Measures Of Spatial Autocorrelation Research Articles

Urban density, household overcrowding and the spread of COVID-19 in Australian cities

The UN-Habitat World Cities Report 2020 highlighted that overcrowded housing, not urban density, is the major contributing factor to the spread of COVID-19. The relatively successful ability of densely populated cities such as Seoul, Singapore, Tokyo and New York City to manage virus spread supports this. We hypothesise that, given the complexity of the interaction between people and place, the relative contribution of density and crowding to the spread of infectious diseases may be contingent on local factors. To directly compare the role of urban density and household overcrowding, we examine each in relation to COVID-19 incidence in the three largest cities in Australia, Sydney, Melbourne and Brisbane, as the pandemic unfolded from July 2021 to January 2022. Using ecological models adjusted for spatial autocorrelation and area-level measures of age and socio-economic factors, we assess the association between population density, overcrowding in homes, and COVID-19 infections in local neighbourhoods. Challenging prevailing assumptions, we find evidence for an effect of both density and overcrowding on COVID-19 infections depending on the city and area within cities; that is, depending on the local context. For example, in the southwestern suburbs of Sydney, the case rate decreases by between 0.4 and 6.4 with every one-unit increase in gross density however the case rate increases by between 0.01 and 9.6 with every one-unit increase in total overcrowding. These findings have important implications for developing pandemic response strategies: public health measures that target either density (e.g., lockdowns and restricted range of travel) or overcrowding (e.g., restricting number of people relative to dwelling, mask-wearing indoors, vaccination prioritisation) must be cognisant of the geographically local contexts in which they are implemented.

Unsupervised Image Segmentation Parameters Evaluation for Urban Land Use/Land Cover Applications

Image segmentation plays an important role in object-based classification. An optimal image segmentation should result in objects being internally homogeneous and, at the same time, distinct from one another. Strategies that assess the quality of image segmentation through intra- and inter-segment homogeneity metrics cannot always predict possible under- and over-segmentations of the image. Although the segmentation scale parameter determines the size of the image segments, it cannot synchronously guarantee that the produced image segments are internally homogeneous and spatially distinct from their neighbors. The majority of image segmentation assessment methods largely rely on a spatial autocorrelation measure that makes the global objective function fluctuate irregularly, resulting in the image variance increasing drastically toward the end of the segmentation. This paper relied on a series of image segmentations to test a more stable image variance measure based on the standard deviation model as well as a more robust hybrid spatial autocorrelation measure based on the current Moran’s index and the spatial autocorrelation coefficient models. The results show that there is a positive and inversely proportional correlation between the inter-segment heterogeneity and the intra-segment homogeneity since the global heterogeneity measure increases with a decrease in the image variance measure. It was also found that medium-scale parameters produced better quality image segments when used with small color weights, while large-scale parameters produced good quality segments when used with large color factor weights. Moreover, with optimal segmentation parameters, the image autocorrelation measure stabilizes and follows a near horizontal fluctuation while the image variance drops to values very close to zero, preventing the heterogeneity function from fluctuating irregularly towards the end of the image segmentation process.

Analysis of the funding of social services from a spatial approach in Andalusia (Spain)

In Andalusia, Community Social Service Centres (CSSCs) are funded by regulations following demographic, geographic, economic, and social disadvantage criteria. This study aims to analyse the geographical distribution of funding per inhabitant of CSSC by catchment area in Andalusia in 2019, and to study the statistical associations between funding and a range of demographic and socioeconomic indicators. The study spatial units (n = 184) included the catchment areas of CSSCs and, in the case of intramunicipal areas in large municipalities, they were grouped at the municipal level. Spatial autocorrelation measures were used to identify spatial clusters of high/low funding rates per inhabitant. Later, nonspatial and spatial regressions were applied to search for associations with different indicators (sex ratio, ageing index, dependency index, emigration rate, immigration rate, unemployment rate, population density, and employment rate in the primary sector). The geographical distribution of the funding of social services in Andalusia was not random since the analyses identified several spatial clusters with significantly high (hot spots) and low (cold spots) funding per inhabitant (p < 0.05). The funding rates were significantly (p < 0.05) and directly associated with the ageing index and the percentage of primary sector employees, and indirectly with the proportion of foreigners in the population and the population density. The hot spots were mainly located in rural and deprived areas, while the cold spots were in urban areas. The variables related to the regulated funding distribution criteria were not fully associated with higher financing. Instead, other additional variables showed significant associations (p < 0.05), such as primary-sector workers and foreign populations. The results showed that spatial analyses may support service assessment and decision-making in social policy.

