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We assemble here properties of certain dissimilarity coefficients and are specially concerned with their metric and Euclidean status. No attempt is made to be exhaustive as far as coefficients are concerned, but certain mathematical results that we have found useful are presented and should help...
Two classes of element-wise transformations are proved to preserve the positive semi-definite nature of coefficient matrices. The correctness of a conjecture by Gower and Legendre on the positive semidefinite nature of a certain coefficient matrix is proved. It is shown that the matrix of...
One of the most important problems in classification is that of quantitative comparison of hierarchical trees. In this note we answer an open problem of Culík and Wood (1982) concerning the nearest neighbor interchange metric by proving that its underlying decision problem is NP-complete.
Each ofn attributes partitions a set of items into equivalence classes. Aconsistent aggregator of then partitions is defined as an aggregate partition that satisfies an independence condition and a unanimity condition. It is shown that the class of consistent aggregators is precisely the class...
The weighted linear choice model is one of the most popular models in the social sciences. In this model the utility of a choice object is represented as a weighted sum of attribute-level desirabilities, where the weights are attribute importances. In many empirical contexts the choice objects...
In this paper we develop a version of the Jackknife which seems especially suited for Multidimensional Scaling. It deletes one stimulus at a time, and combines the resulting solutions by a least squares matching method. The results can be used for stability analysis, and for purposes of cross...
A procedure is presented which permits the analysis of factor analytic problems in which several groups exist. The analysis incorporates a hierarchical scheme of searching for factorial invariance and is an extension of Meredith's (1964) Method One procedure. By overlaying a contextual frame of...
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