scholarly journals Geographically Weighted Regression Analysis for Spatial Economics Data: A Bayesian Recourse

2020 ◽  
pp. 016001762095982 ◽  
Author(s):  
Zhihua Ma ◽  
Yishu Xue ◽  
Guanyu Hu
Keyword(s):  
Variable Selection ◽  
Spatial Data ◽  
Geographically Weighted Regression ◽  
Marginal Likelihood ◽  
Deviance Information Criterion ◽  
Information Criterion ◽  
Bayesian Variable Selection ◽  
Spatial Data Analysis ◽  
Weighted Regression ◽  
Model Assessment

The geographically weighted regression (GWR) is a well-known statistical approach to explore spatial non-stationarity of the regression relationship in spatial data analysis. In this paper, we discuss a Bayesian recourse of GWR. Bayesian variable selection based on spike-and-slab prior, bandwidth selection based on range prior, and model assessment using a modified deviance information criterion and a modified logarithm of pseudo-marginal likelihood are fully discussed in this paper. Usage of the graph distance in modeling areal data is also introduced. Extensive simulation studies are carried out to examine the empirical performance of the proposed methods with both small and large number of location scenarios, and comparison with the classical frequentist GWR is made. The performance of variable selection and estimation of the proposed methodology under different circumstances are satisfactory. We further apply the proposed methodology in analysis of a province-level macroeconomic data of thirty selected provinces in China. The estimation and variable selection results reveal insights about China’s economy that are convincing and agree with previous studies and facts.

scholarly journals Spatial Analysis of Housing Prices and Market Activity with the Geographically Weighted Regression

2020 ◽  
Vol 9 (6) ◽  
pp. 380
Author(s):  
Radosław Cellmer ◽  
Aneta Cichulska ◽  
Mirosław Bełej
Keyword(s):  
Spatial Heterogeneity ◽  
Housing Market ◽  
Spatial Data ◽  
Geographically Weighted Regression ◽  
Housing Prices ◽  
Spatial Diversity ◽  
Spatial Data Analysis ◽  
Weighted Regression ◽  
Market Activity ◽  
Administrative Units

The main part of the study will be to demonstrate that models taking into account spatial heterogeneity (Geographically Weighted Regression and Mixed Geographically Weighted Regression) which reproduce housing market determinants better reflect market relationships than conventional regression models. The spatial heterogeneity of the housing market determinants results in the spatial diversity of the market activity, as well as of real estate prices and values. The main aim of the study was to analyse an effect of these socio-demographic and environmental factors on average housing property prices and on the number of transactions in a spatial approach. In previous research conducted on a national scale, usually all variables were treated in a similar way, i.e., as global or local variables. During the research, an attempt was also made to answer the question of which of the variables adopted for analysis have a local impact on prices and market activity, and which are global. The study was conducted in Poland and used data from the year 2018 on 380 counties (Local Administrative Units). The study showed that determinants both for average prices and for the housing market activity show spatial autocorrelation with high–high and low–low cluster groups. Owing to these models, it was possible to draw specific conclusions on local determinants of flat prices and the market activity in Poland. The study findings have confirmed that they are an extremely effective tool for spatial data analysis.

scholarly journals Bayesian Variable Selection Utilizing Posterior Probability Credible Intervals

2021 ◽  
Author(s):  
Mengtian Du ◽  
Stacy L. Andersen ◽  
Thomas T. Perls ◽  
Paola Sebastiani
Keyword(s):  
Variable Selection ◽  
Posterior Probability ◽  
Deviance Information Criterion ◽  
Information Criterion ◽  
Bayesian Variable Selection ◽  
Model Parameters ◽  
Mixed Effect ◽  
Stochastic Search Variable Selection ◽  
Mixed Effect Models ◽  
Credible Intervals

AbstractIn recent years, there has been growing interest in the problem of model selection in the Bayesian framework. Current approaches include methods based on computing model probabilities such as Stochastic Search Variable Selection (SSVS) and Bayesian LASSO and methods based on model choice criteria, such as the Deviance Information Criterion (DIC). Methods in the first group compute the posterior probabilities of models or model parameters often using a Markov Chain Monte Carlo (MCMC) technique, and select a subset of the variables based on a prespecified threshold on the posterior probability. However, these methods rely heavily on the prior choices of parameters and the results can be highly sensitive when priors are changed. DIC is a Bayesian generalization of the Akaike’s Information Criterion (AIC) that penalizes for large number of parameters, it has the advantage that can be used for selection of mixed effect models but tends to prefer overparameterized models. We propose a novel variable selection algorithm that utilizes the parameters credible intervals to select the variables to be kept in the model. We show in a simulation study and a real-world example that this algorithm on average performs better than DIC and produces more parsimonious models.

