Mathematical Formulation of Multivariate Euclidean Models for Discrimination Methods

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Abstract
Multivariate models for the triangular and duo-trio methods are described in this paper. In both cases, the mathematical formulation of Euclidean models for these methods is derived and evaluated for the bivariate case using numerical quadrature. Theoretical results are compared with those obtained using Monte Carlo simulation which is validated by comparison with previously published theoretical results for univariate models of these methods. This work is discussed in light of its importance to the development of a new theory for multidimensional scaling in which the traditional assumption can be eliminated that proximity measures and perceptual distances are monotonically related.