Multiple imputation and selection of ordinal level 2 predictors in multilevel models: An analysis of the relationship between student ratings and teacher practices and attitudes

The article is motivated by the analysis of the relationship between university student ratings and teacher practices and attitudes, which are measured via a set of binary and ordinal items collected by an innovative survey. The analysis is conducted through a two-level random intercept model, where student ratings are nested within teachers. The analysis must face two issues about the items measuring teacher practices and attitudes, which are level 2 predictors: (a) the items are severely affected by missingness due to teacher non-response and (b) there is redundancy in both the number of items and the number of categories of their measurement scale. We tackle the missing data issue by considering a multiple imputation strategy exploiting information at both student and teacher levels. For the redundancy issue, we rely on regularization techniques for ordinal predictors, also accounting for the multilevel data structure. The proposed solution addresses the problem at hand in an original way, and it can be applied whenever it is required to select level 2 predictors affected by missing values. The results obtained with the final model indicate that ratings on teacher ability to motivate students are related to certain teacher practices and attitudes.