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Activity Number:
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520
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Type:
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Invited
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Date/Time:
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Thursday, August 10, 2006 : 10:30 AM to 12:20 PM
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Sponsor:
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Classification Society of North America
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| Abstract - #304968 |
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Title:
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Similarity Index for Polychotomous Variables
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Author(s):
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Ranjan K. Paul*+ and I-Li Lu
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Companies:
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Boeing Math Group and The Boeing Company
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Address:
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P.O. Box 3707, MC 7L-21, Seattle, WA, 98124-2207,
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Keywords:
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ordinal ; categorical ; similarity ; dissimilarity ; clustering ; classification
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Abstract:
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In this paper, we extend the concept of similarity measure and apply it in order to develop a classification index for data with strings of polychotomous responses. This index generalizes the development of a modified version Jaccard-Tanimoto coefficient from binary to multicategory settings. Asymptotic theory from probability is employed with the stability principle to derive the index weights. Maximum likelihood estimators of the probabilities of occurrence for categories are derived to estimate the index weights. When structures of the probabilities of occurrence are specified by the Dirichlet priors, estimates based on the admissible minimax principle are computed and compared with those estimated by the maximum likelihood procedures. Asymptotic distributions of these indexes are derived.
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