The estimation of RxC ecological inference contingency tables from aggregate data is one of the most salient and challenging problems in the field of quantitative social sciences, with major solutions proposed from both the ecological regression and the mathematical programming frameworks. In recent decades, there has been a drive to find solutions stemming from the former, with the latter being less active. From the mathematical programming framework, this paper suggests a new direction for tackling this problem. For the first time in the literature, a procedure based on linear programming is proposed to attain estimates of local contingency tables. Based on this and the homogeneity hypothesis, we suggest two new ecological inference algorithms. These two new algorithms represent an important step forward in the ecological inference mathematical programming literature. In addition to generating estimates for local ecological inference contingency tables and amending the tendency to produce extreme transfer probability estimates previously observed in other mathematical programming procedures, these two new algorithms prove to be quite competitive and more accurate than the current linear programming baseline algorithm. Their accuracy is assessed using a unique dataset with almost 500 elections, where the real transfer matrices are known, and their sensitivity to assumptions and limitations are gauged through an extensive simulation study. The new algorithms place the linear programming approach once again in a prominent position in the ecological inference toolkit. Interested readers can use these new algorithms easily with the aid of the R package lphom.

中文翻译：

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提高选民转换的估计准确性。两种基于线性规划的生态推理新算法

从聚合数据估计 RxC 生态推理列联表是定量社会科学领域中最突出和最具挑战性的问题之一，主要解决方案来自生态回归和数学规划框架。近几十年来，人们一直在努力寻找源自前者的解决方案，而后者则不太活跃。从数学规划框架出发，本文提出了解决这个问题的新方向。文献中第一次提出了一种基于线性规划的程序来获得局部列联表的估计。基于此和同质性假设，我们提出了两种新的生态推理算法。这两种新算法代表了生态推理数学规划文献向前迈出的重要一步。除了为局部生态推理列联表生成估计值并修正以前在其他数学规划程序中观察到的产生极端转移概率估计值的趋势之外，这两种新算法被证明比当前的线性规划基线算法更具竞争力和更准确。它们的准确性是使用一个包含近 500 次选举的独特数据集进行评估的，其中真实的转移矩阵是已知的，并且它们对假设和限制的敏感性是通过广泛的模拟研究来衡量的。新算法再次将线性规划方法置于生态推理工具包中的突出位置。. _