Analysis of the Spatial Variation of Network-Constrained Phenomena Represented by a Link Attribute Using a Hierarchical Bayesian Model

Abstract

Abstract:The spatial variation of geographical phenomena is a classical problem in spatial data analysis and can provide insight into underlying processes. Traditional exploratory methods mostly depend on the planar distance assumption, but many spatial phenomena are constrained to a subset of Euclidean space. In this study, we apply a method based on a hierarchical Bayesian model to analyse the spatial variation of network-constrained phenomena represented by a link attribute in conjunction with two experiments based on a simplified hypothetical network and a complex road network in Shenzhen that includes 4212 urban facility points of interest (POIs) for leisure activities. Then, the methods named local indicators of network-constrained clusters (LINCS) are applied to explore local spatial patterns in the given network space. The proposed method is designed for phenomena that are represented by attribute values of network links and is capable of removing part of random variability resulting from small-sample estimation. The effects of spatial dependence and the base distribution are also considered in the proposed method, which could be applied in the fields of urban planning and safety research.

Measuring Spatial Distribution Characteristics of Heavy Metal Contaminations in a Network-Constrained Environment: A Case Study in River Network of Daye, China

“…The river network was split into shorter segments using a network segmentation algorithm, with a standard length of 100 m [21,34]. In order to analyze the effect of the number of points in the neighborhood on pollution assessment, the parameter k in netIDW used 4-7 in this study.…”

“…The local Moran's I statistic aims to assess the spatial autocorrelation between a unit and its neighbors; however, the local G statistic measures the concentration of attributes of a variable around a unit [33]. In the context of local-scale cluster detection in a network space, each link is usually connected to a relatively small number of other links, thus, the randomization assumption is preferred, and statistical inference based on the Monte Carlo simulation is recommended in related studies [21,32,34]. In this study, the local-scale clustering of heavy metal pollution in river sediments was analyzed using the ILINCS method, which incorporates a Monte Carlo simulation to assess the statistical significance of the detected clusters.…”

“…Two types of LINCS methods, namely ILINCS and GLINCS, are the network extension of the local Moran's I and the local Getis-Ord G statistics, respectively [31,32]. To detect the spatial patterns at a much finer spatial resolution than that imposed by a given network, the links are usually divided into shorter segments in LINCS methods [21,31].…”

“…Considering the fact that the application of planar analysis methods to network-constrained phenomena could lead to improper pattern inferences, an exploratory methodology, namely local indicators of network-constrained clusters (LINCS), was introduced to detect the local-scale clustering of network events [21,31]. Two types of LINCS methods, namely ILINCS and GLINCS, are the network extension of the local Moran's I and the local Getis-Ord G statistics, respectively [31,32].…”

“…The distribution of high-high spatial clusters of Pb is similar to that of Cu (Figure 4b), which indicates that Cu and Pb could have common pollution sources. In this study, the river network was split into shorter segments, with a standard length of 100 m. However, it is worthwhile searching for the most effective scale of clustering, by examining multiple values of standard length that would reduce potential biases, caused by a presumed cluster size [21].…”