title: Statistical Analysis ofQ-matrix Based Diagnostic Classification Models.
abstract: Diagnostic classification models have recently gained prominence in educational assessment, psychiatric evaluation, and many other disciplines. Central to the model specification is the so-calledQ-matrix that provides a qualitative specification of the item-attribute relationship. In this paper, we develop theories on the identifiability for theQ-matrix under the DINA and the DINO models. We further propose an estimation procedure for theQ-matrix through the regularized maximum likelihood. The applicability of this procedure is not limited to the DINA or the DINO model and it can be applied to essentially allQ-matrix based diagnostic classification models. Simulation studies are conducted to illustrate its performance. Furthermore, two case studies are presented. The first case is a data set on fraction subtraction (educational application) and the second case is a subsample of the National Epidemiological Survey on Alcohol and Related Conditions concerning the social anxiety disorder (psychiatric application).
authors: Columbia University, Statitics, New York, 10027 United States, yunxiao@stat.columbia.edu.
authors: Yunxiao
authors: Y
authors: Chen
authors: Columbia University, Statistics, 1255 Amsterdam Avenue, New York, 10027 United States, jcliu@stat.columbia.edu.
authors: Jingchen
authors: J
authors: Liu
authors: University of Minnesota, Statitics, Minneapolis, United States, xuxxx360@umn.edu.
authors: Gongjun
authors: G
authors: Xu
authors: Columbia University, Statitics, 1255 Amsterdam Avenue, 10th Floor, New York, 10027 United States, zying@stat.columbia.edu.
authors: Zhiliang
authors: Z
authors: Ying
keywords: Categorical Data Analysis; Classification and Clustering; Mathematical Statistics; Model Selection/Variable Selection