From the psychometric perspective, it calls for corrective actions, such as revising questions, re- moving repeated items, or explicitly accounting for the degree of conditional item dependence, for the benefit of making valid inference about the item and person parameters. 

## 7 Discussion 

A major goal of this article has been to provide an analytical tool for identifying local item depen- dence and estimating the degree of such dependency within the DCM framework. The DCM is a statistical approach that models individual response patterns via a small number of latent classes. It determines whether an examinee possesses a particular set of attributes and thereby allows for individualized feedback on the examinee’s cognitive status. Because of its capacity to provide fine- grained information about examinee’s mastery of attributes, the DCM has been widely applied in educational, psychological, and clinical settings for supporting formative assessments (e.g., H. Liu, You, Wang, Ding, & Chang, 2013; Templin & Henson, 2006). 

In DCMs statistical inference about the parameters hinges on a very restrictive assumption that item responses are locally independent within a latent class. The focus of the present article is to relax this assumption and provide a flexible modeling framework for analyzing data encountered in real applications. Specifically, the suggested model, namely the graphical DCM (GDCM), attempts to address surface local dependence in which items are interrelated due to shared features, such as common stimuli, similar wording, carry-over effects, etc. The GDCM is constructed by introducing a Markov network into the DCM such that it can describe pairwise associations of items that cannot be explicated by the latent class being modeled. The design matrix emerged from the Markov network also allows for a graphical representation of a network that underlies the test items. The numerical experiments using simulation suggest that the GDCM reduces bias in parameter estimation and gives an accurate summary of the conditional dependence relationships among the items. The analysis of empirical data indicates that when a test includes items interacting beyond the latent variable, the GDCM can not only improve the model fit but also offer a meaningful description of such dependency. 

The GDCM and the estimation method proposed in this article can have several implications in practice. First, the GDCM is by far the most flexible framework for modeling the cognitive 

