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Although spatially varying coefficient (SVC) models have attracted considerable attention in applied science, they have been criticized as being unstable. The objective of this study is to show that capturing the \"spatial scale\" of each data relationship is crucially important to make SVC modeling more stable and, in doing so, adds flexibility. Here, the analytical properties of six SVC models are summarized in terms of their characterization of scale. Models are examined through a series of Monte Carlo simulation experiments to assess the extent to which spatial scale influences model stability and the accuracy of their SVC estimates. The following models are studied: (1) geographically weighted regression (GWR) with a fixed distance or (2) an adaptive distance bandwidth (GWRa); (3) flexible bandwidth GWR (FB-GWR) with fixed distance or (4) adaptive distance bandwidths (FB-GWRa); (5) eigenvector spatial filtering (ESF); and (6) random effects ESF (RE-ESF). Results reveal that the SVC models designed to capture scale dependencies in local relationships (FB-GWR, FB-GWRa, and RE-ESF) most accurately estimate the simulated SVCs, where RE-ESF is the most computationally efficient. Conversely, GWR and ESF, where SVC estimates are naïvely assumed to operate at the same spatial scale for each relationship, perform poorly. Results also confirm that the adaptive bandwidth GWR models (GWRa and FB-GWRa) are superior to their fixed bandwidth counterparts (GWR and FB-GWR). Key Words: flexible bandwidth geographically weighted regression, Monte Carlo simulation, nonstationarity, random effects eigenvector spatial filtering, spatial scale.

Interest in studying the urban real estate market, especially in investigating the relationship between house prices and related housing characteristics, is rapidly growing. However, this increasing attention is handicapped by a limited consideration of the multi-scale spatial heterogeneity in these relationships. This study uses the rental price data of 72,466 apartments in the Tokyo metropolitan area to examine spatial heterogeneity in the real estate market at multiple spatial scales. Within the framework of spatially varying coefficient (SVC) modeling, we utilized a random effect eigenvector spatial filtering-based SVC (RE-ESF-SVC) model, an approach not previously employed in real estate studies, and compared it with the traditional ESF-SVC model, which has no random effects. Our results show that: (1) except for one housing characteristic that impacts prices consistently throughout the Tokyo metropolitan area, relationships between other characteristics and prices vary from local to global spatial scales; (2) because of the utilization of random effects, RE-ESF-SVC has the unique advantage of making estimations flexibly while maintaining a high performance.

Linear regression models are commonly used for estimating ground PM2.5 concentrations, but the global spatial autocorrelation and local spatial heterogeneity of PM2.5 distribution are either ignored or only partially considered in commonly used models for estimating PM2.5 concentrations. Therefore, taking both global spatial autocorrelation and local spatial heterogeneity into consideration, a global-local regression (GLR) model is proposed for estimating ground PM2.5 concentrations in the Yangtze River Delta (YRD) and in the Beijing, Tianjin, Hebei (BTH) regions of China based on the aerosol optical depth data, meteorological data, remote sensing data, and pollution source data. Considering the global spatial autocorrelation, the GLR model extracts global factors by the eigenvector spatial filtering (ESF) method, and combines the fraction of them that passes further filtering with the geographically weighted regression (GWR) method to address the local spatial heterogeneity. Comprehensive results show that the GLR model outperforms the ordinary GWR and ESF models, and the GLR model has the best performance at the monthly, seasonal, and annual levels. The average adjusted R2 of the monthly GLR model in the YRD region (the BTH region) is 0.620 (0.853), which is 8.0% and 7.4% (6.8% and 7.0%) higher than that of the monthly ESF and GWR models, respectively. The average cross-validation root mean square error of the monthly GLR model is 7.024 μg/m3 in the YRD region, and 9.499 μg/m3 in the BTH region, which is lower than that of the ESF and GWR models. The GLR model can effectively address the spatial autocorrelation and spatial heterogeneity, and overcome the shortcoming of the ordinary GWR model that overfocuses on local features and the disadvantage of the poor local performance of the ordinary ESF model. Overall, the GLR model with good spatial and temporal applicability is a promising method for estimating PM2.5 concentrations.

Eigenvector spatial filtering (ESF) is becoming a popular way to address spatial dependence. Recently, a random effects specification of ESF (RE-ESF) is receiving considerable attention because of its usefulness for spatial dependence analysis considering spatial confounding. The objective of this study was to analyze theoretical properties of RE-ESF and extend it to overcome some of its disadvantages. We first compare the properties of RE-ESF and ESF with geostatistical and spatial econometric models. There, we suggest two major disadvantages of RE-ESF: it is specific to its selected spatial connectivity structure, and while the current form of RE-ESF eliminates the spatial dependence component confounding with explanatory variables to stabilize the parameter estimation, the elimination can yield biased estimates. RE-ESF is extended to cope with these two problems. A computationally efficient residual maximum likelihood estimation is developed for the extended model. Effectiveness of the extended RE-ESF is examined by a comparative Monte Carlo simulation. The main findings of this simulation are as follows: Our extension successfully reduces errors in parameter estimates; in many cases, parameter estimates of our RE-ESF are more accurate than other ESF models; the elimination of the spatial component confounding with explanatory variables results in biased parameter estimates; efficiency of an accuracy maximization-based conventional ESF is comparable to RE-ESF in many cases.