A New Perspective on Moran’s Coefficient: Revisited

Moran’s I (Moran’s coefficient) is one of the most prominent measures of spatial autocorrelation. It is well known that Moran’s I has a representation that is similar to a Fourier series and is therefore useful for characterizing spatial data. However, the representation needs to be modified. This paper contributes to the literature by showing the necessary modification and presenting some further results. In addition, we provide the required MATLAB/GNU Octave and R user-defined functions.

Predictions of runoff and sediment discharge at the lower Yellow River Delta using basin irrigation data

Accurately predicting runoff (Q) and Suspended Sediment Concentration (SSC) is crucial for the environmental and geological evolution of the Yellow River Delta, a region with numerous oil fields and wetlands. However, accurate prediction of Q and SSC in the Yellow River Delta, characterized by the intricate interplay of high-frequency and low-frequency environmental factors, poses significant scientific challenges. This study introduces a novel framework focused on predicting Q and SSC exclusively using irrigation data. In this framework, Spatial Autocorrelation measures potential interactions among irrigation points, while Q-learning Swarm Optimization identifies high-impact irrigation areas. Ridge Regression (RR) is then applied to predict Q and SSC using the irrigation data. To comprehensively assess factors beyond irrigation, Empirical Mode Decomposition decomposes the residuals. The periodicity of each Intrinsic Mode Function (IMF) is ascertained using a zero-crossing method. IMF1, IMF2, and IMF3 are identified as seasonal signals, capturing the alternation between dry and rainy seasons, as well as inter-annual changes. Subsequently, Gated Recurrent Units (GRU) are further employed to extract this IMF information, expanding the dataset using bootstrap techniques. In the culmination of this research, the proposed framework emerges as an amalgamation of the RR model and the GRU models. Numerical examples substantiate the efficacy of this approach, demonstrating its ability to provide one-month ahead forecasts for Q and SSC with a Mean Absolute Percentage Error of 15% and 12%, respectively.

Spatial–temporal analysis and spatial drivers of hepatitis-related deaths in 183 countries, 2000–2019

Hepatitis is the seventh leading cause of mortality worldwide and is the only communicable disease where mortality is increasing, yet the long-term spatial–temporal variation at global scale and its possible causes, i.e., drivers, remain unknown. Firstly, this study employed the measure of spatial autocorrelation, Moran’s I, and the measure of local spatial cluster, Getis-Ord Gi*, to characterize the spatial variation of mortality due to hepatitis in 183 countries globally for years 2000, 2010, 2015 and 2019. Then, a novel spatial statistical method, named the Geographical Detector, was utilized to investigate eight possible influencing factors, i.e., risk factors, of the spatial–temporal variation of mortality due to hepatitis. The results showed significant disparities of hepatitis-related mortality rates among countries. Hot spots, representing locations with higher mortality rates, were consistently observed in Africa, East Asia, and Southeast Asia, while the cold spots, representing locations with lower mortality rates, were predominantly found in Europe and the Americas. Potential spatial drivers of hepatitis mortality, identified by geographical detector, include “health expenditure”, “universal health coverage”, and “per capita income”. However, “hepatitis B immunization” and “total population” were not identified as significant spatial drivers for hepatitis mortality The findings highlighted the critical role of socioeconomic factors in the variations in hepatitis mortality, and pointed out relative importance of increasing health expenditure, per capita income, and improve universal health coverage on alleviating global hepatitis-related mortality.

