Measures Of Spatial Association Research Articles

Scaling Geospatial Data from the Perspective of Complexity: Exploring the Scaling Behavior of the Entropogram

A fundamental challenge in geospatial data science is to determine how a property, or its characterization, changes with a change in the scale of measurement. Except for geostatistical regularization of the variogram, which is theoretically well established, the scaling behaviors of a wide range of alternative measures of spatial association remain unclear. This limits the ability to make inferences at scales beyond the scale of measurement. The scaling behavior of the recently introduced entropogram function also remains unclear. Because the entropogram is essentially the generalization of the variogram to categorical spatial variables, the possibility to derive a scaling model for the entropogram exists. Here, the scaling behavior of the entropogram based on the scale effect of Shannon entropy is derived, providing a theoretical basis for the regularization of the entropogram. To validate the developed regularization model for the entropogram, a series of multiscale data was generated. Both theoretical derivation and experimental results showed that the entropogram is scale-invariant, under certain conditions for the generation of the categorical data. This research, thus, generalizes the entropogram to changes in measurement scale, thereby increasing our ability to characterize spatial data and make inferences about the underlying dynamic process. It also provides a reference for the interactions between patterns and processes at different scales.

Spatial Association from the Perspective of Mutual Information

Measures of spatial association are important to reveal the spatial structures and patterns in geographical phenomena. They have utility for spatial interpolation, stochastic simulation, and causal inference, among others. Such measures are abundantly available for continuous spatial variables, whereas for categorical spatial variables they are less well developed. In this research, we developed a measure of spatial association for categorical spatial variables coined the entropogram, quantifying its spatial association using mutual information. Mutual information concerns information shared by pairs of random variables at different locations as revealed by their observed joint frequency distribution and marginal frequency distributions. The developed new measure is modeled as a function of lag in analogy to the variogram. Whereas existing measures focus mainly on interstate relationships, the entropogram models the spatial correlation in categorical spatial variables holistically. In this way, the entropogram imparts multiple advantages, for example, simplifying the representation of spatial structure for categorical variables and facilitating communication. The entropogram also reflects variation in the spatial correlation between different states. We first explored the properties of the entropogram in a simulation study. Then, we applied the entropogram to analyze the spatial association of land cover types in Qinxian, Shanxi, China. We conclude that the entropogram provides a suitable addition to existing measures of spatial association for applications in a wide range of disciplines where the categorical spatial variable is of interest.

Genetic, maternal, and environmental influences on sociality in a pedigreed primate population

Various aspects of sociality in mammals (e.g., dyadic connectedness) are linked with measures of biological fitness (e.g., longevity). How within- and between-individual variation in relevant social traits arises in uncontrolled wild populations is challenging to determine but is crucial for understanding constraints on the evolution of sociality. We use an advanced statistical method, known as the ‘animal model’, which incorporates pedigree information, to look at social, genetic, and environmental influences on sociality in a long-lived wild primate. We leverage a longitudinal database spanning 20 years of observation on individually recognized white-faced capuchin monkeys (Cebus capucinus imitator), with a multi-generational pedigree. We analyze two measures of spatial association, using repeat sampling of 376 individuals (mean: 53.5 months per subject, range: 6–185 months per subject). Conditioned on the effects of age, sex, group size, seasonality, and El Niño–Southern Oscillation phases, we show low to moderate long-term repeatability (across years) of the proportion of time spent social (posterior mode [95% Highest Posterior Density interval]: 0.207 [0.169, 0.265]) and of average number of partners (0.144 [0.113, 0.181]) (latent scale). Most of this long-term repeatability could be explained by modest heritability (h2social: 0.152 [0.094, 0.207]; h2partners: 0.113 [0.076, 0.149]) with small long-term maternal effects (m2social: 0.000 [0.000, 0.045]; m2partners: 0.000 [0.000, 0.041]). Our models capture the majority of variance in our behavioral traits, with much of the variance explained by temporally changing factors, such as group of residence, highlighting potential limits to the evolvability of our trait due to social and environmental constraints.

