément Calenge. -- Clément CALENGE Cellule d'appui à l'analyse de données Direction des Etudes et de la Recherche Office national de la chasse et de la faune sauvage Saint Benoist - 78610 Auffargis tel. (33) 01.30.46.54.14 _______________________________________________ AniMov mailing list AniMov@faunalia.it http://lists.faunalia.it/cgi-bin/mailman/listinfo/animov
