Řehák, Jan; Řeháková, Blanka Classifications with relations: A model for the description of distributions and their distances. (English) Zbl 0612.62091 Kybernetika 22, 158-175 (1986). Distributions on classifications are met wherever we work with categorical variables and in many practical situations. In this paper some methods for statistical analysis of nominal variables, ordinal variables (partially solved), and cardinal variables (a numerical or quantified classification) are suggested, and a general model to describe measures for distributions on various types of classifications with relations is proposed. The simple, ordered and quantitative classifications will be special cases of this general model. In this way, it is possible to deal with general decision and predictive models as well as with the analysis of generalized categorical variables. Reviewer: Fang Kaitai Cited in 1 ReviewCited in 1 Document MSC: 62H99 Multivariate analysis 62H30 Classification and discrimination; cluster analysis (statistical aspects) Keywords:matrix of scores; Distributions on classifications; nominal variables; ordinal variables; cardinal variables; classifications with relations; generalized categorical variables PDF BibTeX XML Cite \textit{J. Řehák} and \textit{B. Řeháková}, Kybernetika 22, 158--175 (1986; Zbl 0612.62091) Full Text: EuDML References: [1] F. R. Gantmakher: Teoriya matric. (The Theory of Matrices). Second edition. Nauka, Moskva 1966. [2] L. A. Goodman, W. H. Kruskal: Measures of association for cross-classifications. J. Amer. Statist. Assoc. 49 (1954), 732-764. · Zbl 0056.12801 [3] R. I. Light, B. H. Margolin: An analysis of variance for categorical data. J. Amer. Statist. Assoc. 66 (1971), 534- 544. · Zbl 0222.62035 [4] J. Řehák: Základní deskriptivní míry pro rozložení ordinálních dat. (Basic descriptive measures for the distribution of ordinal data). Sociologický časopis 12 (1976), 4, 416-431. [5] J. Řehák, B. Řeháková: Základní charakteristiky proměnných s konečným počtem hodnot a distanční analýza jejich rozložení. (Basic characteristics for finite-values variables and a distance analysis of their distributions). Sociologický časopis 15 (1979), 2, 214-233. [6] J. Řehák, B. Řeháková: Distanční přístup k analýze kategorizovaných dat a jeho aplikace na problém shody. (Distance approach to the analysis of the categorical data and its application to the problem of the goodness-of-fit). Robust 1982 (J. Antoch, J. Jurečková. JČMF, Praha 1982, 76-80. [7] J. Řehák, B. Řeháková: Klassifikacija s numeričeskimi sootnošenijami - D-model dlja analiza respredělenij. (Classification with numerical relations - D-model for an analysis of the distributions). 2-nd Soviet-Czechoslovak seminar ”Analysis and Modelling of the Social and Economic Development of the Regions”, Kemerovo 1984. [8] T. P. Wilson: Critique of ordinal variables. Social Forces 49 (1971), 432-444. This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.