Sodikin, Ikin (2017) Pemodelan Geographically Weighted Regression Dan Bayesian Geographically Weighted Regression Dengan Fungsi Pembobot Adaptive Gaussian Kernel Pada Kasus Kemiskinan Di Provinsi Jawa Barat. Magister thesis, Universitas Brawijaya.
Abstract
Sebagai negara berkembang, hingga saat ini Indonesia masih memiliki salah satu permasalahan cukup serius yaitu kemiskinan. Untuk menanggulangi permasalahan kemiskinan tersebut, pemerintah telah melakukan berbagai upaya, antara lain dengan memperkirakan wilayah-wilayah yang tergolong miskin hingga tingkat administrasi terendah, dengan harapan pengentasan kemiskinan akan menjadi lebih terarah. Pendekatan analisis regresi telah sering digunakan dalam memprediksi tingkat kemiskinan, namun masih bersifat global dan diberlakukan pada seluruh lokasi yang diamati tanpa melibatkan lokasi geografis berdasarkan garis lintang dan bujur bumi. Pengaruh spasial yang muncul menyebabkan asumsi kebebasan antar pengamatan yang diperlukan dalam regresi global sulit dipenuhi. Salah satu model yang sudah banyak dikembangkan untuk mengatasi permasalahan spasial dan dapat mengakomodir pengaruh spasial dalam suatu pendugaan model regresi antara lain Geographically Weighted Regression (GWR). Salah satu permasalahan penting yang muncul dalam pemodelan GWR adalah ragam tidak konstan antar amatan. Hal tersebut muncul sebagai akibat koefisien regresi yang berbeda-beda di tiap lokasi pengamatan. Dampak yang mungkin ditimbulkan yaitu ragam galat juga akan berbeda untuk setiap lokasi serta tidak terpenuhinya asumsi kenormalan galat. Analisis Bayesian GWR yang diperkenalkan oleh Lesage (2001), dinilai sebagai salah satu solusi yang tepat untuk menangani permasalahan yang muncul pada pemodelan GWR. Pada analisis BGWR, ragam galat diasumsikan tidak konstan antar lokasi observasi agar masalah ketidakhomogenan ragam dapat terakomodir. Model BGWR menerapkan algoritma Gibbs Sampling dalam mengestimasi parameter yaitu salah satu metode simulasi dengan pendekatan Markov Chain Monte Carlo (MCMC) untuk memperoleh data contoh bangkitan parameter secara berurutan dari suatu sebaran posterior tertentu sehingga menghasilkan set estimasi yang mendekati sebaran asli dari posterior yang dibentuk dari likelihood data dan informasi awal berupa prior. Dalam penelitian ini digunakan pembobot adaptive Gaussian Kernel dimana bandwidth berbeda-beda antar satu lokasi dengan lokasi lainnya. Berdasarkan kriteria kebaikan model Mean Square Error (MSE), hasil analisis dalam penelitian ini menunjukkan bahwa model BGWR lebih baik daripada model GWR. Pada model BGWR dengan hyperparameter r=35, tingkat kemiskinan 27 kabupaten/kota di Provinsi Jawa Barat dapat dijelaskan dengan baik oleh peubah angka melek huruf, persentase rumah tangga dengan jamban bersama dan persentase rumah tangga penerima beras miskin dengan nilai MSE model sebesar
English Abstract
As a developing country, Indonesia still has one of the most serious problems of poverty. To overcome the problem of poverty, the government has made various efforts, among others by estimating areas that are categorized as poor up to the level of village administration, in the hope that poverty alleviation will become more directed. The regression analysis approach has often been used in predicting poverty rates, but still global and enforced at all observed locations without involving geographical location based on earth's longitude and latitude. The spatial influences that arise caused the assumptions of freedom between observations required in global regressions are difficult to fulfill. One of the models that has been developed to overcome spatial problems is Geographically Weighted Regression (GWR). GWR analysis is an expansion of a global regression analysis that generates parameter estimators to predict each point or location where the data is observed and collected. This analysis can accommodate spatial influence in an estimation of the regression model One of the important issues that arise in GWR modeling is the nonconstant variety between observations. This appears as a result of different regression coefficients in each location of observation. Possible impacts are the variety of errors will also be different for each location and non-fulfillment of the normality assumption of error. The Bayesian GWR (BGWR) analysis introduced by Lesage, rated as one of the right solutions to address the problems that arise in GWR modeling. The Bayesian approach applied to the GWR model is able to produce parameter estimators more effectively than the classical approach. In BGWR analysis, the variance of errors is assumed to be not constant between the observed locations Unlike the estimation of GWR model parameters using Weighted Least Square (WLS) method, the BGWR model applies the Gibbs Sampling algorithm. This algorithm is one of the simulation methods with the Monte Carlo Markov Chain (MCMC) approach to generate sequential sample data from a certain posterior distribution, so a set of estimations can be resulted approximate to the original joints posterior distribution of each parameter. In this study, the weights used are the adaptive Gaussian Kernel function, where the resulting bandwidth varies for each location of observation. This weighting is applied to compare the estimation results of GWR and BGWR model parameters. The results of the analysis show that the BGWR model is better than the GWR model in explaining the variables of literacy rate (%), percentage of households with joint latrine (%), and percentage of households receiving poor rice (%) to district poverty level in West Java Province. This is shown based on the Mean Square Error (MSE) value that is used as the model goodness criterion. The MSE value for the BGWR model is
| Item Type: | Thesis (Magister) |
|---|---|
| Identification Number: | TES/519.536/HAR/p/2017/041707193 |
| Uncontrolled Keywords: | REGRESSION ANALYSIS, GEOGRAPHY - STATISTICAL METHODS, HUMAN GEOGRAPHY - MATHEMATICAL MODELS, SPATIAL ANALYSIS (statistics), BAYESIAN STATISTICAL DECESION THEORY, GAUSSI AR MEASURES, POVERTY, INDONESIA - JAWA BARAT |
| Subjects: | 500 Natural sciences and mathematics > 519 Probabilities and applied mathematics > 519.5 Statistical mathematics > 519.53 Descriptive statistics, multivariate analysis, analysis of variance and covariance > 519.536 Regression analysis |
| Divisions: | S2/S3 > Magister Statistika, Fakultas MIPA |
| Depositing User: | Nur Cholis |
| Date Deposited: | 25 Aug 2017 02:02 |
| Last Modified: | 18 Dec 2020 00:37 |
| URI: | http://repository.ub.ac.id/id/eprint/1676 |
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