Background In Ethiopia, acute respiratory infections (ARIs) are a leading cause of morbidity and mortality among children under five years. Geographically linked data analysis using nationally representative data is crucial to map spatial patterns of ARIs and identify spatially-varying factors of ARI. Therefore, this study aimed to investigate spatial patterns and spatially-varying factors of ARI in Ethiopia. Methods Secondary data from the Ethiopian Demographic Health Survey (EDHS) of 2005, 2011, and 2016 were used. Kuldorff’s spatial scan statistic using the Bernoulli model was used to identify spatial clusters with high or low ARI. Hot spot analysis was conducted using Getis-OrdGi statistics. Eigenvector spatial filtering regression model was carried out to identify spatial predictors of ARI. Results Acute respiratory infection spatially clustered in 2011 and 2016 surveys year (Moran’s I :-0.011621–0.334486 ) . The magnitude of ARI decreased from 12.6% (95%, CI: 0.113–0.138) in 2005 to 6.6% (95% CI: 0.055–0.077) in 2016. Across the three surveys, clusters with a high prevalence of ARI were observed in the North part of Ethiopia. The spatial regression analysis revealed that the spatial patterns of ARI was significantly associated with using biomass fuel for cooking and children not initiating breastfeeding within 1-hour of birth. This correlation is strong in the Northern and some areas in the Western part of the country. Conclusion Overall there has been a considerable decrease in ARI, but this decline in ARI varied in some regions and districts between surveys. Biomass fuel and early initiation of breastfeeding were independent predictors of ARI. There is a need to prioritize children living in regions and districts with high ARI.

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.

Spatial cancer data analyses frequently utilize regression techniques to investigate associations between cancer incidences and potential covariates. Model specification, a process of formulating an appropriate model, is a well-recognized task in the literature. It involves a distributional assumption for a dependent variable, a proper set of predictor variables (i.e., covariates), and a functional form of the model, among other things. For example, one of the assumptions of a conventional statistical model is independence of model residuals, an assumption that can be easily violated when spatial autocorrelation is present in observations. A failure to account for spatial structure can result in unreliable estimation results. Furthermore, the difficulty of describing georeferenced data may increase with the presence of a positive and negative spatial autocorrelation mixture, because most current model specifications cannot successfully explain a mixture of spatial processes with a single spatial autocorrelation parameter. Particularly, properly accounting for a spatial autocorrelation mixture is challenging. This paper empirically investigates and uncovers a possible spatial autocorrelation mixture pattern in breast cancer incidences in Broward County, Florida, during 2000–2010, employing different model specifications. The analysis results show that Moran eigenvector spatial filtering provides a flexible method to examine such a mixture.

Gravity-type spatial interaction models have been popularly utilized in modeling cross-sectional migration data, but their misspecification also has been raised in the literature. This misspecification issue principally concerns an insufficient accounting of underlying effects of spatial structure, including the presence of network autocorrelation among migration flows. Recent studies reveal that spatial interaction models are significantly improved by incorporating network autocorrelation in log-linear or Poisson regression estimation techniques, which are common estimation methods for spatial interaction models. However, when migration flows are structured as a panel data set from multiple time periods, the data set is likely to display temporal correlation within each measurement unit (here, each flow between a dyad of an origin and a destination) as well as network autocorrelation within each time period. Hence, spatial interaction models should be explicitly specified to account for these two different types of correlation structure. Using the eigenvector spatial filtering technique, this article outlines how to model network autocorrelation among migration flows structured through multiple time spans in either a linear or a generalized linear mixed model. An analysis of annual U.S. interstate migration data reported by the U.S. Internal Revenue Service shows that incorporation of two different types of autocorrelation leads to an improvement of model fitting and more intuitive parameter estimates.

Estimating rainfall at a point or region is difficult because complex factors affect rainfall.  A helpful strategy is to utilize the GCM output information from CMIP6-DCPP by forming a functional relationship between GCM output data and rainfall data at a certain point or region, called statistical downscaling.  However, because the resolution of the GCM  output is relatively low, the model could not explain the local effects since the heterogeneity is enormous.  Based on this fact, the current research proposes to add some local characteristics in the downscaling model to improve the performance to predict the rainfall levels.  Further, the rainfall levels have spatial dependencies among points.  Therefore, this research employed the Eigenvector Spatial Filtering-Varying Coefficient (ESF-VC) as the methodology of the modeling. The objective of this research is to perform rainfall predictive modeling with CMIP6-DCPP output and some local characteristic information as predictors using ESF-VC methodology.  The approach was implemented to predict the rainfall level in the Province of Riau in Indonesia.  Based on the results, the ESF-VC model provides good performance in estimating rainfall in Riau.  The variables that provide local effects are  altitude, equator (location), equator (distance), and wet month dummy.  While the variables  ENSO and vegetation (NDVI) have a significant global effect on the model.

PM 2.5 concentrations are commonly estimated using geographically weighted regression (GWR) models, but these models may suffer from multi-collinearity and over-focus on local feature problems. To overcome these shortcomings, a self-adaptive bandwidth eigenvector spatial filtering (SA-ESF) model utilizing the golden section search (GO-ESF) and genetic algorithm (GA-ESF) was proposed. The SA-ESF model was applied to estimate ground PM 2.5 concentrations in the Yangtze River Delta (YRD) region of China both seasonally and annually from December 2015 to November 2016 using remotely sensing data, factory locations, and road networks. The results of the original eigenvector spatial filtering (ESF), GO-ESF, GA-ESF, and GWR models show that the GA-ESF model offers better performance and exhibits a better average adjusted R 2 which is 26.6%, 15.3%, and 10.8% higher than for the ESF, GO-ESF, and GWR models, respectively. We next calculated stochastic site indicators that can describe characteristics of regional concentration from interpolated concentration maps derived from the GA-ESF and GWR models. The concentration maps and stochastic site indicators point to major differences in the PM 2.5 concentrations in mountainous areas. There are notably high concentrations in those areas using the GWR model, in contrast with the GA-ESF results, indicating that there may be overfitting problems using the GWR model. Overall, the proposed SA-ESF model with the genetic algorithm technique can capture both global and local features and achieve promising results.