Exploring Nonstationarity in Spatial Association

This article expands the application of geographical weighting schemes to include indicators of spatial association. Because global measures of spatial association are already spatial models incorporating weights based on the scale of spatial association, calculating distance-based weighting schemes for the spatial association pairs is challenging given that spatial association involves object pairs. It is proposed here that the distance between the focal observation and the object pair be calculated based on the diagonal of a parallelogram formed by the focal point and the two endpoints of the object pair. Traditional local indicators of spatial association are constructed by a decomposition of a global measure into local components of spatial dependency centered on a focal location within a given scale of spatial association, whereas the new geographically weighted (GW) indicator of spatial association aids in measuring the spatial dependency of spatial subregions centered on a focal location within a given frame-of-reference scale. In this sense, they are similar to the spatially varying spatial association indicated by the estimated parameters on the spatially lagged response variable of a GW spatial lag model. Finally, a GW Moran’s I is developed and visualized to illustrate the GW indicator of spatial association.

Convergence of COVID-19 and chronic air pollution risks: Racial/ethnic and socioeconomic inequities in the U.S

Recent research suggests greater COVID-19 prevalence in areas burdened with higher exposure to chronic air pollution, but previous studies have not examined if socially disadvantaged populations are more likely to reside in communities located at the convergence of both COVID-19 and air pollution health risks. This article presents a national scale U.S. study that investigates whether racial/ethnic minorities, socioeconomically deprived residents, and other vulnerable groups are significantly overrepresented in counties where significantly higher COVID-19 incidence spatially coincides with higher respiratory health risks from outdoor exposure to hazardous air pollutants (HAPs). COVID-19 data from the Johns Hopkins Center for Systems Science and Engineering database are linked to respiratory risk estimates from the U.S. Environmental Protection Agency's National Air Toxics Assessment and variables from the 2018 American Community Survey. Bivariate local measures of spatial association are implemented to identify county clusters representing relationships between COVID-19 incidence rate and respiratory risk from HAP exposure. Socio-demographic characteristics of these clusters are compared using bivariate statistical tests and multivariable generalized estimating equations. Counties where greater COVID-19 incidence coincides significantly with higher HAP respiratory risk contain disproportionately higher percentages of non-Hispanic Black, socioeconomically deprived, and uninsured residents than all other U.S. counties, after controlling for spatial clustering, population density, older age, and other contextual factors. These significant socio-demographic inequities represent an important starting point for more detailed investigations of places facing the double burden of elevated COVID-19 prevalence and air pollution exposure, and also emphasize the urgent need to develop mitigation strategies for addressing both COVID-19 and chronic air pollution in socially vulnerable communities.

Local Measures of Spatial Association

Local Measures of Spatial Association

A Spatiotemporal Analysis of Heroin-Related Calls for Emergency Medical Services and Community-Health Centers in Boston, Massachusetts

Using a combination of data derived from the U.S. Census Bureau, the Substance Abuse and Mental Health Service Administration’s Behavioral Health Systems Locator and the Boston Police Department’s Incident Reports, this study examines the spatio-temporal distribution of calls for medical assistance following a heroin-related injury between 2015 and 2018. As well, an examination is conducted regarding the accessibility of Health Care Centers (HCCs) in relation to individuals in need of medical assistance. Distance-based measures of spatial association, including nearest neighbor and K-function analysis, were used to determine the clustering of calls at various spatial scales. Structural neighborhood characteristics (i.e., distance to the closest HCC) and physical and social vulnerability were used to predict the rate of calls for a heroin-related injury per 1,000 persons in the city of Boston using a spatial autoregressive model. HCC catchment areas for the set of medical emergency calls were created using Voronoi tessellations. Results showed that the average nearest neighbor distance (NND) of each call for medical assistance was approximately 187 m or .12 miles. Calls for assistance became more probable and increasingly more spatially concentrated over the study period. The K-function analysis revealed that the calls clustered at different spatial scales and in proximity to HCCs. Average distance to the nearest HCC and Household/Disability vulnerability were significantly associated with the census tract call rate per 1,000 persons. The average travel distance between the calls for medical assistance and the nearest HCC was 941 m, or just over a half-mile. Policy implications for the provision, through HCCs, of a focused and comprehensive community-based support system in a large urban city for individuals with serious drug problems are discussed in context.

