Weighted Regression and Bayesian Geographically Weighted Regression Modelling with Adaptive Gaussian Kernel Weight Function on the Poverty Level in West Java Province (original) (raw)
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In regular regression equation, a response variable is connected with some predictor variables in one main output, which is parameter measurement. This parameter explains relationships of every predictor variable with response variable. However, when it is applied to spatial data, this model is not always valid because the location difference can result in different model estimation. One of the analyses that recommend spatial condition is locally linear regression called Geographically Weighted Regression (GWR). The basic idea from this GWR model is the consideration of geographical aspect or location as weight in estimating the model parameter. Model parameter estimation of GWR is obtained using Weight Least Square (WLS) by giving different weights to every location where the data is obtained. In many analyses of GWR, also in this research, the weight used is Gauss Kernel, which needs bandwidth value as distance parameter that still affects each location. Bandwidth optimum can be obtained by minimalizing cross validation value. In this research, the researcher aims to compare the results of global regression model with GWR model in predicting poverty percentage. The data used as a case study are data from 33 cities and regencies in North Sumatera province.
International Journal of Statistics and Applications, 2014
Life Expectancy Rate (LER) is one of indicators that reflect the degree of health as a reference in planning of health programs in region. LER for each region depends on the potential of region and efforts of local government through programs to improve degree of health. In its application, the potention and effort to improving LER performed by government can be affected by adjacent surrounding areas. This is due to the limited potention in a region that encourage inter-regional cooperation in implementing programs to improve degree of health. The linkage due to location between the regions, is expected to give spatial variation effects in LER. LER modeling using classical regression is less precise due to the assumption of homogeneity which are not met. This problem can be overcome by Geographical weighted regression modeling (GWR). Geographical weighted regression (GWR) is expanded from the classical regression model into locally weighted regression. The selection of weighting functions is one determinant of GWR analysis. Classical regression model has four explanatory variables that significantly affect to response variable LER at 10% significance level. The four explanatory variables are the number of poor people (X 1 ), the number of health facilities (X 2 ), the percentage of health complaints (X 4 ), and the percentage of children under five years old were immunized (X 5 ). The classical regression model applies globally to all districts /cities in East Java province. GWR model gave resullt that eight regions with LER is influenced by three explanatory variables ie, number of poor people (X 1 ), the number of health facilities (X 2 ), and the percentage of children under five years old were immunized variables (X 5 ). They are Pacitan, Ponorogo, Trenggalek, Madiun, Magetan, Ngawi, Bojonegoro districts, and Madiun City. While other thirty regions entered into the second group. They are affected by the four explanatory variables ie, number of poor people (X 1 ), the number of health facilities (X 2 ), the percentage of health complaints (X 4 ), and percentage of children under five years old were immunized (X 5 ).
Optimum: Jurnal Ekonomi dan Pembangunan
Poverty is still the main problem in development both at the national and regional levels. The poverty reduction program carried out has not paid attention to spatial aspects so that the policies taken are often not on target. This study aims to see the spatial pattern of poverty in Java Island which includes Banten, DKI Jakarta, West Java, Central Java, DI Yogyakarta and East Java. The method used is geographically weighted regression (GWR) with addiptive weighting of the Gaussian Kernel which is processed with QGIS, Geoda and GWR4 software. This approach can identify spatial patterns that cannot be identified in ordinary regression analysis as found in previous studies. The data used in this study is secondary data in 2020 sourced from the Badan Pusat Statistik (BPS) and government website. The results of the study showed positive and group spatial autocorrelation in 34 districts/cities. There are 65 districts/cities in Java Island only affected by HDI, 4 districts/cities affected...
The Model of Mixed Geographically Weighted Regression (MGWR) for Poverty Rate in Central Java
This research aims to model the level of poverty in Central Java with spatial effect. The method of analysis that used in this study is Mixed Geographically Weighted Regression (MGWR).MGWR model parameter estimation is obtained by using Weighted Least Square (WLS) with gaussian kernel weighting function. Based on the result of the research, therewere five significant variables predictor that estimated to affect the level of poverty in the district/cityin Central Java, namely a minimum wage (X1), the percentage of the number of families who work in the agricultural sector (X2), the percentage of the number of families that use national health insurance program " Jamkesmas " (X4), the percentage of the number of families that have the facility to defecate(X6), and inflation (X8).Classfication accuracy (R2) of MGWR model is 73,95%, it means that MGWR model is able to explain the variation of the poverty level in 73,95%, the remaining of 26,05% is affected by another factor in the outside of the models with the AIC is180,49.There is no spatial effect or geographical factors influence the rate of poverty in Central Java. These variables predictors had asimiliar effect in each district/city.
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The success of development in a region in Indonesia can be measured by economic growth, especially in the financial sector using the Gross Regional Domestic Product (GRDP) growth rate. The GRDP figure at the Regency and City level in West Java is one of Indonesia's highest and most diverse. This is due to various factors, including the geographical location of West Java, which is directly adjacent to DKI Jakarta, which is the center of the national economy. Although classified as high, the diversity of GRDP values between regions in West Java needs attention to equalize economic growth. The diversity of GRDP values can be modeled by the Improved Geographically and Temporally Weighted Regression (I-GTWR) method by taking samples in 2018-2022. The I-GTWR modeling method considers the influence of spatial heterogeneity and spatialtemporal interaction, which has been proven to produce better results than the GTWR method in modeling GRDP in Central Java in 2011-2015.
