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The paper is motivated by the analysis of the relationship between ratingsand teacher practices and beliefs, which are measured via a set of binary andordinal items collected by a specific survey with nearly half missingrespondents. The analysis, which is based on a two-level random effect model,must face two about the items measuring teacher practices and beliefs: (i)these items level 2 predictors severely affected by missingness; (ii) there isredundancy in the number of items and the number of categories of theirmeasurement scale. tackle the first issue by considering a multiple imputationstrategy based on information at both level 1 and level 2. For the secondissue, we consider regularization techniques for ordinal predictors, alsoaccounting for the multilevel data structure. The proposed solution combinesexisting methods in an original way to solve specific problem at hand, but itis generally applicable to settings requiring to select predictors affected bymissing values. The results obtained with the final model out that some teacherpractices and beliefs are significantly related to ratings about teacherability to motivate students.

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