Global Measures of Spatial Association

Global Measures of Spatial Association

Comparing implementations of global and local indicators of spatial association

Functions to calculate measures of spatial association, especially measures of spatial autocorrelation, have been made available in many software applications. Measures may be global, applying to the whole data set under consideration, or local, applying to each observation in the data set. Methods of statistical inference may also be provided, but these will, like the measures themselves, depend on the support of the observations, chosen assumptions, and the way in which spatial association is represented; spatial weights are often used as a representational technique. In addition, assumptions may be made about the underlying mean model, and about error distributions. Different software implementations may choose to expose these choices to the analyst, but the sets of choices available may vary between these implementations, as may default settings. This comparison will consider the implementations of global Moran’s I, Getis–Ord G and Geary’s C, local $$I_i$$ and $$G_i$$ , available in a range of software including Crimestat, GeoDa, ArcGIS, PySAL and R contributed packages.

A fractal measure of spatial association between landslides and conditioning factors

Measuring the relative importance and assigning weights to conditioning factors of landslides occurrence are significant for landslide prevention and/or mitigation. In this contribution, a fractal method is introduced for measuring the spatial relationships between landslides and conditioning factors (such as faults, rivers, geological boundaries, and roads), and for assigning weights to conditioning factors for mapping of landslide susceptibility. This method can be expressed as ρ=Ce –d, where d is the fractal dimension, and C is a constant. This relationship indicates a fractal relation between landslide density (ρ) and distances to conditioning factors (e). The case of d>0 suggests a significant spatial correlation between landslides and conditioning factors. The larger the d (>0) value, the stronger the spatial correlation is between landslides and a specific conditioning factor. Two case studies in South China were examined to demonstrate the usefulness of this novel method.

Colocation of older adults with successful aging based on objective and subjective measures

Aging of the U.S. and world populations highlights the need to understand how and where people age successfully. Older adults with chronic conditions may rate themselves subjectively as aging successfully despite their objective limitations. A typology of successful aging combining objective and subjective criteria has been tested, but spatial patterns in these dimensions have not been widely studied. Our research explores patterns of successful and unsuccessful aging using the colocation quotient, a measure of spatial association among categories in a population. The colocation quotient assesses the degree to which older adults who age successfully are likely to live near other adults who do not age successfully. Data on 5576 participants in the ORANJ BOWLSM survey, a statewide survey of older adults in New Jersey, were geocoded to the Census block level. Each participant was scored as aging successfully or not on each of the two dimensions. Global and local patterns of colocation of successful and unsuccessful aging in individuals were calculated based on the objective and subjective measures separately and then compared. The analysis reveals a strong regional pattern. In northern New Jersey and along the southeast coast, successful older adults on both dimensions were more likely to be colocated with subjectively unsuccessful older adults. In southern New Jersey, especially in the southwest, successful older adults on both dimensions were more likely to be colocated with the objectively unsuccessful. Spatial analysis of colocation can inform needs assessment for the growing population of older adults by identifying where older people age successfully and where they are aging unsuccessfully.

The impact of the weight matrix on the local indicators of spatial association: an application to per-capita value added in Italy

Making use of the local Moran index and taking as a case study the value added per capita in 103 Italian provinces in 2005, this work investigates how local measures of spatial association are affected by the use of different algorithms to calculate the weights of spatial matrices. We find that three methods we applied (adjacency, K-nn and MaxMin) provide very similar results at the global spatial level. Instead, considering the local spatial analysis, we note some differences in spatial outliers identification.

