标题： 巴西公立学校数学奥林匹克学校表现的分层动态Beta回归模型 显示英文标题

标题： A Hierarchical Dynamic Beta Regression Model of School Performance in the Brazilian Mathematical Olympiads for Public Schools

摘要： 巴西中学奥林匹克竞赛（OBMEP）自2005年起每年举办一次。在2013年的赛事中，有超过47,000所学校注册，涉及近1920万名学生。巴西公共教育系统分为三个行政层级：联邦、州级和市级。参加OBMEP的学生来自三个教育水平，其中两个为小学阶段，一个为中学阶段。我们旨在研究从2006年至2013年参与OBMEP的巴西公立学校的表现。我们提出了一种标准化各学年及教育水平学校平均分数的方法，该方法通过分层动态贝塔回归模型建模。贝塔分布的均值和精度都作为随时间平滑变化的协变量函数进行建模。结果显示，无论教育水平如何，联邦学校的表现优于市级或州级学校。学校的表现随着所在市的人类发展指数（HDI）的增加而提高。此外，联邦学校与州级或市级学校之间的平均表现差异随着HDI的增加而扩大。男孩比例较高的学校在OBMEP的第二和第三教育水平中的平均表现较好。 显示英文摘要

摘要： The Brazilian Mathematical Olympiads for Public Schools (OBMEP) is held every year since 2005. In the 2013 edition there were over 47,000 schools registered involving nearly 19.2 million students. The Brazilian public educational system is structured into three administrative levels: federal, state and municipal. Students participating in the OBMEP come from three educational levels, two in primary and one in secondary school. We aim at studying the performance of Brazilian public schools which have been taking part of the OBMEP from 2006 until 2013. We propose a standardization of the mean scores of schools per year and educational level which is modeled through a hierarchical dynamic beta regression model. Both the mean and precision of the beta distribution are modeled as a function of covariates whose effects evolve smoothly with time. Results show that, regardless of the educational level, federal schools have better performance than municipal or state schools. The mean performance of schools increases with the human development index (HDI) of the municipality the school is located in. Moreover, the difference in mean performance between federal and state or municipal schools tends to increase with the HDI. Schools with higher proportion of boys tend to have better mean performance in the second and third educational levels of OBMEP.