  There has been growing interest in recent years in Q-matrix based cognitive
diagnosis models. Parameter estimation and respondent classification under
these models may suffer due to identifiability issues. Non-identifiability can
be described by a partition separating attribute profiles into groups of those
with identical likelihoods. Marginal identifiability concerns the
identifiability of individual attributes. Maximum likelihood estimation of the
proportion of respondents within each equivalence class is consistent, making
possible a new measure of assessment quality reporting the proportion of
respondents for whom each individual attribute is marginally identifiable.
Arising from this is a new posterior-based classification method adjusting for
non-identifiability.
