5 Simulation Study 5.1 Design In this section we provide a simulation study to validate the performance of the GDCM and the corresponding estimation method under known parameters. The simulation was carried out in a 2 × 3 × 3 factorial design by varying the number of attributes ( K =3, 4), graphical structure (null, pairs, triplets), and sample size ( N =500, 1000, 3000). The test length was fixed at J = 30. The primary purpose of the simulation study is to evaluate parameter recovery of the GDCM under varying degrees of local item dependence and compare the results against those obtained from the standard DCM approach. The three types of graphical structure considered are illustrated in Figure 1. The pair condition represents when items have pairwise relationships. The items are grouped in pairs such that there exist edges between items { 1 , 2 } , { 3 , 4 } , . . . , and { 29 , 30 } . This results in a Φ -matrix that has nonzero values in φ$_{j, j}$$_{+1}$ for j =1, 3, . . . , 29; and 0 otherwise. The triplet condition indicates a situation in which items are grouped in triples, { 1 , 2 , 3 } , { 4 , 5 , 6 } , . . . , { 28 , 29 , 30 } . There exist edges between every pair of the items within a triplet. Accordingly, the Φ -matrix has nonzero values in φ$_{j, j}$$_{+1}$ , φ$_{j, j}$$_{+2}$ , and φ$_{j}$$_{+1}$$_{, j}$$_{+2}$ for j = 1, 4, . . . , 28; and 0 otherwise. Defining the sparsity as the proportion of independent edges in a graph, the three simulated graphs correspond to the sparsity level of 100%, 96.55%, and 93.10%, respectively. These settings amount to zero, 15, and 30 pairs of nonzero edges in Φ . For each of the graphs, we set edge-wise parameters at a positive constant 1 if the graph has an edge between the variables X$_{j}$ and X$_{j}$ ′ and set all the node-wise parameters at 0. For simulating response data, the study considered the DINA model. Note that the proposed GDCM framework and the estimation method can accommodate any restricted DCMs in a gener- alized form and alternative DCMs can also be used as an underlying model. The item parameters for the DINA model were randomly sampled from uniform distributions with endpoints (0.05, 0.2) and (0, 0.2) for guessing ( g ) and slipping ( s ), respectively. Examinees’ attribute profiles were drawn from a multinomial distribution with the success probability 0.5 across all latent dimensions. For indicating item loadings on each latent dimension, a J -by- K matrix Q = ( q$_{j}$ : j = 1 , . . . , J ) was employed. Each entry of q$_{j}$ indicates whether or not the k -th attribute is required for item success. 15