Current methods of multiple correspondence analysis (MCA) provide configurations that are expressed in terms of principal axes. These solutions are not invariant over rotations. The authors propose an approach to MCA that entails an INDSCAL analysis of normalized Burt matrices (as commonly obtained from MCA). The resulting configuration is uniquely oriented and dimension weights also are obtained for each contributory data set. The method is applied to survey data describing relationships among respondent demographic characteristics and recent car purchases.
Get full access to this article
View all access options for this article.
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.
BurtCyril (1950), “The Factorial Analysis of Qualitative Data,”British Journal of Psychology (Statistical Section), 3, 166–85.
3.
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.
4.
CarrollJ. Douglas, and ChangJih-Jie (1970), “Analysis of Individual Differences in Multidimensional Scaling via an N-way Generalization of Eckart-Young Decomposition,”Psychometrika, 35(September), 283–319.
5.
CarrollJ. Douglas, GreenPaul E., and SchafferCatherine M. (1986), “Interpoint Distance Comparisons in Correspondence Analysis,”Journal of Marketing Research, 23(August), 271–80.
6.
CarrollJ. Douglas, GreenPaul E., and SchafferCatherine M. (1987), “Comparing Interpoint Distances in Correspondence Analysis: A Clarification,”Journal of Marketing Research, 24(November), 445–50.
7.
GifiA. (1981), Non-Linear Multivariate Analysis.Leiden, The Netherlands: Department of Data Theory, University of Leiden.
8.
GreenPaul, and withE., and Douglas CarrollJ. (1976), Mathematical Tools for Applied Multivariate Analysis.New York: Academic Press, Inc.
9.
GreenPaul E., RaoVithala R., and DeSarboWayne S. (1978), “Incorporating Group-Level Similarity Judgments in Conjoint Analysis,”Journal of Consumer Research, 5(December), 187–93.
10.
GreenacreMichael J. (1984), Theory and Application of Correspondence Analysis.London: Academic Press, Inc.
11.
GreenacreMichael J., and HastieTrevor (1987), “The Geometric Interpretation of Correspondence Analysis,”Journal of the American Statistical Association, 82(June), 437–47.
12.
HeiserWillem J. (1981), Unfolding Analysis of Proximity Data.Leiden, The Netherlands: Department of Data Theory, University of Leiden.
13.
HoffmanDonna L., and FrankeGeorge R. (1986), “Correspondence Analysis: Graphical Representation of Categorical Data in Marketing Research,”Journal of Marketing Research, 23(August), 213–27.
14.
HolbrookMorris, and MooreWilliam, and WinerRussell S. (1982), “Constructing Joint Spaces from Pick-Any Data: A New Tool for Consumer Analysis,”Journal of Consumer Research, 9(June), 99–105.
15.
JambuM., and LebeauxM. O. (1983), Cluster Analysis and Data Analysis.Amsterdam: North-Holland Publishing Co.
16.
LebartLudovic, and MorineauAlain (1982), “SPAD: A System of FORTRAN Programs for Correspondence Analysis,”Journal of Marketing Research, 19(November), 608–9.
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.
NishisatoShizuhiko, and NishisatoIra (1983), An Introduction to Dual Scaling.Islington, Ontario: MicroStats.
21.
SaportaG. (1980), “About Some Remarkable Properties of Generalized Canonical Analysis,” paper presented at Second European Meeting of the Psychometric Society, Groningen, The Netherlands (June).
