Exploring the Correlation Between Multiple Latent Variables and Covariates in Hierarchical Data Based on the Multilevel Multidimensional IRT Model

Bayesian Analysis of Aberrant Response and Response Time Data

In this article, a highly effective Bayesian sampling algorithm based on auxiliary variables is proposed to analyze aberrant response and response time data. The new algorithm not only avoids the calculation of multidimensional integrals by the marginal maximum likelihood method but also overcomes the dependence of the traditional Metropolis–Hastings algorithm on the tuning parameter in terms of acceptance probability. A simulation study shows that the new algorithm is accurate for parameter estimation under simulation conditions with different numbers of examinees, items, and speededness levels. Based on the sampling results, the powers of the two proposed Bayesian assessment criteria are tested in the simulation study. Finally, a detailed analysis of a high-state and large-scale computerized adaptive test dataset is carried out to illustrate the proposed methodology.