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A Framework for Quantifying Qualitative Responses in Pairwise Experiments

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  • A. H. Al-Ibrahim

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.

Suggested Citation

  • A. H. Al-Ibrahim, 2019. "A Framework for Quantifying Qualitative Responses in Pairwise Experiments," Journal of Classification, Springer;The Classification Society, vol. 36(3), pages 471-492, October.
    • Handle: RePEc:spr:jclass:v:36:y:2019:i:3:d:10.1007_s00357-019-09337-1
    DOI: 10.1007/s00357-019-09337-1
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    References listed on IDEAS

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    1. A.H. Al-Ibrahim, 2015. "The Analysis of Multivariate Data Using Semi-Definite Programming," Journal of Classification, Springer;The Classification Society, vol. 32(3), pages 382-413, October.
    2. Roger Shepard, 1962. "The analysis of proximities: Multidimensional scaling with an unknown distance function. II," Psychometrika, Springer;The Psychometric Society, vol. 27(3), pages 219-246, September.
    3. Michel Tenenhaus & Forrest Young, 1985. "An analysis and synthesis of multiple correspondence analysis, optimal scaling, dual scaling, homogeneity analysis and other methods for quantifying categorical multivariate data," Psychometrika, Springer;The Psychometric Society, vol. 50(1), pages 91-119, March.
    4. Roger Shepard, 1962. "The analysis of proximities: Multidimensional scaling with an unknown distance function. I," Psychometrika, Springer;The Psychometric Society, vol. 27(2), pages 125-140, June.
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