Using an Eigenvector Spatial Filtering-Based Spatially Varying Coefficient Model to Analyze the Spatial Heterogeneity of COVID-19 and Its Influencing Factors in Mainland China

The COVID-19 pandemic has led to many deaths and economic disruptions across the world. Several studies have examined the effect of corresponding health risk factors in different places, but the problem of spatial heterogeneity has not been adequately addressed. The purpose of this paper was to explore how selected health risk factors are related to the pandemic infection rate within different study extents and to reveal the spatial varying characteristics of certain health risk factors. An eigenvector spatial filtering-based spatially varying coefficient model (ESF-SVC) was developed to find out how the influence of selected health risk factors varies across space and time. The ESF-SVC was able to take good control of over-fitting problems compared with ordinary least square (OLS), eigenvector spatial filtering (ESF) and geographically weighted regression (GWR) models, with a higher adjusted R2 and lower cross validation RMSE. The impact of health risk factors varied as the study extent changed: In Hubei province, only population density and wind speed showed significant spatially constant impact; while in mainland China, other factors including migration score, building density, temperature and altitude showed significant spatially varying impact. The influence of migration score was less contributive and less significant in cities around Wuhan than cities further away, while altitude showed a stronger contribution to the decrease of infection rates in high altitude cities. The temperature showed mixed correlation as time passed, with positive and negative coefficients at 2.42 °C and 8.17 °C, respectively. This study could provide a feasible path to improve the model fit by considering the problem of spatial autocorrelation and heterogeneity that exists in COVID-19 modeling. The yielding ESF-SVC coefficients could also provide an intuitive method for discovering the different impacts of influencing factors across space in large study areas. It is hoped that these findings improve public and governmental awareness of potential health risks and therefore influence epidemic control strategies.

Lessons Learned from Applying Varying Coefficient Model to Controlled Simulation Datasets

The development of site- and path-specific (i.e., non-ergodic) ground motion models (GMMs) can drastically improve the accuracy of probabilistic seismic hazard analyses (PSHA). The Varying Coefficient Model (VCM) is a novel technique for developing non-ergodic GMMs, which puts epistemic uncertainty into spatially varying coefficients. The coefficients at nearby locations are correlated by placing a Gaussian process prior on them. The correlation structure is determined by the data, and later used to predict coefficients and their epistemic uncertainties at new locations. It is important to carefully verify the technique before its results can be accepted by the engineering community. In this study, we used a series of simulation-based controlled ground motion datasets from CyberShake to test a modified VCM technique, which partitions the epistemic uncertainty into spatially varying source, site and path terms. Because the simulation parameters (inputs) are known, it is straightforward to verify what is recovered by the VCM from CyberShake simulation. We find that the site effects in CyberShake datasets can be reliably recovered by the VCM. However, the densely-located self-similar events in CyberShake datasets lead to large correlation lengths, which violates the isotropic assumption underlying the method and prevents the VCM from capturing the genuine source effects. For path effects, cell-specific attenuation approaches fail to recover the anelastic attenuation pattern of the 3D velocity model, most likely due to inappropriate assumption of point sources and straight-line wave propagation. Instead, a midpoint approach that only considers the aggregated path effects can better recover the strong attenuation within basins by fixing the correlation length of path effects. Lessons learned in this study not only provide important guidance for future applications of VCM to both simulation and empirical datasets, but also help further development of the technique, notably for the recovery of path effects.

Using an Eigenvector Spatial Filtering Based Spatially Varying Coefficient Model to Analyze the Spatial Heterogeneity of COVID-19 and Its Influencing Factors in Mainland China

Background: The COVID-19 pandemic has led to many deaths and economic disruptions across the world. Several studies have examined the effect of health risk factors on COVID-19 rates in different places, but the problem of spatial heterogeneity has not been adequately addressed.Methods: In this paper, we developed an Eigenvector Spatial Filtering based spatially varying coefficient model (ESF-SVC) to reveal the spatially varying impact of certain health risk factors on the COVID-19 spread. The experiment was conducted during 7 weeks within two study extents (Hubei province and mainland China). Spatial varying coefficient maps were produced for spatial pattern discovery.Results: Results showed that the ESF-SVC model could take good control of over-fitting problems, with average adjusted R2 16.31% (in Hubei province) and 10.25% (in mainland China) higher than that of GWR. The cross validation RMSE of ESF-SVC model was also the lowest. In Hubei province, Population density and wind speed had a significant impact on COVID-19 infection rates and that their effect was constant across cities. While in mainland China, migration score, building density, temperature and altitude showed significant impact and their effect varies across space. The influence of migration score was less contributive and less significant in cities around Wuhan than cities farther away, while the altitude showed stronger contributions in high altitude cities.Conclusions: Our study hopes to provide not only a feasible path to solve the problem of spatial autocorrelation and spatial heterogeneity in COVID-19 characterization but also an intuitive way to discover spatial patterns in large study areas, which could help people and government awareness of the potential health risks and shed some light in COVID-19 control strategies.

Selection of the Bandwidth Matrix in Spatial Varying Coefficient Models to Detect Anisotropic Regression Relationships

The commonly used Geographically Weighted Regression (GWR) fitting method for a spatial varying coefficient model is to select a bandwidth h for the geographic location (u, v), and assign the same weight to the two dimensions. However, spatial data usually present anisotropy. The introduction of a two-dimensional bandwidth matrix not only gives weight from two dimensions separately, but also increases the direction of kernel smoothness. The adaptive bandwidth matrix is more flexible. Therefore, in this paper, a two dimensional bandwidth matrix is introduced into the spatial varying coefficient model for parameter estimation. Through simulation experiments, the results obtained under the adaptive bandwidth matrix are compared with those obtained under the global bandwidth matrix, indicating the effectiveness of introducing the adaptive bandwidth matrix.