Q-matrix is the intermediary between attribute mastery patterns and responses in cognitive diagnostic assessment; therefore, Q-matrix plays a very important role in the assessment. Currently, lacking of reliable method of inferring and validating the expert-specified Q-matrix is the main problem. Based on the algorithm of Liu et al. (2012), three modified algorithms are proposed. There are two major differences between the algorithm of Liu et al. and the modified algorithms, one is to modify the item parameters from fixed to unfixed, the other is to use an “incremental” Q-matrix estimation, which some items named as “base items” have been correctly prespecified, others (or called as new items or raw items whose attributes have not been specified) need to be specified. The modified algorithms “incrementally” add new items to the “base items” one by one, estimate the item parameters and Q-matrix jointly, rather than estimate all of the items simultaneously which would bring more “noise” to affect the accuracy of estimation. Simulation studies showed that the modified algorithms could get satisfactory results, and the empirical study showed that the proposed algorithms could offer useful information about the Q-matrix specification. 
Model identification and Q-matrix incremental inference in cognitive diagnosis