Cognitive diagnostic assessment (CDA) is an effective data mining approach in education. It aims to discover diagnostic information about students' cognitive strengths and weaknesses. A large number of CDA statistical models are developed and based on different assumptions about how attributes or combinations of attributes influence item response. However, the relationship between attributes and item response is unknown in reality. This challenges the researcher to make a conscious thought on the mechanism of item response and model selection before data analysis. This article introduced the reversible jump Markov Chain Monte Carlo (RJMCMC) method for the determination of three conjunctive diagnostic models that based on different assumptions in order to achieve better model-data fit and higher correct classification rate. Firstly, three conjunctive cognitive diagnostic models were described briefly. Secondly, the algorithm of RJMCMC for automatic model selection was established. Finally, a simulation study and an analysis of real data were presented to verify the algorithm. The simulation and the real data analysis results demonstrated that the model selection algorithm of RJMCMC can work well among three models.
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