<Emphasis Type="Italic">k</Emphasis>-Adic Similarity Coefficients for Binary (Presence/Absence) Data |
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Authors: | Matthijs J Warrens |
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Institution: | (1) Psychometrics and Research Methodology Group, Leiden University Institute for Psychological Research, Leiden University, Wassenaarseweg 52, P.O. Box 9555, 2300 RB Leiden, The Netherlands |
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Abstract: | k-Adic formulations (for groups of objects of size k) of a variety of 2-adic similarity coefficients (for pairs of objects) for binary (presence/absence) data are presented.
The formulations are not functions of 2-adic similarity coefficients. Instead, the main objective of the the paper is to present
k-adic formulations that reflect certain basic characteristics of, and have a similar interpretation as, their 2-adic versions.
Two major classes are distinguished. The first class is referred to as Bennani-Heiser similarity coefficients, which contains
all coefficients that can be defined using just the matches, the number of attributes that are present and that are absent
in k objects, and the total number of attributes. The coefficients in the second class can be formulated as functions of Dice’s
association indices.
The author thanks Willem Heiser and three anonymous reviewers for their helpful comments and valuable suggestions on earlier
versions of this article. |
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Keywords: | Indices of association Resemblance measures Simple matching coefficient Jaccard coefficient Dice/S?renson coefficient Rand index Global order equivalence |
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