ForLion：一般参数统计模型下混合因子D最优设计的新算法
ForLion: A New Algorithm for D-optimal Designs under General Parametric Statistical Models with Mixed Factors
AI总结：
提出ForLion算法，在一般参数统计模型下高效搜索混合因子D最优设计，平均减少25%实验设置或提升17.5%相对效率。
摘要：
本文研究在相当一般的参数统计模型下，设计同时包含离散因子和连续因子的实验方案的问题。我们提出了一种名为ForLion的新算法，用于在D准则下搜索局部最优近似设计。该算法在混合因子的设计空间中进行穷举搜索，同时保持高效率并减少不同实验设置的数目。其最优性由一般等价定理保证。我们给出了多项logit模型（MLM）和广义线性模型（GLM）的相关理论结果，并利用MLM和GLM下的真实实验证明了我们的算法优于最先进的设计算法。我们的模拟研究表明，ForLion算法平均可以减少25%的实验设置数量，或将设计的相对效率提高17.5%。我们的算法可以帮助实验者降低时间成本、减少实验设备的使用，从而在保持设计高效率的同时降低实验总成本。
英文摘要：
In this paper, we address the problem of designing an experimental plan with both discrete and continuous factors under fairly general parametric statistical models. We propose a new algorithm, named ForLion, to search for locally optimal approximate designs under the D-criterion. The algorithm performs an exhaustive search in a design space with mixed factors while keeping high efficiency and reducing the number of distinct experimental settings. Its optimality is guaranteed by the general equivalence theorem. We present the relevant theoretical results for multinomial logit models (MLM) and generalized linear models (GLM), and demonstrate the superiority of our algorithm over state-of-the-art design algorithms using real-life experiments under MLM and GLM. Our simulation studies show that the ForLion algorithm could reduce the number of experimental settings by 25% or improve the relative efficiency of the designs by 17.5% on average. Our algorithm can help the experimenters reduce the time cost, the usage of experimental devices, and thus the total cost of their experiments while preserving high efficiencies of the designs.
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