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

Hu, Xueping; Lu, Yaori; Zhang, Huiguo; Jiang, Haijun; Shi, Qingdong

doi:10.3390/math9182343

Cited by 3 publications

(3 citation statements)

References 27 publications

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“…This could be problematic when the true data generating process varies considerably within some areas but only varies to a small degree within other areas; or when some elements of the regression coefficient φ have a large geographical variation whereas other elements of φ have a small geographical variation. Spatially-varying bandwidth or parameter-specific distance metrics have been proposed for standard GWR models ( Leong and Yue, 2017 ; Fotheringham et al, 2017 ; Lu et al, 2017 ; Hu et al, 2021 ), but the extension of these methods within a Bayesian framework is not straightforward computationally because a basic implementation would involve repeated evaluation of the geographically weighted kernel for all locations. Fourth, it would be appropriate in some applications to account for temporal effects, rather than ignoring potential temporal non-stationarity as we do in the current framework.…”

Section: Discussionmentioning

confidence: 99%

Generalized Geographically Weighted Regression Model within a Modularized Bayesian Framework

Liu

Goudie

2024

Bayesian Anal.

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Geographically weighted regression (GWR) models handle geographical dependence through a spatially varying coefficient model and have been widely used in applied science, but its general Bayesian extension is unclear because it involves a weighted log-likelihood which does not imply a probability distribution on data. We present a Bayesian GWR model and show that its essence is dealing with partial misspecification of the model. Current modularized Bayesian inference models accommodate partial misspecification from a single component of the model. We extend these models to handle partial misspecification in more than one component of the model, as required for our Bayesian GWR model. Information from the various spatial locations is manipulated via a geographically weighted kernel and the optimal manipulation is chosen according to a Kullback–Leibler (KL) divergence. We justify the model via an information risk minimization approach and show the consistency of the proposed estimator in terms of a geographically weighted KL divergence.

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Section: Discussionmentioning

confidence: 99%

Generalized Geographically Weighted Regression Model within a Modularized Bayesian Framework

Liu

Goudie

2024

Bayesian Anal.

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“…Varying coefficient models, in which the coefficients vary over a spatial location or are spatially varying, have been commonly applied by researchers in various fields. Research applying varying coefficient models in relation to spatial heterogeneity can be found in works such as [20], which employs geographically weighted regression for the selection of bandwidth, and [21], which conducts a comparison of geographically weighted regression and eigenvector spatial filtering. Additionally, studies pertaining to spatial autoregression include [22], which applies a Bayesian approach utilizing P-splines quantile regression in partial linear varying coefficient spatial autoregressive models.…”

Section: Introductionmentioning

confidence: 99%

Quantile Regression in Space-Time Varying Coefficient Model of Upper Respiratory Tract Infections Data

et al. 2023

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Space-time varying coefficient models, which are used to identify the effects of covariates that change over time and spatial location, have been widely studied in recent years. One such model, called the quantile regression model, is particularly useful when dealing with outliers or non-standard conditional distributions in the data. However, when the functions of the covariates are not easily specified in a parametric manner, a nonparametric regression technique is often employed. One such technique is the use of B-splines, a nonparametric approach used to estimate the parameters of the unspecified functions in the model. B-splines smoothing has potential to overfit when the number of knots is increased, and thus, a penalty is added to the quantile objective function known as P-splines. The estimation procedure involves minimizing the quantile loss function using an LP-Problem technique. This method was applied to upper respiratory tract infection data in the city of Bandung, Indonesia, which were measured monthly across 30 districts. The results of the study indicate that there are differences in the effect of covariates between quantile levels for both space and time coefficients. The quantile curve estimates also demonstrate robustness with respect to outliers. However, the simultaneous estimation of the quantile curves produced estimates that were relatively close to one another, meaning that some quantile curves did not depict the actual data pattern as precisely. This suggests that each district in Bandung City not only has different categories of incidence rates but also has a heterogeneous incidence rate based on three quantile levels, due to the difference in the effects of covariates over time and space.

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“…Yuan et al [13] examined the effects of AIC and their different bandwidths on GWR results. Hu et al [14] introduced a twodimensional bandwidth matrix for parameter estimation in the GWR model. Punzo et al [15] examined local differences in the effects of the main sociodemographic, economic, and institutional determinants of land consumption by using the bandwidth adjusted AIC in the GWR method.…”

Section: Introductionmentioning

confidence: 99%

Bandwidth Selection in Geographically Weighted Regression Models via Information Complexity Criteria

Koç

2022

Journal of Mathematics

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The geographically weighted regression (GWR) model is a local spatial regression technique used to determine and map spatial variations in the relationships between variables. In the GWR model, the bandwidth is very important as it can change the parameter estimates and affect the model performance. In this study, we applied the information complexity (ICOMP) type criteria in the selection of fixed bandwidth for the first time in the literature. The ICOMP-type criteria use a complexity measure that measures how parameters in the model relate to each other. A real dataset example and a simulation study have been conducted. Results of the simulation demonstrate that GWR models created with the bandwidth selection by ICOMP-type criteria show superior performance. In addition, when the bandwidth is selected according to the ICOMP-type criteria and the GWR model is created for the actual total fertility rate data, it is seen that the spatial distribution of the total fertility rate estimates is quite compatible with the distribution of the actual total fertility rate. According to the results, ICOMP-type criteria can be used effectively instead of the classical criteria in the literature in the selection of bandwidth in the GWR model.

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

Cited by 3 publications

References 27 publications

Generalized Geographically Weighted Regression Model within a Modularized Bayesian Framework

Generalized Geographically Weighted Regression Model within a Modularized Bayesian Framework

Quantile Regression in Space-Time Varying Coefficient Model of Upper Respiratory Tract Infections Data

Bandwidth Selection in Geographically Weighted Regression Models via Information Complexity Criteria

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