The Colocation Quotient: A New Measure of Spatial Association Between Categorical Subsets of Points. 协同区位商：点集分类子集间空间关联性的新度量标准

en

Analysing spatio-temporal autocorrelation with LISTA-Viz

Many interesting analysis problems (e.g. disease surveillance) would become more tractable if their spatio-temporal structure was better understood. Specifically, it would be helpful to be able to identify autocorrelation in space and time simultaneously. Some of the most commonly used measures of spatial association are LISA statistics, such as the Local Moran's I or the Getis-Ord Gi*; however, these have not been applied to the spatio-temporal case (including many time steps) because of computational limitations. We have implemented a spatio-temporal version of the Local Moran's I and claimed two advances: first, we exploit the fact that there are a limited number of topological relationships present in the data to make Monte Carlo's estimation of probability densities computationally practical, and thereby bypass the ‘curse of dimensionality’. We term this approach ‘spatial memoization’. Second, we developed a tool (LISTA-Viz) for interacting with the spatio-temporal structure uncovered by the statistics that contains a novel coordination strategy. The potential usefulness of the method and the associated tool are illustrated by an analysis of the 2009 H1N1 pandemic, with the finding that there was a critical spatio-temporal ‘inflection point’ at which the pandemic changed its character in the United States.

On A Comparison between Two Measures of Spatial Association

Two measures of spatial association between two variables were used by many researchers. These are the Wartenberg (1985) and Lee (2001) measures. Based on simulation for lattice data, the sensitivity of both measures was studied and compared with different choices of spatial structures, spatial weights and sample sizes using bias and mean square error. Different scenarios are used in terms of assumed numbers and sample sizes. Moran’s I is used to examine the spatial autocorrelation of such a variable with itself. Both the Wartenberg and Lee measures are found to be sensitive, however, Wartenberg’s measure is found to be somewhat better than Lee’s measure because it is slightly more sensitive when sample size is small.

A Generalized Randomization Approach to Local Measures of Spatial Association

This article establishes a unified randomization significance testing framework upon which various local measures of spatial association are commonly predicated. The generalized randomization approach presented is composed of two testing procedures, the extended Mantel test and the generalized vector randomization test. These two procedures employ different randomization assumptions, namely total and conditional randomization, according to the way in which they incorporate local measures. By properly specifying necessary matrices and vectors for a particular local measure of spatial association under a particular randomization assumption, the generalized randomization approach as a whole yields a reliable set of equations for expected values and variances, which then is confirmed by a Monte Carlo simulation utilizing random permutations.

Heterogeneity characteristics of an inland wetland environment through spatio-spectral analysis

To manage wetlands, resource managers require information on the size, shape, condition, and spatial distribution of vegetation types at both the community and species levels. Remote sensing methods currently used for generating maps of wetland ecosystems are largely based on spectral transformations of image data, preferably using high spatial resolution data. However, airborne hyperspectral imagery contains not only high spectral content but also considerable spatial information. To date, use of the spatial information in such imagery, particularly to determine biodiversity, has not been fully exploited. In this study, spatial heterogeneity in the reflectance values of hyperspectral imagery recorded over an inland wetland complex in South Dumfries Township, Ontario, Canada, is determined on a per-pixel basis by measuring the degree of local spatial association (local Moran’s Ii) within a 3 × 3 neighbourhood of pixels. These new spatio-spectral Moran’s Ii bands are then classified into heterogeneity categories using a modified version of the spectral angle mapper algorithm. Results show that the extraction of spatial information from hyperspectral data contributes to wetland management initiatives by providing quantitative information on the spatial arrangement of measured biological elements. The use of Moran’s Ii, a local measure of spatial association, also provides a statistical basis on which to map heterogeneity characteristics of elements within a wetland environment and to determine how these characteristics change over time.

