项目反应理论中常假设潜在特质服从正态分布，但教育、心理、医学的实际测量中多维、非正态的数据广泛存在。若正态性假设不正确则将导致参数估计有偏，进而影响后续分析。本项目拟从理论与实践层面针对多维项目反应理论的潜在特质分布为非正态的情况进行系统分析，最终目标是提出高效精准的参数估计、模型拟合和项目拟合检验方法。为解决上述问题，本项目计划从以下三个方面进行研究：（1）将Davidian曲线嵌入MH算法，提出相应的NUTS算法，做无偏修正并与之进行比较；（2）构建贝叶斯模型拟合指标，以应对测量灵活的潜在特质分布；（3）构建项目拟合检验统计量，以便于检验反应数据存在随机缺失时的项目拟合。通过美国重症后诊疗的活动性测量数据验证方法的可行性和可靠性，进一步扩展贝叶斯方法的使用范围，并在此基础上，尝试分析我国教育质量监测数据，探索经验，为我国教育质量监测提供切实可行的分析方法，为我国教育现代化建设服务。

Item response theory (IRT) models play an important role in measurement theory. Many educational, psychological and medical assessment, including those for large-scale applications, are inherently multidimensional. Normality of latent traits is a common assumption made when estimating parameters for IRT models, but these assumptions may be violated. Violation of normality assumption may lead biased parameter estimations, then mislead the subsequent analysis. This project focuses on parameter estimation, item fit, and goodness-of-fit test for non-normal distribution. The purposes of this project were to (i) extend the MH algorithm with Davidian curves (DCs) to handle multidimensional models, present a new No-U-Turn sampler with DCs with flexible latent trait distributions (i.e., skewed and bimodal), and compare their performances; (ii) assess item-level fit under normality/non-normality assumption, when response data were missing at random; (iii) in different environments, quantify and test the closed form distribution of latent traits under non-normality assumption. Finally, we will fit Activity Measure for Post-Acute Care (AM-PAC) data, which was undertaken by Boston University, using the proposed methods. Overall, this project will broaden the application area of Bayesian method, propose an available and effective method to fit Chinese Education Quality Monitoring data, and play a positive role in promoting the education modernization.