This file includes the dataset of spatial distances and city population in 2000, global Moran’s indexes and Geary’s coefficients, three sets of local Moran’s index, and three sets of local Geary’s coefficients. The original data and calculation process are displayed for readers. (XLSX)

Spatial autocorrelation plays an important role in geographical analysis; however, there is still room for improvement of this method. The formula for Moran’s index is complicated, and several basic problems remain to be solved. Therefore, I will reconstruct its mathematical framework using mathematical derivation based on linear algebra and present four simple approaches to calculating Moran’s index. Moran’s scatterplot will be ameliorated, and new test methods will be proposed. The relationship between the global Moran’s index and Geary’s coefficient will be discussed from two different vantage points: spatial population and spatial sample. The sphere of applications for both Moran’s index and Geary’s coefficient will be clarified and defined. One of theoretical findings is that Moran’s index is a characteristic parameter of spatial weight matrices, so the selection of weight functions is very significant for autocorrelation analysis of geographical systems. A case study of 29 Chinese cities in 2000 will be employed to validate the innovatory models and methods. This work is a methodological study, which will simplify the process of autocorrelation analysis. The results of this study will lay the foundation for the scaling analysis of spatial autocorrelation.

In numerous developing nations, challenges such as insufficient investment in innovation and limited capabilities for conversion impede the growth of the construction sector, thus affecting the overall economic well-being of these regions. This paper focuses on construction industry innovation (CII) and its correlation with region economic development (RED), providing valuable insights to overcome these challenges and promote sustainable economic advancement. This study references existing literature to devise an evaluation indicator system dedicated for CII and RED. It then proceeds with an empirical analysis of the integration and synergy between CII and the economic development across 31 Chinese provinces from 2012 to 2021. Furthermore, this paper employs ArcGIS and Geoda software to meticulously dissect the spatial distribution characteristics underlying this coordination. The main conclusions are succinctly summarized as follows: CII in China is intricately connected to RED, exhibiting a strong connection that diminishes from south to north. Nonetheless, the coordination level between these factors remains relatively low, with notable regional disparities, particularly from southeast to northwest. The primary obstacles to effective coordination are related to innovation input, output, and economic scale. Additionally, spatial correlation analysis demonstrates pronounced regional clustering, showing stability despite slight fluctuations over the study period. This research underscores the concept of coupling coordination between CII and RED, underpinned by scientific analytical methods. The outcomes provide a definitive guide for advancing the transformation and enhancement of the construction industry while promoting RED.

The long-term and stable development of agriculture is the key to China’s economic development and social stability. Agricultural total factor productivity and the digital economy have become new kinetic energy and new engines driving agricultural high-quality development. It is of great significance to verify whether there are significant spatial and threshold effects in the process of high-quality development of agriculture and to explore the intrinsic relationship between high-quality development of agriculture and agricultural total factor productivity and digital economy. This paper takes 31 provinces in China from 2011 to 2020 as the research object. The coefficient of variation method is used to estimate the comprehensive evaluation index of agricultural high-quality development and digital economy. And Dea-Malmquist index method is used to estimate agricultural total factor productivity. On this basis, the spatial Durbin model and threshold regression model are constructed to explore the spatial and threshold effects of agricultural total factor productivity, digital economy and other factors and high-quality agricultural development. The conclusion is as follows: the high-quality development of agriculture has significant spatial autocorrelation. Agricultural total factor productivity and digital economy have significant direct effect and indirect spillover effect on the high-quality development of agriculture. Agricultural total factor productivity has stage differences in each range of digital economy level, but its influence on agricultural high-quality development shows a positive state. Based on this, the paper puts forward some countermeasures to promote the high-quality development of agriculture.

China’s univariate global Moran’s index of public health and air pollution.

It provides four Matlab programs for calculating spatial autocorrelation function (ACF) and partial autocorrelation function (PACF). Among the four programs, two are significant: one is based on diagonal elements and variable weights, and the other is based on zero diagonal elements and fixed weights. Readers can employ the programs to carry out spatial ACF and PACF analyses by substituting the author’s data with their own data. (M)

As a new type of economic format, digital economy has three major characteristics: technical, innovative, energy-saving and environmentally friendly. Acting on various sectors of the national economy, it is beneficial for improving carbon emission efficiency and is of great significance for achieving China’s two major goals of carbon peak and carbon neutrality. Firstly, theoretical analysis of the impact mechanism of digital economy on carbon emission efficiency, proposing research hypotheses on the direct effect, mediating effect, and spatial effect of digital economy on carbon emission efficiency. Secondly, based on panel data from 279 cities in China from 2011 to 2020, the econometric models are constructed to empirically analyze the direct, mediating, and spatial effects of digital economy on carbon emission efficiency. The results show that: 1) Digital economy can improve carbon emission efficiency; 2) The impact of digital economy on carbon emission efficiency has a “U”-shaped relationship, which is consistent with the "Environmental Kuznets Curve" hypothesis; 3) The impacts of digital economy on carbon emission efficiency exist in urban heterogeneity, specifically manifested as regional heterogeneity and urban scale heterogeneity; 4) Technological innovation is an important mediator for improving carbon emission efficiency in digital economy, and promoting technological innovation in digital economy can improve carbon emission efficiency; 5) Digital economy has spatial effect on carbon emission efficiency, which can improve the carbon emission efficiency of neighboring cities. Finally, based on the above results, suggestions are proposed from three aspects: promoting important industries and key areas for deep cultivation of carbon emission in digital economy, emphasizing regional balance in the development of digital economy, and strengthening regional cooperation in the development of digital economy, in order to continue to play a positive role in improving carbon emission efficiency through digital economy.

