plays a dominant role in determining the item performances. It is also noteworthy that the existing parametric models are mainly designed for confirmatory analysis in which item subsets that are suspected of local dependence need to be determined beforehand. The present modeling involves no such pre-identification and hence can be applied to more general contexts, for example, when dependence structure underlying test items is unknown or when one wishes to explore any lurking violations of the local independence assumption. For modeling conditional (in)dependence of items, this study considers an undirected graphical model, also known as Markov random field. A graphical model is a powerful tool for summarizing stochastic dependency of random variables in multivariate data and has been used in a wide vari- ety of scientific domains, including spatial statistics, image analysis, natural language processing, among others. In this study, a sparse Markov network is considered for characterizing relationships among categorical variables by means of a sparse graph. The sparsity constraint is imposed such that the latent class of concern accounts for most variation in observed response profile and only a fraction of variation is ascribed to interdependency of items. Such assumption is easily fulfilled in most psychometric settings as it implies lack of test validity otherwise. The proposed modeling framework has two distinct merits. First, it is arguably more flexible than standard DCMs as it allows for nesting of items that cannot be explained by latent classes intended. In addition, it is parsimonious enough to offer a succinct interpretation of the model parameters in virtue of a sparse graph. In applied settings, the new modeling approach can serve as useful means for exploring the possible existence of local item dependence or analyzing data with such dependency. The remainder of this article is laid out as follows. Section 2 presents a specific parameterization of the suggested model, namely the graphical diagnostic classification model (GDCM), followed by a brief introduction of the DCM and Markov network. A parameter estimation scheme and corresponding computational methods are given in Sections 3 and 4, respectively. Section 5 presents a simulation study to verify the performance of the proposed methods in terms of parameter recovery. The practicability of the GDCM is examined in Section 6 using real data from a well- known personality questionnaire. The overall model fit issue is also addressed in this section. Lastly, some discussions are provided in Section 7 on the suggested model and future research directions. 4