Application of the double kernel density approach to the multivariate analysis of attributeless event point datasets

Abstract

Attributeless event point datasets (AEPDs) are datasets composed of discrete events or observations defined by their geographical location only and lacking any other additional attributes. Examples of such datasets include spotted criminal events, road accidents and residential locations of disease patients. A commonly used approach to the analysis of such datasets involves their aggregation into predefined areal units, such as neighborhoods or census tracts. However, this approach does not perform effectively when the events of interests are geographically localized and the number of areal units available for aggregation is small. An alternative approach to the analysis of AEPDs is based on double kernel density (DKD) smoothing, according to which events of interest are transformed into continuous density surfaces and then normalized by the density of the entire population from which the events of interest are drawn. In the present study, the applicability of the DKD approach to multivariate analysis is tested for estimation consistency, sensitivity to the number of input observations and potential bias attributed to the spatial dependency of neighboring observations. Our analysis indicates that the DKD approach provides reasonably stable and consistent estimates, if the following three preconditions are met: (a) the kernel estimation parameters are properly defined, (b) the number of reference points, used for transformation of continuous DKD surfaces into discrete observations, is sufficiently large, and (c) the spatial dependency of neighboring observations is taken into account using spatial analysis tools.

Application of the double kernel density approach to the analysis of cancer incidence in a major metropolitan area

“…In this way, each reference point was assigned the values of lung and NHL density surfaces being closest to it [For a detailed description of this procedure, see Zusman et al (2012Zusman et al ( , 2015]. …”

“…As well established, larger values of the bandwidth produce a smoother density surface, while a small value might lead to a spiked surface Zusman et al, 2015). In order to select the kernel bandwidth for the present analysis we followed the methodological approach outlined in Zusman et al (2015), according to which the regression fit and likelihood parameters were used to compare models estimated for different bandwidths. Since the study in question was carried out in the same metropolitan area (i.e., in the City of Haifa and its suburbs), we adopted Zusman et al's (2015) recommendations and set the bandwidth to 1000 m.…”

“…Choosing the correct bandwidth size and its type (i.e., fixed vs adaptive bandwidth) can be challenging and should be considered at the decision making stage. Another potential weakness of the DKD technique is a high likelihood of spatial autocorrelation, caused by the fact that in the DKD analysis individual observations are drawn from continuous surfaces (Zusman et al, 2015). For dealing with potential autocorrelation issues, spatial dependency modelling (Anselin, 1995) can be implemented in future studies.…”