  We propose an innovative statistical method, called Ordinal Mixed-Effect
Random Forest (OMERF), that extends the use of random forest to the analysis of
hierarchical data and ordinal responses. The model preserves the flexibility
and ability of modeling complex patterns of both categorical and continuous
variables, typical of tree-based ensemble methods, and, at the same time, takes
into account the structure of hierarchical data, modeling the dependence
structure induced by the grouping and allowing statistical inference at all
data levels. A simulation study is conducted to validate the performance of the
proposed method and to compare it to the one of other state-of-the art models.
The application of OMERF is exemplified in a case study focusing on predicting
students performances using data from the Programme for International Student
Assessment (PISA) 2022. The model identifies discriminating student
characteristics and estimates the school-effect.
