# Spatial Autoregressive Regression Modeling with Heteroskedasticity Using Bayesian Approach on GRDP of Java

• Fitri Ramadhini Department of Statistics, Faculty of Mathematics and Natural Sciences, IPB University, Dramaga Campus, Bogor 16680, Indonesia
• Anik Djuraidah Department of Statistics, Faculty of Mathematics and Natural Sciences, IPB University, Dramaga Campus, Bogor 16680, Indonesia
• Aji Hamim Wigena Department of Statistics, Faculty of Mathematics and Natural Sciences, IPB University, Dramaga Campus, Bogor 16680, Indonesia
Keywords: Bayesian, Spatial autoregressive, Spatial dependence, Heteroskedasticity, GRDP.

### Abstract

Area data is aggregation data according to the area and location information. Modeling the area data needs to concern to the dependency and heteroskedasticity between areas. Heteroskedasticity occurs because units in the area generally differ in size and characteristics. The spatial autoregressive (SAR) regression models only consider dependence on the response variable. Most of SAR estimators are valid if there is no violation in the error assumption. In the condition of heteroskedasticity, the SAR parameter estimator with the maximum likelihood (ML) method becomes invalid. An alternative method that can be used is Bayesian method, that solves the problem of heteroskedasticity by modeling the structure of variance-covariance matrix. In this study, the Bayesian method was applied to Java’s GRDP in 2017. This data contains spatial dependence and heteroskedasticity so the ML method is not suitable to be applied. The explanatory variables were used in this study are number of workers, regional revenue, regional minimum wage, and human development index. The result shows that number of workers, regional revenue, and regional minimum wage are statistically significant affecting Java’s GRDP in 2017. This model provides a pseudo R2 value of 74%, which means it is good enough to illustrate the diversity of Java’s GRDP in 2017.

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Published
2019-07-23
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