  Cognitive diagnosis models (CDMs) are useful statistical tools to provide
rich information relevant for intervention and learning. As a popular approach
to estimate and make inference of CDMs, the Markov chain Monte Carlo (MCMC)
algorithm is widely used in practice. However, when the number of attributes,
$K$, is large, the existing MCMC algorithm may become time-consuming, due to
the fact that $O(2^K)$ calculations are usually needed in the process of MCMC
sampling to get the conditional distribution for each attribute profile. To
overcome this computational issue, motivated by Culpepper and Hudson (2018), we
propose a computationally efficient sequential Gibbs sampling method, which
needs $O(K)$ calculations to sample each attribute profile. We use simulation
and real data examples to show the good finite-sample performance of the
proposed sequential Gibbs sampling, and its advantage over existing methods.