Spatial structure effects on the detection of patches boundaries using local operators

Landscapes exhibit various degrees of spatial heterogeneity according to the differential intensity and interactions among processes and disturbances that they are subjected to. The management of these spatially dynamical landscapes requires that we can accurately map them and monitor the evolution of their spatial arrangement through time. Such a mapping requires first the delineation of various spatial features present in the landscape such as patches and their boundaries. However, there are several environmental (spatial variability) as well as technical (spatial resolution) factors that impair our ability to accurately delineate patches and their boundaries as polygons. Here, we investigate how the spatial structure and spatial resolution of the data affect the accuracy of detecting patches and their boundaries over simulated landscapes and real data. Simulated landscapes consisted of two patches with parameterized spatial properties (patches’ level of spatial autocorrelation, mean value and variance) separated by a boundary of known location. Real data allowed the investigation of a more complex landscape where there is a known transition between two forest domains with unknown spatial properties. Boundary locations are defined using the lattice-wombling edge detector at various aggregation levels and the degree of patch homogeneity is determined using Getis-Ord’s G*. Results show that boundary detection using a local edge detector is greatly affected by the spatial conditions of the data, namely variance, abruptness of the spatial gradient between two patches and patches’ level of spatial autocorrelation. They also suggest that data aggregation is not a panacea for bringing out the ecological process creating the patches and that indicators derived from local measures of spatial association can be complementary tools for analysing spatial structures affecting boundary delineation.

Secular changes recorded in mineralization of African crust

Variations in enrichment of mineral deposits in continental crust over time may be one way to test for secular changes in crustal genesis. We present spatial and chemical information about African mineral deposits with which to ‘fingerprint’ the metal endowment of African crust of different age. We then compare three regions of juvenile African crust, all with similar geology, tectonic history, and mineral deposits, but each of a different age. Each region was formed during rapid accretion of similar tectonic units derived from the mantle over ∼500 million years, and is apparently devoid of older recycled continental crust. Together, the three areas span 2500 million years of Earth history, from 0.5 Ga to 3.0 Ga, (e.g. the Zimbabwe Craton (2.5–3.0 Ga), the Birimian Shield (1.8–2.3 Ga), and the Arabian–Nubian Shield (0.5–1.0 Ga)). The three areas have a studied total of 2671 mineral deposits that are divided into six groups according to their geochemical affinities. Using these known deposits, a measure of spatial association (spatial coefficient) is derived. We show that each region has a unique metal endowment and that, per unit area, there is a greater concentration of mineral deposits in the crust of the Archean Zimbabwe Craton relative to the younger crust of the Birimian Shield and in turn the Arabian–Nubian Shield. This study quantitatively corroborates past studies that suggest older crust is more mineral diverse and enriched in mineral deposits than younger crust. Thus, a secular change in mineralization is implicated, and the mantle derived metal endowment of the African crust has undergone major evolutionary changes from Archean to Neoproterozoic time.

Spatial Characteristics of the Invasion of Acer platanoides on a Temperate Forested Island

We examined the spatial pattern of an introduced population of Norway maple (Acer platanoides L.) on a temperate forested island in order to quantify the influence of landscape context on invasion pattern. The spatial location of every Norway maple tree and sapling (≥0.5 m tall) that had invaded the island forest (n = 4496) was mapped using a global positioning system. The influence of landscape context was examined with the aid of a geographic information system and indices of spatial association. We found that the coniferous forest type was the most heavily invaded (71.9% of all Norway maple stems) when compared to either the hardwood or mixed conifer–hardwood forest types (5.4% and 19.3%, respectively). Across all forest types (excluding urban trees), the population was highly aggregated around roads and other Norway maple trees. For example, 90% of the population was within 40.8 m of a road with an average distance from road of 21.02 ± 0.40 m. This association around roads was significantly greater than would be predicted by chance alone (P < 0.001). Similarly, nearest neighbor distances averaged 4.5 ± 0.2 m with 90% of individuals within 8.3 m of another Norway maple. Measures of spatial association indicated that the invasion was significantly aggregated at both the stand and island scale. Nevertheless, a comparatively small but potentially influential set of individuals were observed at relatively long distances from the main invasion front. Ramifications of these disjunct establishments and other observed patterns are discussed in the context of current spread pattern theory, invasive species monitoring, and control efforts.