Testing the Importance of the Explanatory Variables in a Mixed Geographically Weighted Regression Model

10.1068/a3768 ◽  
2006 ◽  
Vol 38 (3) ◽  
pp. 587-598 ◽  
Author(s):  
Chang-Lin Mei ◽  
Ning Wang ◽  
Wen-Xiu Zhang
Keyword(s):  
Regression Model ◽  
Spatial Data ◽  
Geographically Weighted Regression ◽  
Statistical Modelling ◽  
Spatial Data Analysis ◽  
Weighted Regression ◽  
P Value ◽  
Bootstrap Procedure ◽  
Explanatory Variables ◽  
Geographically Weighted Regression Model

A mixed geographically weighted regression (MGWR) model is a kind of regression model in which some coefficients of the explanatory variables are constant, but others vary spatially. It is a useful statistical modelling tool in a number of areas of spatial data analysis. After an MGWR model is identified and calibrated, which has been well studied recently, one of the important inference problems is to evaluate the influence of the explanatory variables in the constant-coefficient part on the response of the model. This is useful in the selection of the variables and for the purpose of explanation. In this paper, a statistical inference framework for this issue is suggested and, besides the F-approximation, which has been frequently used in the literature of the geographically weighted regression technique, a bootstrap procedure for deriving the p-value of the test is also suggested. The performance of the test is investigated by extensive simulations. It is demonstrated that both the F-approximation and the bootstrap procedure work satisfactorily.

Second-hand housing batch evaluation model of zhengzhou city based on big data and MGWR model

2021 ◽  
pp. 1-20
Author(s):  
Chaojie Liu ◽  
Jie Lu ◽  
Wenjing Fu ◽  
Zhuoyi Zhou
Keyword(s):  
Real Estate ◽  
Geographically Weighted Regression ◽  
Euclidean Distance ◽  
Evaluation Model ◽  
Housing Prices ◽  
Information Criterion ◽  
Access Point ◽  
Least Square ◽  
Weighted Regression ◽  
Spatial Error

How to better evaluate the value of urban real estate is a major issue in the reform of real estate tax system. So the establishment of an accurate and efficient housing batch evaluation model is crucial in evaluating the value of housing. In this paper the second-hand housing transaction data of Zhengzhou City from 2010 to 2019 was used to model housing prices and explanatory variables by using models of Ordinary Least Square (OLS), Spatial Error Model (SEM), Geographically Weighted Regression (GWR), Geographically and Temporally Weighted Regression (GTWR), and Multiscale Geographically Weighted Regression (MGWR). And a correction method of Barrier Line and Access Point (BLAAP) was constructed, and compared with three correction methods previously studied: Buffer Area (BA), Euclidean Distance (ED), and Non-Euclidean Distance, Travel Distance (ND, TT). The results showed: The fitting degree of GWR, MGWR and GTWR by BLAAP was 0.03–0.07 higher than by ND. The fitting degree of MGWR was the highest (0.883) by BLAAP but the smallest by Akaike Information Criterion (AIC), and 88.3% of second-hand housing data could be well interpreted by the model.

scholarly journals Measuring Bandwidth Uncertainty in Multiscale Geographically Weighted Regression Using Akaike Weights

2019 ◽  
Author(s):  
Ziqi Li ◽  
Alexander Stewart Fotheringham ◽  
Taylor M. Oshan ◽  
Levi John Wolf
Keyword(s):  
Geographically Weighted Regression ◽  
Regression Models ◽  
Bandwidth Selection ◽  
Information Criterion ◽  
Weighted Regression ◽  
Parameter Estimates ◽  
Multi Scale ◽  
Single Scale ◽  
Heterogeneous Processes ◽  
Key Parameter

Bandwidth, a key parameter in geographically weighted regression models, is closely related to the spatial scale at which the underlying spatially heterogeneous processes being examined take place. Generally, a single optimal bandwidth (geographically weighted regression) or a set of covariate-specific optimal bandwidths (multiscale geographically weighted regression) is chosen based on some criterion such as the Akaike Information Criterion (AIC) and then parameter estimation and inference are conditional on the choice of this bandwidth. In this paper, we find that bandwidth selection is subject to uncertainty in both single-scale and multi-scale geographically weighted regression models and demonstrate that this uncertainty can be measured and accounted for. Based on simulation studies and an empirical example of obesity rates in Phoenix, we show that bandwidth uncertainties can be quantitatively measured by Akaike weights, and confidence intervals for bandwidths can be obtained. Understanding bandwidth uncertainty offers important insights about the scales over which different processes operate, especially when comparing covariate-specific bandwidths. Additionally, unconditional parameter estimates can be computed based on Akaike weights accounts for bandwidth selection uncertainty.

The Survivor Problem Continued: Introduction to Bayesian Model Selection

2019 ◽  
pp. 308-324
Author(s):  
Therese M. Donovan ◽  
Ruth M. Mickey
Keyword(s):  
Parameter Estimation ◽  
Model Selection ◽  
Bayesian Model ◽  
Formal Education ◽  
Deviance Information Criterion ◽  
Information Criterion ◽  
Bayesian Model Selection ◽  
Assessment Model ◽  
Model Fit ◽  
Model Assessment

This chapter provides a very brief introduction to Bayesian model selection. The “Survivor Problem” is expanded in this chapter, where the focus is now on comparing two models that predict how long a contestant will last in a game of Survivor: one model uses years of formal education as a predictor, and a second model uses grit as a predictor. Gibbs sampling is used for parameter estimation. Deviance Information Criterion (commonly abbreviated as DIC) is used as a guide for model selection. Details of how this measure is computed are described. The chapter also discusses model assessment (model fit) and Occam’s razor.