Are preferences for soil-based ecosystem services driven by spatial phenomena?

Agricultural soils provide multiple ecosystem services that affect human well-being. Soils’ potential to provide these ecosystem services varies spatially. Socio-demographic and other drivers of environmental preferences are also spatially variable. Therefore, preferences for soil-based ecosystem services are likely to be spatially heterogeneous, which may result in different policy priorities across locations. Understanding this spatial heterogeneity of preferences is therefore essential to guide public policy to protect healthy soils. We present a study that combines explorative and hypothesis-driven approaches to understand the spatial heterogeneity of preferences for four soil-based ecosystem services: climate regulation, clean water provision, drought protection and flood protection. Based on the results of a discrete choice experiment conducted on a representative sample of the German public, we first use global and local spatial autocorrelation measures to test whether there are any obvious patterns in the spatial distribution of preferences. Second, we use spatial lag models to test a number of hypotheses to explain the observed preference heterogeneity. We particularly focus on the spatial variability of relevant phenomena such as floods, droughts or nitrate pollution of groundwater, and their effects on the studied preferences. Lastly, we compare the results from both approaches in order to see whether the identified patterns are consistent with each other. We find weak patterns of spatial heterogeneity, but our hypotheses are all rejected. This suggests that salience of relevant phenomena and individual affectedness do not have an effect on preferences for soil-based ecosystem services.

Flow-Data-Based Global Spatial Autocorrelation Measurements for Evaluating Spatial Interactions

Spatial autocorrelation analysis is essential for understanding the distribution patterns of spatial flow data. Existing methods focus mainly on the origins and destinations of flow units and the relationships between them. These methods measure the autocorrelation of gravity or the positional and directional autocorrelations of flow units that are treated as objects. However, the intrinsic complexity of actual flow data necessitates the consideration of not only gravity, positional, and directional autocorrelations but also the autocorrelations of the variables of interest. This study proposes a global spatial autocorrelation method to measure the variables of interest of flow data. This method mainly consists of three steps. First, the proximity constraints of the origin and destination of a flow unit are defined to ensure similarity of flow units in terms of direction, distance, and position. This undertaking aims to determine the neighborhood of flow units and generate their adjacent matrices. Second, a spatial autocorrelation measurement model for flow data is constructed on the basis of the adjacent matrix generated. Artificial data sets are also employed to test the validity of the model. Finally, the proposed method is applied to the flow data analysis of population migration in central and eastern China to prove the practical application value of the model. The proposed method is universal and can be generalized to the global spatial autocorrelation analysis of any type of flow data.

A Multifactor Eigenvector Spatial Filtering-Based Method for Resolution-Enhanced Snow Water Equivalent Estimation in the Western United States

Accurate snow water equivalent (SWE) products are vital for monitoring hydrological processes and managing water resources effectively. However, the coarse spatial resolution (typically at 25 km from passive microwave remote sensing images) of the existing SWE products cannot meet the needs of explicit hydrological modeling. Linear regression ignores the spatial autocorrelation (SA) in the variables, and the measure of SA in the data assimilation algorithm is not explicit. This study develops a Resolution-enhanced Multifactor Eigenvector Spatial Filtering (RM-ESF) method to estimate daily SWE in the western United States based on a 6.25 km enhanced-resolution passive microwave record. The RM-ESF method is based on a brightness temperature gradience algorithm, incorporating not only factors including geolocation, environmental, topographical, and snow features but also eigenvectors generated from a spatial weights matrix to take SA into account. The results indicate that the SWE estimation from the RM-ESF method obviously outperforms other SWE products given its overall highest correlation coefficient (0.72) and lowest RMSE (56.70 mm) and MAE (43.88 mm), compared with the AMSR2 (0.33, 131.38 mm, and 115.45 mm), GlobSnow3 (0.50, 100.03 mm, and 83.58 mm), NCA-LDAS (0.48, 98.80 mm, and 81.94 mm), and ERA5 (0.65, 67.33 mm, and 51.82 mm), respectively. The RM-ESF model considers SA effectively and estimates SWE at a resolution of 6.25 km, which provides a feasible and efficient approach for SWE estimation with higher precision and finer spatial resolution.

