两群组分层线性模型群体参数的A-和R-最优设计
A- and R-optimal Design for Hierarchical Linear Model with Two-Group Assignments
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摘要: 本文讨论两群组分层线性模型的最优试验设计问题.分别基于群体参数的估计定义了A-最优准则和R-最优准则,推导了相应的等价性定理,并以随机截距模型为例说明了如何应用等价性定理.Abstract: This paper discusses the optimal design problem for the hierarchical linear model with twogroup assignments. A-optimal and R-optimal designs are considered for the estimation of the fixed effects. We establish two equivalence theorems to determine the A-optimality and R-optimality of a given design, respectively, and provide an illustrative example to find A- and R-optimal designs for the straight line model with random intercept.