title: Theory of the Self-learningQ-Matrix.
abstract: Cognitive assessment is a growing area in psychological and educational measurement, where tests are given to assess mastery/deficiency of attributes or skills. A key issue is the correct identification of attributes associated with items in a test. In this paper, we set up a mathematical framework under which theoretical properties may be discussed. We establish sufficient conditions to ensure that the attributes required by each item are learnable from the data.
authors.affiliation: Department of Statistics, Columbia University, 1255 Amsterdam Avenue New York, NY 10027, USA.
authors.forename: Jingchen
authors.initials: J
authors.lastname: Liu
authors.affiliation: Department of Statistics, Columbia University, 1255 Amsterdam Avenue New York, NY 10027, USA.
authors.forename: Gongjun
authors.initials: G
authors.lastname: Xu
authors.affiliation: Department of Statistics, Columbia University, 1255 Amsterdam Avenue New York, NY 10027, USA.
authors.forename: Zhiliang
authors.initials: Z
authors.lastname: Ying
keywords: Classification model; Q-matrix; cognitive assessment; consistency; diagnostic; self-learning