Cancer survival analysis and spatial distribution during 2014–2016 in Shandong Province, China

We aimed to analyse cancer survival and its spatial distribution in Shandong Province. A total of 609,861 cancer cases from 2014 to 2016 were included in the analysis. Survival analysis was performed using strs in Stata. Spatial analysis was performed with GeoDa to determine measures of global and local spatial autocorrelation. Hotspot analysis was used to identify spatial clusters of high values (hotspots) and low values (cold spots) through ArcGIS. The 5-year relative survival rates were 37.85% for all cancers combined, 29.29% for males and 48.88% for females. After age standardisation, the survival rates were 34.47% for all cancers, 28.43% for males and 41.56% for females. Cancers with higher survival rates included thyroid (78.80%), breast (69.52%), uterus (64.51%) and bladder (62.54%) cancers. However, cancers with lower survival rates included pancreatic (11.34%), liver (13.19%), lung (18.39%), bone (19.71%), gallbladder (19.78%), oesophagus (24.52%), and stomach (28.85%) cancers and leukaemia (26.30%). Cancer survival rates in urban areas (37.53%) were higher than those in rural areas (32.83%). From the geographic distribution of cancer survival, we observed that the survival rate displayed a downward trend from east to west and from north to south. The hotspot analysis revealed that some counties of Qingdao, Jinan, Zibo, Dongying and Yantai cities were hotspots, whereas almost all counties of Linyi city and some counties of Weifang, Heze, Rizhao, and Dezhou cities were cold spots. In conclusion, the cancer survival rate in Shandong is still lower than that in China overall. The early diagnosis and treatment of lung and digestive tract cancers need to be further strengthened. Nevertheless, our results reflect a critical first step in obtaining and reporting accurate and reliable estimates of survival in Shandong.

Geographic Information System Based Economic And Financial Risk Analysis: The Case Of Europe And Central Asia

The study has two purposes. The first purpose is, using the economic and financial risk factors determined by the International Country Risk Guide (ICRG) rating agency, to reclassify the scores that countries get from these factors with the Jenks Natural Breaks (JNB) classification technique and to compare countries by creating their thematic maps according to this classification. The second purpose of our study is to create economic and financial risk maps of countries by using the Geographical Weighted Regression (GWR) method, which is one of the Geographical Information System (GIS) analysis techniques, based on the economic and financial risk factors determined by the ICRG. Before the GWR analysis for the variables included in the research, Moran Index analysis was performed as the main measurement of spatial autocorrelation. As a result of the Moran analysis, it was determined that there was a statistically significant positive autocorrelation between the countries. In other words, it has been seen that the countries examined have spatial dependence on each other in terms of economic and financial risk. According to the results of the GWR analysis, risk maps of the examined countries were created and more dynamic, more meaningful or more sensitive, more specific and visually easier to understand results were revealed. And according to these results, it has been seen that the GWR technique can also be used in the fields of economy and finance. In addition, the study brought a different interdisciplinary perspective by bringing together the fields of economy, finance and geography.

