My primary research interests lie broadly in statistical methodologies with applications to educational assessment and measurement. In general, I enjoy interdisciplinary work and believe that the best research is driven by interesting applications. This is especially so in statistical modeling and inference concerning educational data, where my research has been to help diagnose students' latent abilities, improve the testing mode to design efficient tests, both with a final objective of improving education quality. My doctoral dissertation focused on the theoretical and applied development in latent variable modeling and adaptive testing, which are the two research areas I am primarily interested in. The theoretical results and methodologies I developed can improve the model estimation procedure, provide guidelines for model selection and validation in cognitive learning and design more flexible and efficient adaptive testing mode.