D-optimal Designs with Ordered Categorical Data
D-optimal Designs with Ordered Categorical Data
复制标题
具有有序分类数据的 D 最优设计
DOI：
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发表时间：
2015
期刊：
影响因子：
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通讯作者：
A. Mandal
中科院分区：
文献类型：
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作者：
Jie Yang;Liping Tong;A. Mandal
累积链接模型已被广泛用于有序分类响应。实验单元的统一分配是实践中常用的方法，但往往缺乏效率。我们考虑具有有序分类响应和累积链接模型的D-最优设计。对于一组预定的设计点，我们推导出的必要条件和充分条件的分配是局部D-最优的，并制定有效的算法，获得近似和精确的设计。我们证明了在最小支持设计中支持点的数量只取决于预测变量的数量，而预测变量的数量可以比模型中参数的数量少得多。我们表明，在这种情况下，D-最优的最小支持分配通常是不均匀的支持点。此外，我们提供EW D-最优设计作为贝叶斯D-最优设计的高效替代。它们都可以比均匀设计更健壮。
Cumulative link models have been widely used for ordered categorical responses. Uniform allocation of experimental units is commonly used in practice, but often suffers from a lack of efficiency. We consider D-optimal designs with ordered categorical responses and cumulative link models. For a predetermined set of design points, we derive the necessary and sufficient conditions for an allocation to be locally D-optimal and develop efficient algorithms for obtaining approximate and exact designs. We prove that the number of support points in a minimally supported design only depends on the number of predictors, which can be much less than the number of parameters in the model. We show that a D-optimal minimally supported allocation in this case is usually not uniform on its support points. In addition, we provide EW D-optimal designs as a highly efficient surrogate to Bayesian D-optimal designs. Both of them can be much more robust than uniform designs.