Spatial changes in the Hungarian and Slovenian cattle sector before and after accession to the European Union

Abstract A comparative analysis of the spatial transformation of two different farm-size cattle systems, in Hungary and Slovenia, is presented in this paper. Concentration, mobility, and spatial autocorrelation measures are used to study spatial cattlestock distribution and their changes over time, as well as spatial cattle-stock clustering using data from two agricultural censuses. Results confirm the decline in cattle stock on large-size farms in Hungary and on small-size farms in Slovenia, with a relative increase in the importance of medium-size farms in both countries. The decline and spatial changes in cattle stock are greater in Hungary than in Slovenia. Hungarian cattle clusters are concentrated in flat areas with medium- and large-size largely commercial farms, whilst in Slovenia they predominate in mainly hilly grassland and partly cornsilage areas on small and some medium-size family farms. Such specific cattle clustering is linked to geographical and farm-size structural characteristics that can also be linked to agricultural-policy-measure-related support for cattle and dairy, associated with less-favoured or disadvantaged-area status linked to geographical and structural land and farm characteristics typical of Slovenian mountain and particularly hilly areas. These spatial changes in the cattle sector have socioeconomic, land use, and environmental implications in terms of ecological sustainability and rural livelihoods.

VASA: an exploratory visualization tool for mapping spatio-temporal structure of mobility – a COVID-19 case study

ABSTRACT Exploratory data analysis tools designed to measure global and local spatial autocorrelation (e.g. Moran’s I statistic) have become standard in modern GIS software. However, there has been little development in amending these tools for visualization and analysis of patterns captured in spatio-temporal data. We design and implement an exploratory mapping tool, VASA (Visual Analysis for Spatial Association), that streamlines analytical pipelines in assessing spatio-temporal structure of data and enables enhanced visual display of the patterns captured in data. Specifically, VASA applies a set of cartographic visual variables to map local measures of spatial autocorrelation and helps delineate micro and macro trends in space-time processes. Two visual displays are presented: recency and consistency map and line-scatter plots. The former combines spatial and temporal data view of local clusters, while the latter drills down on the temporal trends of the phenomena. As a case study, we demonstrate the usability of VASA for the investigation of mobility patterns in response to the COVID-19 pandemic throughout 2020 in the United States. Using daily county-level and grid-level mobility metrics obtained from three different sources (SafeGraph, Cuebiq, and Mapbox), we demonstrate cartographic functionality of VASA for a swift exploratory analysis and comparison of mobility trends at different regional scales.

A Simulation Study to Explore Inference about Global Moran's I with Random Spatial Indexes

Inference procedures for spatial autocorrelation statistics assume that the underlying configurations of spatial units are fixed. However, sometimes this assumption can be disadvantageous, for example, when analyzing social media posts or moving objects. This article examines for the case of point geometries how a change from fixed to random spatial indexes affects inferences about global Moran's I, a popular spatial autocorrelation measure. Homogeneous and inhomogeneous Matérn and Thomas cluster processes are studied and for each of these processes, 10,000 random point patterns are simulated for investigating three aspects that are key in an inferential context: the null distributions of I when the underlying geometries are varied; the effect of the latter on critical values used to reject null hypotheses; and how the presence of point processes affects the statistical power of Moran's I. The results show that point processes affect all three characteristics. Inferences about spatial structure in relevant application contexts may therefore be different from conventional inferences when this additional source of randomness is taken into account.

Spatial disparities and associated factors of Under-five diarrhea disease in Ilubabore Zone, Oromia Regional State, Ethiopia

Background Diarrhea is commonly a sign of an infection in the intestinal tract that is caused by different bacteria, viruses, and parasitic entities. It is one of the leading causes of child mortality worldwide, especially in sub-Saharan African countries including Ethiopia. The main objective of this study was to identify spatial disparities and associated factors of underfive diarrhea disease in Ilubaborazone, Oromia regional state, Ethiopia. Study Design: A community based cross sectional study design was used Methods The study was carried out in the Ilu Aba Borazon of entire districts, and the data is essentially both primary and secondary, obtained from each woreda health office in the Ilu Aba Borazon and the corresponding mother or care giver of the sampled child. Spatial disparities in under-five diarrhea were identified using global and local measures of spatial autocorrelation. A Geo-additive regression model was used to identify the spatial disparities and associated factors of under-five diarrheal diseases. Results The value of global and local measures of spatial autocorrelation shows that under-five diarrheal disease varies according to geographical location and shows significant positive spatial autocorrelation. The results of the Geo-additive regression model showed a statistically significant relationship between under-five diarrhea disease and independent variables. Conclusion There is evidence of significant under-five diarrheal disease clustering in the Ilu Aba Borazon, southwest Ethiopia. Model-based data analysis showed that there is a significant relationship between under-five diarrhea and covariates (mother’s age, mother’s education, source of drinking water, quality of toilet facility, DPT 3 vaccination, Polio 3 vaccination, and household wealth index).

