Spatial confounding in hurdle multilevel beta models: the case of the Brazilian Mathematical Olympics for Public Schools
Among the many disparities for which Brazil is known is the difference in performance across students who attend the three administrative levels of Brazilian public schools: federal, state and municipal. Our main goal is to investigate whether student performance in the Brazilian Mathematical Olympics for Public Schools is associated with school administrative level and student gender. For this, we propose a hurdle hierarchical beta model for the scores of students who took the examination in the second phase of these Olympics, in 2013. The mean of the beta model incorporates fixed and random effects at the student and school levels. We explore different distributions for the random school effect. As the posterior distributions of some fixed effects change in the presence, and distribution, of the random school effects, we also explore models that constrain random school effects to the orthogonal complement of the fixed effects. We conclude that male students perform slightly better than female students and that, on average, federal schools perform substantially better than state or municipal schools. However, some of the best municipal and state schools perform as well as some federal schools. We hypothesize that this is due to individual teachers who successfully motivate and prepare their students to perform well in the mathematical Olympics.