This dissertation presents a comprehensive review of the evolution of DIF analysis within educational measurement from the 1980s to the present. The review elucidates the concept of DIF, particularly emphasizing the crucial role of grouping for exhibiting DIF. Then, the dissertation introduces an innovative modification to the newly developed…

Multidimensional Item Response Theory (MIRT) has been widely used in educational and psychological assessments. It estimates multiple constructs simultaneously and models the correlations among latent constructs. While it provides more accurate results, the unidimensional IRT model is still dominant in real applications. One major reason is that…

Categorical data become increasingly ubiquitous in the modern big data era. In this dissertation, we propose novel statistical learning and inference methods for large-scale categorical data, focusing on latent variable models and their applications to psychometrics. In psychometric assessments, the subjects' underlying aptitude often cannot be…

An online learning system has the capacity to offer customized content that caters to individual learner's need and has seen growing interest from industry and academia alike in recent years. Noting the similarity between online learning and the more established adaptive testing procedures, research has focused on applying the techniques of…