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.

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跨栏式多层Beta模型中的空间混淆：巴西公立学校数学奥运会的案例

在巴西众所周知的众多差异中，参加巴西公立学校三个行政级别（联邦，州和市政）的学生之间的表现差异。我们的主要目标是调查巴西公立学校数学奥林匹克运动会的学生表现是否与学校行政管理水平和学生性别相关。为此，我们针对在2013年奥运会第二阶段参加考试的学生的分数，提出了一个跨栏的分级beta模型。beta模型的平均值包含了学生和学校级别的固定和随机效应。我们探索随机学校效应的不同分布。由于某些固定效应的后验分布在随机学校效应的存在和分布方面发生了变化，我们还探索了将随机学校效应限制为固定效应的正交互补的模型。我们得出的结论是，男学生的成绩略好于女学生，而且平均而言，联邦学校的成绩明显好于州立或市政学校。但是，一些最好的市政和州立学校的表现和一些联邦学校一样。我们假设这是由于个别老师成功地激励和准备了学生在数学奥林匹克运动会上的良好表现。一些最好的市政和州立学校的表现以及一些联邦学校。我们假设这是由于个别老师成功地激励和准备了学生在数学奥林匹克运动会上的良好表现。一些最好的市政和州立学校的表现以及一些联邦学校。我们假设这是由于个别老师成功地激励和准备了学生在数学奥林匹克运动会上的良好表现。