Seemingly Unrelated Regression Spatial Autoregressive Bayesian Modeling on Heteroscedasticity Case

The phenomenon encountered occasionally on complications involving spatial data, is that there is a tendency of heteroscedasticity since every region has distinct characteristics. Thus, it requires the approach which is more appropriate with the problem by using the Bayesian method. Bayesian method on spatial autoregressive model to contend the heteroscedasticity by applying prior distribution on variance parameter of error. To detect heteroscedasticity, it is shown from several responses correlating with the predictors. The method abled to estimate some responses is Seemingly Unrelated Regression (SUR). SUR is an econometrics model that used to be being utilized in solving some regression equations in which of them has their own parameter and appears to be uncorrelated. However, by correlation of error in differential equations, the correlation would occur among them. With the condition of the Bayesian SUR spatial autoregressive model, it is able to overcome heteroscedasticity cases from the vision of spatial. Further, the model involves four kinds of parameter priors’ distributions estimated by using the process of MCMC.

Spatiotemporal Dynamic of COVID-19 Diffusion in China: A Dynamic Spatial Autoregressive Model Analysis

COVID-19 has seriously threatened people’s health and well-being across the globe since it was first reported in Wuhan, China in late 2019. This study investigates the mechanism of COVID-19 transmission in different periods within and between cities in China to better understand the nature of the outbreak. We use Moran’s I, a measure of spatial autocorrelation, to examine the spatial dependency of COVID-19 and a dynamic spatial autoregressive model to explore the transmission mechanism. We find that the spatial dependency of COVID-19 decreased over time and that the transmission of the disease could be divided into three distinct stages: an eruption stage, a stabilization stage, and a declination stage. The infection rate between cities was close to one-third of the infection rate within cities at the eruption stage, while it reduced to zero at the declination stage. We also find that the infection rates within cities at the eruption stage and declination stage were similar. China’s policies for controlling the spread of the epidemic, specifically with respect to limiting inter-city mobility and implementing intra-city travel restrictions (social isolation), were most effective in reducing the viral transmission of COVID-19. The findings from this study indicate that the elimination of inter-city mobility had the largest impact on controlling disease transmission.

Bayesian Estimation of Partially Linear Additive Spatial Autoregressive Models with P-Splines

In this paper, we aim to develop a partially linear additive spatial autoregressive model (PLASARM), which is a generalization of the partially linear additive model and spatial autoregressive model. It can be used to simultaneously evaluate the linear and nonlinear effects of the covariates on the response for spatial data. To estimate the unknown parameters and approximate nonparametric functions by Bayesian P-splines, we develop a Bayesian Markov Chain Monte Carlo approach to estimate the PLASARM and design a Gibbs sampler to explore the joint posterior distributions of unknown parameters. Furthermore, we illustrate the performance of the proposed model and estimation method by a simulation study and analysis of Chinese housing price data.

Perbandingan Spatial Autoregressive Model dan Spatial Error Model dalam Pemodelan Indeks Pembangunan Manusia di Provinsi Jawa Timur

Indeks Pembangunan Manusia (IPM) merupakan indikator untuk mengukur keberhasilan upaya pembangunan kualitas hidup manusia yang telah dicapai. Pertumbuhan IPM di suatu wilayah dapat dipengaruhi oleh faktor geografis yaitu besarnya angka IPM di suatu wilayah dapat memengaruhi angka IPM pada wilayah yang berdekatan sehingga faktor geografis diduga dapat memengaruhi dan memberikan efek dependensi spasial pada nilai IPM di Provinsi Jawa Timur. Penelitian ini bertujuan untuk melakukan pemodelan pada faktor yang berpengaruh terhadap Indeks Pembangunan Manusia di Provinsi Jawa Timur. Unit pengamatan pada penelitian ini adalah 38 kabupaten/kota di Provinsi Jawa Timur. Data yang digunakan adalah data sekunder dari Badan Pusat Statistik Jawa Timur tahun 2017. Metode analisis yang digunakan dalam penelitian ini adalah metode Spatial Autoregressive Model (SAR) dan Spatial Error Model (SEM). Hasil penelitian menunjukkan bahwa berdasarkan nilai uji Lagrange Multiplier (lag) dan Lagrange Multiplier (error) terdapat dependensi lag dan error. Variabel prediktor yang secara signifikan berpengaruh terhadap nilai IPM pada model SAR dan SEM antara lain Angka Harapan Hidup, Rata-rata Lama Sekolah, Angka Harapan Lama Sekolah dan Kemampuan daya beli masyarakat. Berdasarkan hasil penelitian didapatkan model SEM dengan nilai R2 terbesar dan nilai AIC terkecil sehingga model SEM lebih baik digunakan untuk menganalisis nilai IPM di Provinsi Jawa Timur dibandingkan model SAR dan model regresi OLS.