Eco-evolutionary model on spatial graphs reveals how habitat structure affects phenotypic differentiation

Differentiation mechanisms are influenced by the properties of the landscape over which individuals interact, disperse and evolve. Here, we investigate how habitat connectivity and habitat heterogeneity affect phenotypic differentiation by formulating a stochastic eco-evolutionary model where individuals are structured over a spatial graph. We combine analytical insights into the eco-evolutionary dynamics with numerical simulations to understand how the graph topology and the spatial distribution of habitat types affect differentiation. We show that not only low connectivity but also heterogeneity in connectivity promotes neutral differentiation, due to increased competition in highly connected vertices. Habitat assortativity, a measure of habitat spatial auto-correlation in graphs, additionally drives differentiation under habitat-dependent selection. While assortative graphs systematically amplify adaptive differentiation, they can foster or depress neutral differentiation depending on the migration regime. By formalising the eco-evolutionary and spatial dynamics of biological populations on graphs, our study establishes fundamental links between landscape features and phenotypic differentiation.

TOWARDS AN OPEN SOURCE PYTHON LIBRARY FOR AUTOMATED EXPLORATORY SPATIAL DATA ANALYSIS

Abstract. The exploratory spatial data analysis (ESDA) process refers to the use of various functions to gain an initial understanding of a spatial dataset. These include measures of spatial heterogeneity and spatial autocorrelation. Currently, the ESDA process is repetitive and time-consuming. Additionally, while different results arise for different datasets, how these results are generated does not change significantly. Results are also generated individually for each variable which means that they cannot be easily compared or shared.The automation of the ESDA process would therefore have multiple benefits as it would not only save time, but it would also allow the data analyst to keep up with the rapid rate at which we generate data. This paper aims to introduce the first iteration of autoESDA – a Python library capable of automating the ESDA process by summarising the results into a single report.In this paper, we present the defined high-level requirements for the implementation of autoESDA. Various dependency libraries are discussed and a high-level overview of the workflow of autoESDA is described. The library is then evaluated against the requirements laid out earlier in the study. Semi-structured interviews were carried out, which yielded a wealth of feedback and suggestions from the participants, describing how the output report could be improved. Finally, a roadmap of proposed further developments and improvements is discussed.The first version demonstrates that the automation of ESDA is possible and lays the foundation for further development in this regard. This is an important contribution to understanding spatial data as it enables the data analyst to keep up with the magnitude of data that is generated on a daily basis.

Explaining Neighbourhood Disparities in Cardiovascular Disease in Hamilton, Ontario, Canada