International Journal of Engineering, 2018
Geographically weighted regression (GWR) is a regression method for exploring spatial nonstationarity by allowing different relationships at different locations. In the GWR, the response at each location is locally fitted by a linear function of a set of explanatory variables. In fact, it may have nonlinear relationship with one or more explanatory variables. Thus, the GWR model may not be able to accommodate the fact. In dealing with the problem, we attempt to introduce a geographically weighted polynomial regression (GWPolR) model. In this study, the GWPolR model is performed to explore spatially varying relationships between poverty and its factors in East Java Province, Indonesia. The factors studied here are the percentage of people educated less than elementary school, the percentage of people aged at least 10 years who cannot read and write, and the percentage of people working in the trading sector. Factually, the first and third factors tend to have nonlinear relationships with the poverty. Compared with the previous models in such condition, the GWPolR model gives a significant improvement and more complete understanding of how each explanatory variable was related to the poverty. This should allow improved planning of poverty alleviation strategies.
Proceedings of the 2nd International Conference Postgraduate School, 2018
Underdevelopment problem of a region can be seen from the dimensions of the economy, human resources, financial capability, infrastructure, accessibility, and regional characteristics. One method to see a region is underdeveloped or not is by looking the percentage of people living in poverty in a region in the publication data of underdeveloped regional indicators issued by the Central Bureau of Statistics (BPS). The results showed that the percentage of people in East Java Province who are living in poverty using linear regression is not yet appropriate. The percentage of people living in poverty spread spatially because there is heterogeneity between the observation sites which means that the observation of a location depends on the observation in another location with adjacent distance so that the spatial regression modeling was done with Adaptive Bisquare Kernel function. The grouping results with GWR resulted in nine groups based on significant variables. Each group eas characterized by life expectancy, mean years of schooling, expenditure and literacy rate.
Enthusiastic, 2022
Unemployment is one of the problems that hinder employment development programs. Based on East Java BPS data, the Open Unemployment Rate in East Java in 2019 is about 3.92 percent. In 2020, unemployment increased by 466.02 thousand people. On the other hand, OUR increased by 2.02 percent to 5.84 percent in August 2020. In addition to the indicators affecting OUR, each observation location has different characteristics, so multiple linear regression modeling is inappropriate. Geographically Weighted Regression is one of the spatial analyses developed from multiple linear regression for data containing spatial heterogeneity effects. The weighting functions used for this GWR model are Kernel Fixed and Adaptive functions (Gaussian, Bi-Square, Tricube, and Exponential). The analytical step carried out in estimating the parameters is to use WLS. The best weighting was obtained in the test, namely the Adaptive Tricube. Based on the study results, the GWR model with Adaptive Tricube weighted resulted in the value of R-Squared = 87.02%. However, the best model is obtained from the GWR model with exponential weighting with the smallest Akaike Information Criterion (AIC) value compared to the others, AIC = 95.77804 with R-Squared = 77.41.
International Journal of Sciences: Basic and Applied Research, 2020
Geographically and temporally weighted regression (GTWR) is a method applied when there is spatial and temporal diversity in the observation. GTWR model just considers local influences of spatial-temporal response variable on the explanatory variables. The GTWR model can add an autoregressive component of response variable, the resulting model is known as a geographically and temporally weighted autoregressive model (GTWAR). This study aims to perform GTWAR modeling which is applied to the data on the proportion of poor people by districts/cities in Java in 2012-2018. The results showed that GTWAR produced Akaike Information Criterion (AIC) smaller than GTWR, and the coefficient of determination (R 2) is higher than GTWR.
Bayesian spatial modeling of poverty risk in Kelantan
IOP Conference Series: Earth and Environmental Science, 2021
Poverty data vary in rural areas, in certain states or regions, and some urban areas. These areal data tends to have spatial autocorrelation. A Bayesian hierarchical model is commonly used to estimates the risks using a combination of available covariate data and a set of spatial random effects. These random effects are commonly modelled by conditional autoregressive (CAR) prior distributions, a type of Markov random field model. Spatial autocorrelation between the random effects, in CAR models is induced by a × neighbourhood matrix, W. However, many studies assumed that the W is fixed when fitting the model. Therefore, this study evaluates the performance of the Poisson-log linear Leroux Conditional Autoregressive (CAR) model with m-nearest neighbourhood weight matrices using a simulation study. This study creates simulated poverty data for 66 districts of Kelantan with different scenarios that related with random effects and covariate. A Poisson log-linear Leroux CAR model with m=1, 5 and 10 nearest neighbours are applied to the simulated poverty data. The performance of the models is evaluated using bias, Root Mean Square of Error (RMSE) and Deviance Information Criterion (DIC). The results show that the choice of m=1, 5 and 10 neighbourhood matrices and scenarios do not affect the bias for either the regression parameter β or the risk Rk and RMSE for the risk Rk. Nevertheless, there is the dissimilarity of the performance of the models in the RMSE of regression parameter β. The results suggest that the Poisson log-linear Leroux CAR model with the m=5 nearest neighbours performed overall best for simulated poverty data. It consistently gives good results across different strength of spatial autocorrelation of random effects and covariate. The model also gives the lowest DIC in all the scenarios, indicating a better fitting model than other models. The findings of this study give guidance in choosing the suitable m-nearest neighbourhood matrices to estimate the poverty risk in Kelantan.