process and item interaction simultaneously. The cognitive component is defined on the generalized form and thus can accommodate a wide range of restricted DCMs. The graphical model provides an explicit description of item relations without requiring prior knowledge about the underlying structure, thereby supporting exploratory investigation into a set of test items. In practice the information provided by the design matrix can serve as evidence of test validity or can be utilized at test development or assembly stages to improve the quality of assessments. Second, the present framework ensures interpretability of the model parameters by means of a sparse graph. The sparsity constraint imposed on the Markov network can further expedite the estimation of a graph in that the coordinate descent algorithm cycles through only a small subset of nonzero edges (most coordinates that are zero never become nonzero). Third, the GDCM, though aimed at surface local dependence, can also be used for examining underlying local item dependence that arises from testlets such as reading passage, graph or chart problems, or laboratory scenarios. This is because a testlet itself can be considered a common stimulus that invokes inter-item correlation. 

While this is only an initial research effort to expand the DCMs to realistic settings, the im- plied results are promising enough to warrant further study. An important extension would be to explore the potential use of the GDCM in complex settings, such as missing data, stochastic test design, polytomous response data, and data with covariates. In particular, given the increasing popularity of performance task items and constructed response items, an extension of the GDCM to the polytomous response data seems worthy of follow-up research. A common strategy for cal- ibrating polytomous data within the DCM framework has been to dichotomize item responses so that they can be analyzed using dichotomous models (e.g., Johnson et al., 2013; Su, 2013). The dichotomization of polytomous items, however, can result in loss of information. In preference fu- ture research could consider directly incorporating a Markov network into polytomous DCMs (e.g., de la Torre, 2010; Hansen, 2013; Templin, Henson, Rupp, Jang, & Ahmed, 2008; von Davier, 2008) in an analogous manner with the dichotomous case. 

Second, the assumption of a known item-attribute loading matrix may be relaxed in the future. While the present study has assumed that the item loading matrix is correctly identified for the sake of simplicity of discussion, in practice a true Q -matrix is hardly known, and it may be subject to fallible judgment. Provided that a misidentified Q -matrix can have a deleterious effect on the recovery of model parameters (e.g., Rupp & Templin, 2008), additional work needs to be done in 