Introduction: In 2010, Hamilton’s local newspaper published a series of articles highlighting the inequities in numerous health outcomes across the city, with cardiovascular disease (CVD) Emergency Room (ER) visits among them (DeLuca et al., 2012). In Canada CVD is the second leading cause of death and the leading cause of hospitalizations, however, previous research has demonstrated that CVD risk may vary geographically (Chu et al., 2019). Furthermore, health analyses are rarely conducted in ways accessible to non-scientific communities. Given inequities in the distribution of COVID-19 across Hamilton communities, the need for population level analysis of comorbidities and risk factors is of heightened importance. The aim of this study is to identify the underlying factors that explain neighbourhood differences in the rate of CVD across Hamilton, Ontario. Methods: Census Tract (CT) aggregated Ontario Marginalization (ON-Marg) values and health data from Cancer Care Ontario were used. The material deprivation dimension of ON-Marg includes information on income, employment, education, and lone parent households, which have previously been linked to increased CVD risk, while the dependency dimension represents those who do not have income from employment which captures older age and disability (Matheson &amp; van Ingen, 2018). Factor analysis was performed to identify underlying factors that account for common variance. Spatial associations were analyzed using choropleth maps as well as measures of both global spatial autocorrelation (i.e., global Moran’s I) and local indicators of association (i.e., local Moran’s I). Contiguity was based on rook-weights (sharing a common boundary). Exploratory ordinary least squares (OLS) regression was performed to understand which indicators may explain geographic variation in CVD ER visits. Linear regression assumptions were assessed by testing the residuals for heteroskedasticity using the Koenker test, spatial autocorrelation using Global Moran’s I, and normality using the Kolmogorov-Smirnov test. Results: Initial analysis from 2016 and 2017 revealed that the rate of CVD ER visits in Hamilton is spatially autocorrelated (global Moran’s I score of 0.516 (p&lt;0.001) and ranged from less than 3 in 1000 to over 30 in 1000 people per year. For regression analysis, factor scores for material deprivation and dependency domains of the well validated ON-Marg Index were used together with the percentage of patients with no family physician. OLS regression using the four regressors resulted in a statistically significant model (F=65.94, p&lt;0.001) that explains about 65% of the variability in CVD ER visits in Hamilton (R2 = 0.653). Residuals were tested for heteroscedasticity (Koenker = 4.33, p=0.363), autocorrelation (global Moran’s I = 0.042, p = 0.367) and normality (Kolmogorov-Smirnov = 0.072, p = 0.079). Discussion: This information can help inform neighbourhood-level public health interventions and broader policy decisions to help address local CVD disparities. Patterns of high CVD and poorer socioeconomic conditions also correspond with COVID-19 disparities and support the need for greater neighbourhood-level research of both infectious and chronic conditions. Furthermore, geographic outputs of this work also provide visual and interactive neighbourhood-level health information accessible to non-scientific audiences that may support community-centred health and social action.

Computation-free nonparametric testing for local spatial association with application to the US and Canadian electorate

Measures of local and global spatial association are key tools for exploratory spatial data analysis. Many such measures exist including Moran’s I, Geary’s C, and the Getis–Ord G and G∗ statistics. A parametric approach to testing for significance relies on strong assumptions, which are often not met by real world data. Alternatively, the most popular nonparametric approach, the permutation test, imposes a large computational burden especially for massive graphical networks. Hence, we propose a computation-free approach to nonparametric permutation testing for local and global measures of spatial autocorrelation stemming from generalizations of the Khintchine inequality from functional analysis and the theory of Lp-spaces. Our methodology is demonstrated both on the conservative party’s performance in the 2019 federal Canadian election in the province of Alberta—a small network with n=34—and Donald Trump’s countywise performance in the 2016 US presidential election—a large network with n=3105. Neither dataset is normal, and running a classic permutation test locally for every node, considering various test statistics and neighbourhood structures, and including multiple testing correction would require the simulation of millions of permutations. We achieve similar statistical power on these datasets to the permutation test without the need for tedious simulation.

Influence of Industry-University Cooperation on Economic Development: A Mathematical Statistical Analysis

Technical innovation is an important means to achieve sustainable development. Industry-university cooperation is a new form of technological innovation. Most of the existing researches on industry-university cooperation focus on the analysis of industry-university cooperation models, but there are few researches on the examination of the relationship between industry-university cooperation and economic development. Using the spatial autocorrelation and spatial measurement model, the relationship between China’s industry-university cooperation and economic development was empirically investigated. The results indicate that, first, the nighttime light data could be used as a proxy variable for GDP data to characterize China’s economic development. Second, industry-university cooperation had a positive effect on China’s economic development. Third, industry-university cooperation affected China’s economic development through technological innovation.