Seleção de modelos multiníveis para dados de avaliação educacional
Resumen
When a dataset contains a hierarchical data structure, a possible approach is the multilevel
regression modelling, which is justified by the significative amout of the data variability that can
be explained by macro level processes. In this work, a selection of multilevel regression models
for educational data is developed. This analysis is divided into two parts: variable selection and
model selection. The latter is subdivided into two categories: classical and Bayesian modeling.
Traditional criteria for model selection such as Lasso, AIC, BIC, and WAIC, among others
are used in this study as an attempt to identify the factors influencing ninth grade students’
performance in Mathematics of elementary education in the State of São Paulo. Likewise, an
investigation was conducted to evaluate the performance of each variable selection criteria and
model selection methods applied to fitted models that will be mentioned throughout this work. It
was possible to conclude that, under the frequentist approach, BIC is the most efficient, whereas
under the bayesian approach, WAIC presented better results. Using Lasso under the frequentist
approach, a decrease of 34% on the number of predictors was observed. Finally, we identified
that the performance in Mathematics of students in the ninth year of elementary school in the
state of São Paulo is most influenced by the following covariates: mother’s educational level,
frequency of book reading, time spent with recreation in classroom, the fact of liking Math,
school global performance in Mathematics, performance in Portuguese, school administrative
dependence, gender, father’s educational degree, failures and age-grade distortion.