The inflow of foreign R&D has brought vigor and vitality to the development of the high-tech industry (HTI). Using the panel data of HTI in 23 provinces (autonomous provinces and municipalities) in China from 2007 to 2016, this paper firstly calculates the Moran index of HTI’s innovation performance (IP), and finds a spatial agglomeration effect. After rigorous testing, we determine the most suitable spatial metering model. Finally, the spatial effect is further decomposed into three kinds of effects: direct effect, indirect effect, and total effect. This paper studies the impact of foreign research and development (R&D) on IP of HTI and its spatial spillover effects. According to the research, foreign R&D has a significant role in promoting IP of HTI in China, and has specific spatial spillover effects. Significantly, foreign R&D has substantial positive spillover effects of space. When IP of HTI is measured by product innovation, there is no obvious space overflow. However, panel regression showed a significant positive effect. In terms of the influence on product IP of HTI, foreign R&D plays an almost equal role as local R&D. In terms of the impact on technological IP of HTI, foreign R&D input plays a positive role. It has a spatial spillover effect, the degree of impact is lower than that of domestic R&D input. Local governments should formulate relevant policies to encourage the fluidity of technical knowledge and overcome the sticky problem of foreign R&D technical knowledge, which is an essential aspect of absorbing foreign R&D technical knowledge in the future.

The threshold values of Moran’s index, Geary’s coefficient and the revised results.

Comparison of three sets of local Moran index values in two years.

Global Moran Index of Digital Technology Innovation Vitality.

Global Moran’s I index of construction land expansion intensity in the center of Chongqing city.

ABSTRACT. This study aimed to identify areas that showed spatial autocorrelation for corn yield and its predictive variables (i.e., average air temperature, rainfall, solar radiation, soil agricultural potential and altitude) and to determine the most appropriate spatial regression model to explain this culture. The study was conducted using data from the municipalities of the state of Paraná relating to the summer harvests in 2011/2012, 2012/2013, and 2013/2014. The statistical diagnostic of the OLS (Ordinary Least Square regression model) was employed to determine the most suitable regression model to predict corn yield. The SAR (Spatial Lag Model) was recommended for all crop years; however, the Spatial Error Model (CAR) was recommended only for the 2013/2014 crop year. The SAR and CAR spatial regressions chosen to predict corn yield in the various years had better results when compared to a regression model that does not incorporate data spatial autocorrelation (OLS). The coefficient of determination (R²), the Bayesian information criteria (BIC) and the maximum value of the logarithm of likelihood function proved to be better for the estimation of corn yield when SAR and CAR were used.

Against the backdrop of global economic transformation and sustainable development, green technological innovation has become a core driver for enhancing national competitiveness and addressing environmental challenges. With the profound changes in production methods and technological innovation, new quality productive forces (NQPF) have emerged as a key driver of green technological innovation. This study aims to explore the mechanisms through which NQPF influence Regional Green Technology Innovation (RGTI), with a particular focus on the mediating role of intellectual property protection (IPP). Using panel data from 31 provinces in China from 2011 to 2022, we conduct an empirical analysis employing a spatial Durbin model and a spatial mediation effect model. The results indicate that NQPF significantly promote RGTI, particularly in enhancing resource utilization efficiency and greening production processes. However, the study also identifies an inverted U-shaped relationship between NQPF and green technological innovation, primarily driven by local dynamics, where the positive effect diminishes after reaching a certain threshold. Further analysis reveals that IPP plays a crucial mediating role, not only directly fostering green innovation but also amplifying the positive effects of NQPF by enhancing the efficiency of innovation outcomes. Based on these findings, this study offers policy recommendations for promoting RGTI, emphasizing the need to strengthen support for NQPF, improve IPP mechanisms, and build a regional collaborative innovation system.

Comparison of the results of spatial statistics associated with disease of Aplysina cauliformis two populations at different time points. Each statistic tests for slightly different spatial characteristics. Contact connectedness was best able to explain clustering patterns within the study grids. The results of the Moran’s Index best represented individual connections shown by direct contact join-counts for ARBS infected sponges. *Range represents scale of significant clustering for the Ripley’s K statistic. Clusters and Outliers are individual Thiessen polygons in the grids that exhibited significant values for the Getis-Ord General G and the Moran’s Index Statistics. BP = Big Point, RG = Rainbow Gardens.

Moran’s I index of high-quality development level of resource-based cities from 2003–2018.

Note: a–threshold value; b–expected value. The expected values of the constants are the threshold values of Geary’s coefficient.

Moran’s I index of TEG.

Datasets for spatial autocorrelation functions based on Geary’s coefficient and Getis-Ord’s index (Partial results).

Datasets for spatial correlation dimension and spatial autocorrelation analysis (Partial results).