  This paper establishes fundamental results for statistical inference of
diagnostic classification models (DCM). The results are developed at a high
level of generality, applicable to essentially all diagnostic classification
models. In particular, we establish identifiability results of various modeling
parameters, notably item response probabilities, attribute distribution, and
Q-matrix-induced partial information structure. Consistent estimators are
constructed. Simulation results show that these estimators perform well under
various modeling settings. We also use a real example to illustrate the new
method. The results are stated under the setting of general latent class
models. For DCM with a specific parameterization, the conditions may be adapted
accordingly.
