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On Robinsonian dissimilarities, the consecutive ones property and latent variable models. (English) Zbl 1284.62317

Summary: A dissimilarity measure on a set of objects is Robinsonian if its matrix can be symmetrically permuted so that its elements do not decrease when moving away from the main diagonal along any row or column. The Robinson property of a dissimilarity reflects an order of the objects. If a dissimilarity is not observed directly, it must be obtained from the data. Given that an ordinal structure is assumed to underlie the data, the dissimilarity function of choice may or may not recover the order correctly. For four dissimilarity measures for binary data it is investigated what ordinal data structure of 0s and 1s is correctly recovered. We derive sufficient conditions for the dissimilarity functions to be Robinsonian. The sufficient conditions differ with the dissimilarity measures. The paper concludes with some limitations of the study.

MSC:

62H05 Characterization and structure theory for multivariate probability distributions; copulas
62H20 Measures of association (correlation, canonical correlation, etc.)
62H30 Classification and discrimination; cluster analysis (statistical aspects)
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