  Structured latent attribute models (SLAMs) are a special family of discrete
latent variable models widely used in social and biological sciences. This
paper considers the problem of learning significant attribute patterns from a
SLAM with potentially high-dimensional configurations of the latent attributes.
We address the theoretical identifiability issue, propose a penalized
likelihood method for the selection of the attribute patterns, and further
establish the selection consistency in such an overfitted SLAM with diverging
number of latent patterns. The good performance of the proposed methodology is
illustrated by simulation studies and two real datasets in educational
assessment.
