广义线性混合效应模型的若干试验设计问题

项目名称： 广义线性混合效应模型的若干试验设计问题

项目编号： No.11301332

项目类型： 青年科学基金项目

立项/批准年度： 2014

项目学科： 数理科学和化学

项目作者： 周晓东

作者单位： 上海对外经贸大学

项目金额： 22万元

中文摘要： 离散观测数据常见于公共卫生学、医药学、社会学、经济学等研究领域。数据之间通常存在一定的相关性。随着现代优化技术和计算机技术的发展，广义线性混合效应模型被广泛应用于上述数据的建模。如何科学有效地安排试验使得能用少量的试验次数获得对所建模型具有最有效的统计信息，是本项目的研究宗旨。国际上有关广义线性混合效应模型的试验设计研究是在近十多年间逐渐兴起的，有关的理论与方法还只有有限的结果，迫切需要深入与完善。本项目借鉴并发展固定效应广义线性模型下的试验设计理论与方法，研究单响应或多响应具有混合效应的广义线性模型的最优设计和稳健设计；研究贝叶斯框架理论下广义线性混合效应模型的最优设计理论；研究广义线性混合效应模型的模型判别设计问题；研究计算最优设计、稳健设计、模型判别设计的算法。期望将所得设计理论和方法与不同的具体领域结合，解决不同应用领域中的重要问题。

中文关键词： 广义线性混合效应模型；稳健设计；最优设计；等价性定理；粒子群优化算法

英文摘要： Discrete data are common in such areas of research as public health, medical sciences, social sciences, and economic sciences. Generally,data encountered in such areas are correlated. With the rapid development of modern optimization methods and computer technology, generalized linear mixed effects models are widely applied to model such kinds of data. In this project, our target is to effectively arrange the experiments to extract as much information as possible through minimum trials for statistical inferences. In recent years, experimental design for generalized linear mixed effects model (GLMM) has gradually become a hotspot of research. But up to now,there are only limited results. So there is a need to develop deeply and perfect design theories and methods in this area. In this project, we will bring and further extend the ideas generated from experimental design for generalized linear fixed effects model to: (1)Investigate optimal design and robust design for GLMM with single or multiple responses, (2) Develop some optimal Bayesian design theories for GLMM, (3)Derive optimal discrimination designs for GLMM, (4)Propose the algorithms for computing optimal design, robust design and discrimination design. We hope that the design theories and methods developed in this project could be widely used in some con

英文关键词： Generalized linear mixed model；Robust design；Optimal design；Equivalence theorem；Particle swarming optimization algorithm