Efficient Metropolis-Hastings Robbins-Monro Algorithm for High-Dimensional Diagnostic Classification Models

The expectation-maximization (EM) algorithm is a commonly used technique for the parameter estimation of the diagnostic classification models (DCMs) with a prespecified Q-matrix; however, it requires O(2^K) calculations in its expectation-step, which significantly slows down the computation when the number of attributes, K, is large. This study proposes an efficient Metropolis-Hastings Robbins-Monro (eMHRM) algorithm, needing only O(K + 1) calculations in the Monte Carlo expectation step. Furthermore, the item parameters and structural parameters are approximated via the Robbins-Monro algorithm, which does not require time-consuming nonlinear optimization procedures. A series of simulation studies were conducted to compare the eMHRM with the EM and a Metropolis-Hastings (MH) algorithm regarding the parameter recovery and execution time. The outcomes presented in this article reveal that the eMHRM is much more computationally efficient than the EM and MH, and it tends to produce better estimates than the EM when K is large, suggesting that the eMHRM is a promising parameter estimation method for high-dimensional DCMs.