Marketing Letters 3:3, (1992): 259-272
© 1992 Kluwer Academic Publishers, Manufactured in the Netherlands.
Interpreting Multiple Correspondence Analysis as a
Multidimensional Scaling Method
DONNA L. HOFFMAN*
S«hool of Management, University of Texas at Dallas, JO 5.1, Riehardson, TX 75083-0688, (2t4)
690-2545, E-mail: dlhoff@vm.utdallas.edu
JAN DE LEEUW
Department of Mathematics, 7228 MSB, UCLA, Los Angeles CA 90024-1555, (213) 825-9550, E-
mail: deeleuw@laplace.sscnet.ucla.edu
Key words: Graphical Representation of Categorical Data, Homogeneity, Nonlinear Multivariate
Analysis
[January 1992]
Abstract
We formulate multiple correspondence analysis (MCA) as a nonlinear multivariate analysis method
that integrates ideas from multidimensional scaling. MCA is introduced as a graphical technique
that minimizes distances between connecting points in a graph plot. We use this geometrical ap-
proach to show how questions posed of categorical marketing research data may be answered with
MCA in terms of closeness. We introduce two new displays, the star plot and line plot, which help
illustrate the primary geometric features of MCA and enhance interpretation. Out approach, which
extends Gifi (1981, 1990), emphasizes easy-to-interpret and managerially relevant MCA maps.
Multiple correspondence analysis (MCA) is weil on its way to becoming a popular
tool in marketing research (Hoffman & Franke, 1986). For example, Green, Krie-
ger, and Carroll (1987) use MCA to analyze the relationship between consumers'
choice profile predictions from a conjoint task and consumer demographic char-
acteristics. In a similar vein, Kaciak and Louviere (1990) illustrate how MCA may
be used to analyze data from discrete choice experiments. Carroll and Green
(1988) apply individual differences MDS to normalized Burt matrices (a principal
data matrix in MCA) to determine the relationship between consumer demograph-
ics and automobile characteristics with respect to number of cars in the house-
hold. More recently, Valette-Florence and Rapacchi (1991) perform an MCA on
the attributes-consequences-values matrix derived from a laddering task to con-
struct a product positioning map and Hoffman and Batra (1991) apply MCA to
study the association between television program types and audience viewing be-
haviors.
*The authors thank J. Douglas Carroll, Don Lehmann, Donald Morrison, and two anonymous
reviewers for their helpful comments on a previous version of this manuscript.