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A Framework for Quantifying Qualitative Responses in Pairwise Experiments

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An Erratum to this article was published on 14 August 2019

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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.

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  • 14 August 2019

    The original version of this article unfortunately contained a mistake in Title and reference Thurstone, L. L. (1927).

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The original version of this article unfortunately contained a mistake in Title and reference Thurstone, L. L. (1927).

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Al-Ibrahim, A.H. A Framework for Quantifying Qualitative Responses in Pairwise Experiments. J Classif 36, 471–492 (2019). https://doi.org/10.1007/s00357-019-09337-1

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