  The paper is motivated by the analysis of the relationship between ratings
and teacher practices and beliefs, which are measured via a set of binary and
ordinal items collected by a specific survey with nearly half missing
respondents. 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 is
redundancy in the number of items and the number of categories of their
measurement scale. tackle the first issue by considering a multiple imputation
strategy based on information at both level 1 and level 2. For the second
issue, we consider regularization techniques for ordinal predictors, also
accounting for the multilevel data structure. The proposed solution combines
existing methods in an original way to solve specific problem at hand, but it
is generally applicable to settings requiring to select predictors affected by
missing values. The results obtained with the final model out that some teacher
practices and beliefs are significantly related to ratings about teacher
ability to motivate students.
