Journal
MULTIVARIATE BEHAVIORAL RESEARCH
Volume 57, Issue 5, Pages 840-858Publisher
ROUTLEDGE JOURNALS, TAYLOR & FRANCIS LTD
DOI: 10.1080/00273171.2021.1896352
Keywords
Cognitive diagnosis model; Markov chain Monte Carlo; sequential Gibbs sampling
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Funding
- National Natural Science Foundation of China [12001092]
- Fundamental Research Funds for the Central Universities [2412020QD004]
- Key Laboratory of Applied Statistics of MOE
- China Scholarship Council [201806620039]
- NSF [SES1659328, SES-1846747]
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In this study, a computationally efficient sequential Gibbs sampling method is proposed for estimating cognitive diagnosis models, which outperforms existing methods.
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's earlier work in 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.
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