Bayesian Multilevel Bivariate Spatial Modelling of Italian School Data

TL;DR

This study uses Bayesian multilevel bivariate spatial modeling to analyze how school infrastructure impacts student performance in Italian municipalities, revealing both infrastructure effects and spatial effects.

Contribution

It introduces a Bayesian multilevel bivariate spatial model with ICAR latent effects for analyzing spatially correlated educational data.

Findings

Significant link between school infrastructure and student outcomes.

Spatial effects are essential to explain outcome variability.

Model effectively captures spatial correlation in data.

Abstract

This paper studies the relationship between the student's 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 standardized 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 by the Integrated Nested Laplace Approximation (INLA), implemented in the \texttt{R-INLA} package. We find that alongside 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.