Learning Item-Attribute Relationship in Q-Matrix Based Diagnostic   Classification Models
  Recent surge of interests in cognitive assessment has led to the developments of novel statistical models for diagnostic classification. Central to many such models is the well-known Q-matrix, which specifies the item-attribute relationship. This paper proposes a principled estimation procedure for the Q-matrix and related model parameters. Desirable theoretic properties are established through large sample analysis. The proposed method also provides a platform under which important statistical issues, such as hypothesis testing and model selection, can be addressed. 
Jingchen Liu, Gongjun Xu, and Zhiliang Ying
stat.ME math.ST stat.TH