Agenda

Prof. Leonardo Grilli, University of Florence

 Title: Combining multiple imputation and the knockoff filter for variable selection, with an application to large-scale assessment data

Abstract: 

Large-scale assessment data, such as those collected in Italy by Invalsi, typically include several student background variables, which can be exploited as predictors in modelling student achievement. Unfortunately, the student background variables are usually affected by missing values, posing serious challenges to the model selection procedures. As a further complication, many of the predictors are variables with unordered categories. We propose combining multiple imputation and variable selection methods in a setting with categorical predictors. In particular, we implement multiple imputation by chained equations (MICE). At the same time, for variable selection, we exploit a recently proposed method based on the knockoff filter, where the knockoff copies are generated using a sequential procedure that properly handles both continuous and categorical predictors. A simulation study shows that the proposed approach performs well, also in comparison with other knockoff-based approaches and the classical lasso. In the application to the Invalsi test data, once the student background variables have been selected, we fit a random intercept model to analyse the determinants of the math score at grade 5. The proposed approach is computationally feasible and highly flexible.