Bayesian multilevel bivariate spatial modelling of Italian school data
使用贝叶斯多层次双变量空间模型，研究意大利高中学生能力与市政基础设施的关系，发现基础设施与成绩显著相关，但空间结构效应仍不可忽略。
Abstract This paper studies the relationship between the student abilities in the second year of high school and the infrastructural endowment in all Italian municipalities, using spatial Bayesian modelling. Municipal student scores are obtained by averaging standardised and spatially homogeneous indicators of student outcomes provided by the INVALSI Institute for two subjects: Italian and mathematics. Given the nature of the data, we employ a multilevel regression model assuming a bivariate intrinsic conditionally autoregressive (ICAR) latent effect to explain the spatial variability and account for the correlation between the two subjects. Bayesian model estimation is obtained using the integrated nested Laplace approximation (INLA), implemented in the package. We find that along with a significant association with the current state of school infrastructure and facilities, spatially structured latent effects are still necessary to explain the different student outcomes across municipalities.