  A number of parametric and nonparametric methods for estimating cognitive
diagnosis models (CDMs) have been developed and applied in a wide range of
contexts. However, in the literature, a wide chasm exists between these two
families of methods, and their relationship to each other is not well
understood. In this paper, we propose a unified estimation framework to bridge
the divide between parametric and nonparametric methods in cognitive diagnosis
to better understand their relationship. We also develop iterative joint
estimation algorithms and establish consistency properties within the proposed
framework. Lastly, we present comprehensive simulation results to compare
different methods, and provide practical recommendations on the appropriate use
of the proposed framework in various CDM contexts.
