Browsing by Author "Krus, David J."
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Item Dimensionality of hierarchical and proximal data structures(1980) Krus, David J.; Krus, Patricia H.The coefficient of correlation is a fairly general measure which subsumes other, more primitive relationships. At the fundamental classification level, similarities among objects and cladistic relationships were conceptualized as generic concepts underlying formation of proximal and hierarchical structures. Examples of these structures were isolated from data obtained by replicating Thurstone’s classical study of nationality preferences and were subsequently interpreted.Item Dominance, information, and hierarchical scaling of variance space(1979) Krus, David J.; Ceurvorst, Robert W.A method for computation of dominance relations and for construction of their corresponding hierarchical structures is presented. It is shown that variance can be computed from the squared pairwise differences between scores and that dominance indices are actually linear transformations of variances. The interpretation of variance as a quantitative measure of information is suggested and conceptual partition of variance into components associated with relational spaces is proposed. The link between dominance and variance allows integration of the mathematical theory of information with least squares statistical procedures without recourse to logarithmic transformations of the data.Item Logical basis of dimensionality(1978) Krus, David J.The isolation of dimensions from a data matrix has been traditionally formulated in terms of an algebraic or geometric model. Order analysis was developed as a method of multidimensional analysis and scaling based on the theory of Boolean algebra. The order analytic algorithm utilizes functions of the propositional calculus in lieu of eigenvalues and eigenvectors of the general linear model. Also, the graphic presentation of latent space in coordinates of the Euclidian space is paralleled in ordering-theoretic models by dendrograms of the test space. A conceptual outline of order analysis is presented, followed by an empirical comparison of factor and order analysis solutions of a sample data problem. Resulting factor and order analytic structures are evaluated in terms of meeting criteria of simple structure and correct reflection of broad cognitive categories. In addition, the relations of proximity and dominance are discussed from the perspectives of both Cartesian and Leibnitzian theories of dimensionality as pertaining to problems of multivariate analysis and scaling.