多响应线性混合效应模型的A最优设计

A-optimal Designs for Multi-response Linear Mixed Models

线性混合效应模型在统计领域应用广泛,但多响应线性混合效应模型的设计问题很少被关注。研究了多响应线性混合效应模型的A最优设计,以随机效应的精准预测为目标定义最优准则,推导出相应的等价性定理来刻画最优设计。以一个具体模型为例,求解了具体的A最优设计。

The linear mixed-effects model is widely used in statistical fields,however the design of multi-response one is rarely discussed.This paper studied the A-optimal designs for multi-response linear mixed models.An optimal criterion was defined with the objective of accurate prediction of random effects,and the equivalence theorem was derived to describe the optimal designs.The A-optimal designs was solved with a specific model as an example.