A General Framework for Estimation and Inference of Geographically Weighted Regression Models: 2. Spatial Association and Model Specification Tests

2002 ◽  
Vol 34 (5) ◽  
pp. 883-904 ◽  
Author(s):  
Antonio Páez ◽  
Takashi Uchida ◽  
Kazuaki Miyamoto
Keyword(s):  
Spatial Data ◽  
Geographically Weighted Regression ◽  
Spatial Association ◽  
Global Perspective ◽  
Model Specification ◽  
Weighted Regression ◽  
Spatial Effects ◽  
Modeling Framework ◽  
Spatial Error ◽  
Special Cases

Spatial association effects, perhaps the most important concern in the analysis of spatial data, have been amply studied from a global perspective in the exploratory and modeling domains, and more recently also from a local perspective in the realm of exploratory data analysis. In a local modeling framework, however, the issue of how to detect and model spatial association by using geographically weighted regression (GWR) remains largely unresolved. In this paper we exploit a recent development that casts GWR as a model of locational heterogeneity, to formulate a general model of spatial effects that includes as special cases GWR with a spatially lagged objective variable and GWR with spatial error autocorrelation. The approach also permits the derivation of formal tests against several forms of model misspecification, including locational heterogeneity in global models, and spatial error autocorrelation in GWR models. Application of these results is exemplified with a case study.

scholarly journals Geographically varying relationships of COVID-19 mortality with different factors in India

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Asif Iqbal Middya ◽  
Sarbani Roy
Keyword(s):  
Geographically Weighted Regression ◽  
Information Criterion ◽  
Driving Factors ◽  
Least Square ◽  
Weighted Regression ◽  
Related Factors ◽  
Local Method ◽  
Ordinary Least Square ◽  
Local Methods ◽  
Global And Local

AbstractCOVID-19 is a global crisis where India is going to be one of the most heavily affected countries. The variability in the distribution of COVID-19-related health outcomes might be related to many underlying variables, including demographic, socioeconomic, or environmental pollution related factors. The global and local models can be utilized to explore such relations. In this study, ordinary least square (global) and geographically weighted regression (local) methods are employed to explore the geographical relationships between COVID-19 deaths and different driving factors. It is also investigated whether geographical heterogeneity exists in the relationships. More specifically, in this paper, the geographical pattern of COVID-19 deaths and its relationships with different potential driving factors in India are investigated and analysed. Here, better knowledge and insights into geographical targeting of intervention against the COVID-19 pandemic can be generated by investigating the heterogeneity of spatial relationships. The results show that the local method (geographically weighted regression) generates better performance ($$R^{2}=0.97$$ R 2 = 0.97 ) with smaller Akaike Information Criterion (AICc $$=-66.42$$ = - 66.42 ) as compared to the global method (ordinary least square). The GWR method also comes up with lower spatial autocorrelation (Moran’s $$I=-0.0395$$ I = - 0.0395 and $$p < 0.01$$ p < 0.01 ) in the residuals. It is found that more than 86% of local $$R^{2}$$ R 2 values are larger than 0.60 and almost 68% of $$R^{2}$$ R 2 values are within the range 0.80–0.97. Moreover, some interesting local variations in the relationships are also found.

A geographically weighted regression approach to examine the dynamics of fertility differentials across Africa

2020 ◽  
Vol 36 ◽  
pp. 87-102
Author(s):  
Aniefiok Henry Ekong ◽  
Olaniyi Mathew Olayiwola
Keyword(s):  
Geographically Weighted Regression ◽  
Information Criterion ◽  
Ordinary Least Squares ◽  
Fertility Rate ◽  
Weighted Regression ◽  
Negative Consequences ◽  
African Countries ◽  
Factors Affecting ◽  
Western Africa ◽  
Republic Of The Congo

Studies have shown that fertility rate in Africa is still among the highest in the world. However, there are few spatial investigations into the variation of fertility rate and its determinant in Africa. This study aimed to examine the spatial distribution of fertility rate as well as highlight its significant determinants. Ordinary Least Squares (OLS) regression was carried out on dataset for 53 African countries on Total Fertility Rate (TFR) and eleven determinant factors to obtain a best model, which was then used for Geographically Weighted Regression (GWR). The study showed that TFR was significantly influenced by adolescent fertility rates, contraceptive prevalence rates and gross domestic product per capita. GWR model diagnostics of Akaike Information Criterion and adjusted R-squared showed that GWR fitted TFR in Africa better than OLS model. Also, countries around Middle to Western Africa comprising Burundi, Democratic Republic of the Congo, Central African Republic, Chad, Nigeria, Niger, Benin, Burkina Faso and Mali, were regions with high TFRs that impacted Africa’s positive TFR spatial autocorrelation. More intense works could therefore be carried out in these countries to manage the identified significant factors affecting TFR to address the negative consequences of high TFR in Africa.

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