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Candel, Math J. J. M. – Psychometrika, 1997
Explored the use of additive tree models to represent set-symmetric distances for feature arrangements in set-theoretic or feature models. Studied arrangements of feature sets that have been proposed to represent qualitative and quantitative variation among objects in situations in which feature structures are defined in various ways. (SLD)
Descriptors: Mathematical Models, Set Theory
Peer reviewed Peer reviewed
Becker, Johannes; Pipahl, Werner – Psychometrika, 1974
Descriptors: Models, Multidimensional Scaling, Set Theory, Stimuli
Peer reviewed Peer reviewed
van den Burg, Willem; Lewis, Charles – Psychometrika, 1988
Measures of multivariate association, based on Wilks'"lambda" or the Bartlett-Nanda-Pillai trace criterion "V", are compared in terms of properties of univariate R-squared, which they generalize. A unified set of derivations of properties is provided, which is self-contained and not restricted to decompositions in canonical…
Descriptors: Equations (Mathematics), Multivariate Analysis, Set Theory, Symmetry
Peer reviewed Peer reviewed
Leenen, Iwin; Van Mechelen, Iven; De Boeck, Paul; Rosenberg, Seymour – Psychometrika, 1999
Presents a three-way, three-mode extension of the two-way, two-mode hierarchical classes model of P. De Boeck and S. Rosenberg (1998) for the analysis of individual differences in binary object x attribute arrays. Illustrates the model with data on psychiatric diagnosis and discusses the relation between the model and other extant models. (SLD)
Descriptors: Algorithms, Individual Differences, Models, Set Theory
Peer reviewed Peer reviewed
de Leeuw, Jan; van der Heijden, Peter G. M. – Psychometrika, 1988
Correspondence analysis (CA) aids analysis of residuals from independence models and decomposes the departure from independence in a two-way contingency table. CA of incomplete tables is proposed that decomposes the departure from the quasi-independence model. This procedure is equivalent to the French procedure for missing data--reconstitution of…
Descriptors: Evaluation Methods, Research Methodology, Set Theory, Statistical Analysis
Peer reviewed Peer reviewed
van der Heijden, Peter G. M.; Worsley, Keith J. – Psychometrika, 1988
With reference to the authors' previous paper (1985), it is proposed that loglinear analysis can be used to detect interactions in a multiway contingency table and explore the form of these interactions with correspondence analysis. Correspondence analysis assists in finding a model with restrictions on the interaction parameters. (TJH)
Descriptors: Factor Analysis, Mathematical Models, Research Methodology, Set Theory
Peer reviewed Peer reviewed
Choulakian, Vartan – Psychometrika, 1988
L. A. Goodman's loglinear formulation for bi-way contingency tables is extended to tables with or without missing cells and is used for exploratory purposes. Three-way tables and generalizations of correspondence analysis are deduced, and a generalized version of Goodman's algorithm is used to estimate scores in all cases. (Author/TJH)
Descriptors: Algorithms, Equations (Mathematics), Mathematical Models, Maximum Likelihood Statistics
Peer reviewed Peer reviewed
van der Burg, Eeke; de Leeuw, Jan – Psychometrika, 1988
Homogeneity analysis (multiple correspondence analysis), which is usually applied to "k" separate variables, was applied to sets of variables by using sums within sets. The resulting technique, OVERALS, uses optimal scaling. The corresponding OVERALS computer program minimizes a least squares loss function via an alternating least…
Descriptors: Algorithms, Factor Analysis, Least Squares Statistics, Multidimensional Scaling