Multiple imputation and selection of ordinal level-2 predictors in multilevel models

We devise a strategy to handle ordinal level-2 predictors of a two-level random effect model in a setting characterized by two nontrivial issues: (i) level-2 predictors are severely affected by missingness; (ii) there is redundancy in both the number of predictors and the number of categories of their measurement scale. We tackle the first issue by considering a multiple imputation strategy based on information at both level-1 and level-2. We tackle the second issue by means of regularization techniques for ordinal predictors, also accounting for the multilevel data structure. The work is motivated by a case study at the University of Padua about the relationship between student ratings of a course and several characteristics of the course, including teacher feelings (ordinal predictors) and practices (binary predictors) collected by a specific survey with nearly half missing respondents.