In this paper, we develop and apply novel machine learning and statistical methods to analyse the determinants of students' PISA 2015 test scores in nine countries:

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This paper assesses the differences in educational attainments between students across classes and schools they are grouped by, in the context of Italian educational system. The purpose is to identify a relationship between pupils' reading test scores and students' characteristics, stratifying for classes, schools and geographical areas. The dataset contains detailed information about more than 500,000 students at the first year of junior secondary school in the year 2012/2013. By means of multilevel linear models, it is possible to estimate statistically significant school and class effects, after adjusting for pupil's characteristics, including prior achievement. The results show that school and class effects are very heterogeneous across macro-areas (Northern, Central and Southern Italy), and that there are substantial discrepancies between and within schools; overall, class effects on achievement tend to be larger than school ones.

We propose a new statistical method, called generalized mixed-effects random forest (GMERF), that extends the use of random forest to the analysis of hierarchical data, for any type of response variable in the exponential family. The method maintains the flexibility and the ability of modeling complex patterns within the data, typical of tree-based ensemble methods, and it can handle both continuous and discrete covariates. At the same time, GMERF takes into account the nested structure of hierarchical data, modeling the dependence structure that exists at the highest level of the hierarchy and allowing statistical inference on this structure. In the case study, we apply GMERF to Higher Education data to analyze the university student dropout phenomenon. We predict engineering student dropout probability by means of student-level information and considering the degree program students are enrolled in as grouping factor.