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

In many large-scale tests, it is very common that students are nested within classes or schools and that the test designers try to measure their multidimensional latent traits (e.g., logical reasoning ability and computational ability in the mathematics test). It is particularly important to explore the influences of covariates on multiple abilities for development and improvement of educational quality monitoring mechanism. In this study, motivated by a real dataset of a large-scale English achievement test, we will address how to construct an appropriate multilevel structural models to fit the data in many of multilevel models, and what are the effects of gender and socioeconomic-status differences on English multidimensional abilities at the individual level, and how does the teachers' satisfaction and school climate affect students' English abilities at the school level. A full Gibbs sampling algorithm within the Markov chain Monte Carlo (MCMC) framework is used for model estimation. Moreover, a unique form of the deviance information criterion (DIC) is used as a model comparison index. In order to verify the accuracy of the algorithm estimation, two simulations are considered in this paper. Simulation studies show that the Gibbs sampling algorithm works well in estimating all model parameters across a broad spectrum of scenarios, which can be used to guide the real data analysis. A brief discussion and suggestions for further research are shown in the concluding remarks.