Abstract Suppose an experiment is conducted on pairs of objects with outcome response a continuous variable measuring the interactions among the pairs. Furthermore, assume the response variable is hard to measure numerically but we may code its values into low and high levels of interaction (and possibly a third category in between if neither label applies). In this paper, we estimate the interaction values from the information contained in the coded data and the design structure of the experiment. A novel estimation method is introduced and shown to enjoy several optimal properties including maximum explained variance in the responses with minimum number of parameters and for any probability distribution underlying the responses. Furthermore, the interactions have the simple interpretation of correlation (in absolute value), size of error is estimable from the experiment, and only a single run of each pair is needed for the experiment. We also explore possible applications of the technique. Three applications are presented, one on protein interaction, a second on drug combination, and the third on machine learning. The first two applications are illustrated using real life data while for the third application, the data are generated via binary coding of an image.

中文翻译：

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用定性响应分析成对实验的框架

摘要 假设在对象对上进行实验，结果响应是一个测量对象对之间相互作用的连续变量。此外，假设响应变量很难用数字衡量，但我们可以将其值编码为低级和高级交互（如果两个标签都不适用，也可能是介于两者之间的第三类）。在本文中，我们根据编码数据中包含的信息和实验的设计结构来估计交互值。引入了一种新的估计方法，并显示出其具有多种优化特性，包括具有最少参数的响应中的最大解释方差以及响应基础的任何概率分布。此外，相互作用具有对相关性（绝对值）的简单解释，误差的大小可以从实验中估计出来，并且实验只需要每对运行一次。我们还探索了该技术的可能应用。介绍了三个应用程序，一个关于蛋白质相互作用，第二个关于药物组合，第三个关于机器学习。前两个应用程序使用现实生活数据进行说明，而对于第三个应用程序，数据是通过图像的二进制编码生成的。