regards to the behavior of the GDCM under modest misspecification of Q . Associated with this problem, it would be fruitful to consider statistical methods for a fully exploratory situation in which neither Φ nor Q are known. The useful literature in this connection is Y. Chen, Liu, Xu, and Ying (2015), which explores regularized maximum likelihood estimation of B in the absence of Q . A similar technique can be employed to simultaneously identify Q and Φ during the model estimation. Finally, the present GDCM assumes no particular distribution on the underlying attributes. If, however, latent attributes are structured with a specific form (e.g., Leighton, Gierl, & Hunka, 2004; Su, 2013; Templin, Henson, Templin, & Roussos, 2008; von Davier, 2010), it seems more reasonable to estimate the model parameters under such restriction. A natural question arises as to the robustness of the GDCM in this event. It would also be worthwhile to investigate how the assumed attribute structure would shape the resulting dependence relationships among the items. References Akaike, H. (1974). A new look at the statistical model identification. IEEE Transactions on Automatic Control , 19 , 716–723. Besag, J. (1975). Statistical analysis of non-lattice data. The Statistician , 24 , 179–195. Bishop, Y. M. M., Fienberg, S. E., & Holland, P. W. (1975). Discrete multivariate analysis . Cambridge, MA: MIT Press. Bradlow, E., Wainer, H., & Wang, X. (1999). A Bayesian random effects model for testlets. Psychometrika , 64 , 153–168. Cai, L. (2010). A two-tier full-information item factor analysis model with applications. Psychome- trika , 75 , 581-612. Chen, C.-T., & Wang, W.-C. (2007). Effects of ignoring item interaction on item parameter estimation and detection of interacting items. Applied Psychological Measurement , 31 , 388– 411. Chen, W., & Thissen, D. (1997). Local dependence indexes for item pairs using item response theory. Journal of Educational and Behavioral Statistics , 22 , 265–289. Chen, Y., Liu, J., Xu, G., & Ying, Z. (2015). Statistical analysis of Q-matrix based diagnostic 28