Variable Selection in Multilevel Models via Knockoffs: the Case of INVALSI National Tests

We aim to evaluate the performance of the knockoffs method to select the predictors in a model for math achievement in grade 5. We exploit a rich dataset collected by INVALSI with several student background variables. The task is complicated by the multilevel nature of the model, with students nested into schools, and by the missing values in some predictors. To reduce the dependence on Monte Carlo variability, we use derandomized knockoffs. The preliminary results show that, for large-scale assessment data, the proposed approach is feasible and a valuable alternative to traditional model selection methods.