Correspondence anal/sis is a metric technique for finding a spatial representation of data that has particular applicability to the analysis of cross tabulations (or contingency tables). The authors focus on some of the geometric underpinnings of the procedure and the kinds of statements that can be made about interobject similarity based on a distance model. In particular, a rationale is developed, along with a scaling of coordinates, that enables one to compare both between-set and within-set squared distances. This scaling differs from the conventional scaling currently used in correspondence analysis, where only one set of distances usually are compared.
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References
1.
BenzécriJ. P. (1969), “Statistical Analysis as a Tool to Make Patterns Emerge from Data,” in Methodologies of Pattern Recognition, WatanabeS., ed. New York: Academic Press, Inc., 35–74.
2.
BenzécriJ. P. (1973), L'Analyse des Données, Vol. I, La Taxinomie; Vol. II, L'Analyse des Correspondances.Paris: Dunod.
3.
BourocheJ. M., and SaportaG. (1980), L'Analyse des Données.Paris: Presses Universitaires de France.
4.
CarrollJ. Douglas (1968), “Generalization of Canonical Correlation Analysis to Three or More Sets of Variables,” in Proceedings of 76th Annual Conference of the American Psychological Association, 3, 227–8.
5.
CarrollJ. Douglas (1980), “Models and Methods for Multidimensional Analysis of Preferential Choice (or Other Dominance) Data,” in Similarity and Choice, LantermannE. D., and FegerH., eds. Vienna: Hans Huber Publishers.
6.
de LeeuwJan (1973), Canonical Analysis of Categorical Data, unpublished doctoral dissertation, Psychological Institute, University of Leiden, The Netherlands.
7.
EckartC., and YoungGale (1936), “The Approximation of One Matrix by Another of Lower Rank,”Psychometrika, 1(September), 211–8.
8.
GifiA. (1981), Non-Linear Multivariate Analysis.Leiden, The Netherlands: Department of Data Theory, University of Leiden.
9.
GowerJ. C., and DigbyP. G. N. (1981), “Expressing Complex Relationships in Two Dimensions,” in Interpreting Multivariate Data, BarnettV., ed. Chichester, UK: John Wiley & Sons, Inc., 83–118.
10.
GreenPaul, and withE., and Douglas CarrollJ. (1976), Mathematical Tools for Applied Multivariate Analysis.New York: Academic Press, Inc.
11.
GreenacreMichael J. (1981), “Practical Correspondence Analysis,” in Interpreting Multivariate Data, BarnettV., ed. Chichester, UK: John Wiley & Sons, Inc., 119–46.
12.
GreenacreMichael J. (1984), Theory and Application of Correspondence Analysis.London: Academic Press, Inc.
13.
HeiserWillem J. (1981), Unfolding Analysis of Proximity Data.Leiden, The Netherlands: Department of Data Theory, University of Leiden.
14.
HillM. O. (1974), “Correspondence Analysis: A Neglected Multivariate Method,”Applied Statistics, 23(3), 340–54.
15.
HillM. O. (1982), “Correspondence Analysis,” in Encyclopedia of Statistical Sciences, Vol. 2, KotzS., and JohnsonN. L., eds. New York: John Wiley & Sons, Inc., 204–10.
16.
HoffmanDonna L., and FrankeGeorge R. (1986), “Correspondence Analysis: Graphical Representation of Categorical Data in Marketing Research,”Journal of Marketing Research, 23(August), 213–27.
17.
LebartLudovic, and MorineauAlain, and WarwickKenneth M. (1984), Multivariate Descriptive Statistical Analysis: Correspondence Analysis and Related Techniques for Large Matrices.New York: John Wiley & Sons, Inc.
18.
MeulmanJacqueline (1982), Homogeneity Analysis of Incomplete Data.Leiden, The Netherlands: DSWO Press.
19.
NishisatoShizuhiko (1980), Analysis of Categorical Data: Dual Scaling and Its Applications.Toronto: University of Toronto Press.
20.
SaportaG. (1980), “About Some Remarkable Properties of Generalized Canonical Analysis,” paper presented at the Second European Meeting of the Psychometric Society, Groningen, The Netherlands (June).
21.
YoungG. (1941), “Maximum Likelihood Estimation and Factor Analysis,”Psychometrika, 6, 49–53.
