Generalized Geographically Weighted Regression Model within a Modularized Bayesian Framework

Liu, Yang; Goudie, Robert J. B.

doi:10.1214/22-ba1357

Cited by 5 publications

(4 citation statements)

References 91 publications

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“…OLS regression model is a global regression model that assumes a fixed relationship between variables 29 . GWR model is a local regression model that considers the spatial non-stationarity of the relationship between variables 30 . STWR model is a spatiotemporal regression model that considers the temporal heterogeneity of the relationship between variables.…”

Section: Comparison Of the Fitting Impacts Of Ols Regression Gwr And ...mentioning

confidence: 99%

Exploring the spatiotemporal relationship between influenza and air pollution in Fuzhou using spatiotemporal weighted regression model

Chen,

Zheng,

et al. 2024

Sci Rep

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Air pollution has become a significant concern for human health, and its impact on influenza, has been increasingly recognized. This study aims to explore the spatiotemporal heterogeneity of the impacts of air pollution on influenza and to confirm a better method for infectious disease surveillance. Spearman correlation coefficient was used to evaluate the correlation between air pollution and the influenza case counts. VIF was used to test for collinearity among selected air pollutants. OLS regression, GWR, and STWR models were fitted to explore the potential spatiotemporal relationship between air pollution and influenza. The R2, the RSS and the AICc were used to evaluate and compare the models. In addition, the DTW and K-medoids algorithms were applied to cluster the county-level time-series coefficients. Compared with the OLS regression and GWR models, STWR model exhibits superior fit especially when the influenza outbreak changes rapidly and is able to more accurately capture the changes in different regions and time periods. We discovered that identical air pollutant factors may yield contrasting impacts on influenza within the same period in different areas of Fuzhou. NO2 and PM10 showed opposite impacts on influenza in the eastern and western areas of Fuzhou during all periods. Additionally, our investigation revealed that the relationship between air pollutant factors and influenza may exhibit temporal variations in certain regions. From 2013 to 2019, the influence coefficient of O3 on influenza epidemic intensity changed from negative to positive in the western region and from positive to negative in the eastern region. STWR model could be a useful method to explore the spatiotemporal heterogeneity of the impacts of air pollution on influenza in geospatial processes. The research findings emphasize the importance of considering spatiotemporal heterogeneity when studying the relationship between air pollution and influenza.

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Section: Comparison Of the Fitting Impacts Of Ols Regression Gwr And ...mentioning

confidence: 99%

Exploring the spatiotemporal relationship between influenza and air pollution in Fuzhou using spatiotemporal weighted regression model

Chen,

Zheng,

et al. 2024

Sci Rep

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“…GWR employs weights based on the distance between one observation location and another. The GWR model can be formulated as in Equation 2 [20].…”

Section: Geographically Weighted Regression (Gwr)mentioning

confidence: 99%

Unraveling Geospatial Determinants: Robust Geographically Weighted Regression Analysis of Maternal Mortality in Indonesia

Rahayu,

Ulfa,

Sasmita

et al. 2023

Infolitika J. Data Sci.

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Maternal Mortality Rate (MMR) in Indonesia has experienced a concerning annual increase, reaching 4,627 deaths in 2020 compared to 4,221 in 2019. This upward trajectory underscores the urgency of investigating the factors contributing to MMR. Recognizing the spatial heterogeneity and outliers in the data, our study employs the Robust Geographically Weighted Regression (RGWR) method with the Least Absolute Deviation approach. Using secondary data from the 2020 Indonesian Health Profile publication, the research seeks to establish province-specific models for MMR in 2020 and identify the key influencing factors in each region. Standard regression analyses fall short in addressing the complexities present in the data, making the RGWR approach crucial for understanding the nuanced relationships. The chosen RGWR model utilizes the Least Absolute Deviation method and a fixed kernel exponential weighting function. Notably, this model maintains a consistent bandwidth value across all locations, showcasing its robustness. In evaluating the model variations, the exponential fixed kernel weighting function emerges as the most optimal, boasting the smallest Akaike Information Criterion (AIC) value of 23.990 and the highest coefficient of determination value of 93.66%. The outcomes of this research yield 24 distinct models, each tailored to the unique characteristics of every province in Indonesia. This nuanced, location-specific approach is vital for developing effective interventions and policies to address the persistently high MMR. By providing insights into the complex interplay of factors influencing maternal mortality in different regions, the study contributes to the groundwork for targeted and impactful public health initiatives across Indonesia.

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“…LeSage [15] suggested an early version of BGWR, where the prior distribution of the parameters depends on expert knowledge. More recent approaches have been proposed by Ma et al [5], who proposed BGWR based on the weighted log-likelihood, and Liu & Goudie [16] proposed BGWR based on a weighted least-squares approach.…”

Section: Introductionmentioning

confidence: 99%

“…More recent approaches have been proposed by Ma et al . [ 5 ], who proposed BGWR based on the weighted log-likelihood, and Liu & Goudie [ 16 ] proposed BGWR based on a weighted least-squares approach.…”

Section: Introductionmentioning

confidence: 99%

Bayesian cluster geographically weighted regression for spatial heterogeneous data

Draidi Areed,

Price,

Thompson

et al. 2024

R. Soc. Open Sci.

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Spatial statistical models are commonly used in geographical scenarios to ensure spatial variation is captured effectively. However, spatial models and cluster algorithms can be complicated and expensive. One of these algorithms is geographically weighted regression (GWR) which was proposed in the geography literature to allow relationships in a regression model to vary over space. In contrast to traditional linear regression models, which have constant regression coefficients over space, regression coefficients are estimated locally at spatially referenced data points with GWR. The motivation for the adaption of GWR is the idea that a set of constant regression coefficients cannot adequately capture spatially varying relationships between covariates and an outcome variable. GWR has been applied widely in diverse fields, such as ecology, forestry, epidemiology, neurology and astronomy. While frequentist GWR gives us point estimates and confidence intervals, Bayesian GWR enriches our understanding by including prior knowledge and providing probability distributions for parameters and predictions of interest. This paper pursues three main objectives. First, it introduces covariate effect clustering by integrating a Bayesian geographically weighted regression (BGWR) with a post-processing step that includes Gaussian mixture model and the Dirichlet process mixture model. Second, this paper examines situations in which a particular covariate holds significant importance in one region but not in another in the Bayesian framework. Lastly, it addresses computational challenges in existing BGWR, leading to enhancements in Markov chain Monte Carlo estimation suitable for large spatial datasets. The efficacy of the proposed method is demonstrated using simulated data and is further validated in a case study examining children’s development domains in Queensland, Australia, using data provided by Children’s Health Queensland and Australia’s Early Development Census.

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Generalized Geographically Weighted Regression Model within a Modularized Bayesian Framework

Cited by 5 publications

References 91 publications

Exploring the spatiotemporal relationship between influenza and air pollution in Fuzhou using spatiotemporal weighted regression model

Exploring the spatiotemporal relationship between influenza and air pollution in Fuzhou using spatiotemporal weighted regression model

Unraveling Geospatial Determinants: Robust Geographically Weighted Regression Analysis of Maternal Mortality in Indonesia

Bayesian cluster geographically weighted regression for spatial heterogeneous data

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