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

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