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This paper studies the relationship between the territorial endowment of school infrastructure and services in Italy and the performance of high school students, expressed by the Invalsi scores for the second year of high school, by means of spatial modelling. We fit a multilevel Bayesian regression model with a latent spatial effect modelled as a conditional autoregressive (CAR) process. Since the Invalsi scores regard two subjects (Italian and Mathematics) we fit a bivariate model, in which the relationship between the two subjects is accounted for by the random effect. The computation follows the method of the Integrated Nested Laplace Approximation (INLA), implemented in the R-INLA software.

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Multilevel Bivariate Areal Modelling for School Data: An Application with R-INLA

  • 会议论文

  • 发表日期：

    2025年

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  • Leonardo Cefalo,
  • Virgilio Gómez-Rubio

摘要

This paper studies the relationship between the territorial endowment of school infrastructure and services in Italy and the performance of high school students, expressed by the Invalsi scores for the second year of high school, by means of spatial modelling. We fit a multilevel Bayesian regression model with a latent spatial effect modelled as a conditional autoregressive (CAR) process. Since the Invalsi scores regard two subjects (Italian and Mathematics) we fit a bivariate model, in which the relationship between the two subjects is accounted for by the random effect. The computation follows the method of the Integrated Nested Laplace Approximation (INLA), implemented in the R-INLA software.