A Graphical Diagnostic Classification Model Hyeon-Ah Kang, Jingchen Liu, Zhiliang Ying Columbia University A framework is presented to model instances and degrees of local item dependence within the context of diagnostic classification models (DCMs). The study considers an undirected graphical model to describe dependent structure of test items and draws inference based on pseudo-likelihood. The new modeling framework explicitly addresses item interactions beyond those explained by latent classes and thus is more flexible and robust against the violation of local independence. It also facilitates concise interpretation of item relations by regulating complexity of a network underlying the test items. The viability and effectiveness are demonstrated via simulation and a real data example. Results from the simulation study suggest that the proposed methods adequately recover the model parameters in the presence of locally dependent items and lead to a substantial improvement in estimation accuracy compared to the standard DCM approach. The analysis of real data demonstrates that the graphical DCM provides a useful summary of item interactions in regards to the existence and extent of local dependence. The cognitive diagnostic analysis makes use of statistical probability models to characterize re- sponse patterns on a test. In psychometric context these models are often referred to as diagnostic classification models (DCMs; e.g., de la Torre, 2011; Haertel, 1989; Henson, Templin, & Willse, 2009; Junker & Sijtsma, 2001; Templin & Henson, 2006; von Davier, 2005). The primary function of the DCM is to classify individuals with respect to an array of attributes and summarize response profiles with a small number of latent classes. The underlying attribute is typically denoted by a binary value, indicating whether or not an examinee possesses the attribute being examined. In practice the presence or absence of particular attributes serves as useful diagnostic information 1 Introduction 1 arXiv:1707.06318v1 [stat.ME] 19 Jul 2017 Abstract