An Analysis and Synthesis of Multiple Correspondence Analysis, Optimal Scaling, Dual Scaling, Homogeneity Analysis and Other Methods for Quantifying Categorical Multivariate Data
- 1 March 1985
- journal article
- Published by Cambridge University Press (CUP) in Psychometrika
- Vol. 50 (1) , 91-119
- https://doi.org/10.1007/bf02294151
Abstract
We discuss a variety of methods for quantifying categorical multivariate data. These methods have been proposed in many different countries, by many different authors, under many different names. In the first major section of the paper we analyze the many different methods and show that they all lead to the same equations for analyzing the same data. In the second major section of the paper we introduce the notion of a duality diagram, and use this diagram to synthesize the many superficially different methods into a single method.Keywords
This publication has 21 references indexed in Scilit:
- An approach to the scaling of categorized attributesBiometrika, 1976
- PRINCIPAL COMPONENT ANALYSIS OF TAXONOMIC DATA WITH MULTI‐STATE DISCRETE CHARACTERSTaxon, 1976
- Reciprocal Averaging: An Eigenvector Method of OrdinationJournal of Ecology, 1973
- SCALE ANALYSIS AND FACTOR ANALYSISBritish Journal of Statistical Psychology, 1953
- A NOTE ON SIR CYRIL BURT'S ‘FACTORIAL ANALYSIS OF QUALITATIVE DATA’British Journal of Statistical Psychology, 1953
- Multidimensional quantificationAnnals of the Institute of Statistical Mathematics, 1953
- On the quantification of qualitative data from the mathematico-statistical point of viewAnnals of the Institute of Statistical Mathematics, 1950
- THE PRECISION OF DISCRIMINANT FUNCTIONSAnnals of Eugenics, 1940
- The approximation of one matrix by another of lower rankPsychometrika, 1936
- A Connection between Correlation and ContingencyMathematical Proceedings of the Cambridge Philosophical Society, 1935