A Model for the Analysis of Asymmetric Data in Marketing Research

Abstract

Over the last decade, numerous methods for the multidimensional scaling (MDS) of perceptions and preferences have been applied by researchers in marketing. However, one notable gap in MDS methodology has been the lack of suitable models for analyzing inherently asymmetric data relationships. Recently, Harshman (Harshman, R. A. 1978. Models for analysis of asymmetrical relationships among objects or stimuli. Paper presented at the First Joint Meeting of the Psychometric Society and the Society for Mathematical Psychology. McMaster University, Hamilton, Ontario, August; Harshman, R. A. 1982a. DEDICOM: A family of models generalizing factor analysis and multidimensional scaling for decomposition of asymmetric relationships. Unpublished manuscript, University of Western Ontario.) has proposed a new family of models—called DEDICOM (DEcomposition into Directional COMponents)—for analyzing data matrices that are intrinsically asymmetric. In this article, the single-domain DEDICOM model is described and applied to two illustrative cases in marketing research. The examples demonstrate that DEDICOM solutions will sometimes make more substantive sense and provide significantly better fits to asymmetric data than solutions obtained by factor analysis or MDS. DEDICOM also provides a novel type of information—a description of asymmetric relations among dimensions or clusters. Such information will often have useful marketing implications.multidimensional scaling, factor analyses

Desicom: Decomposition of Asymmetric Relationships Data into Simple Components

“…Therefore, we reanalyzed the car switching data set (Harshman, et al, 1982) for which Kiers and Takane (1993, p. 345) reported a constrained DEDICOM solution (see left-hand side of Table 3). We used 20 random starts, and E=10-6 as in the small simulation study above.…”

“…The first component in the DESICOM solution can be interpreted as "Thick ness" and the second as "Vigor" (just as in Harshman, et al, 1982). The values in A indicate that the words "Body" and "Fullness" are much more representative of the Thickness component than the words "Bouncy" and "Manageable"; similarly, "Zesty" is relatively unrepresentative of the Vigor component .…”

“…For more details on the interpretation of the (constrained) DEDICOM model we refer to Harshman, et al (1982) and Kiers and Takane (1993).…”

Asymmetric Multidimensional Scaling of Brand Switching Among Margarine Brands

“…There are four main analytical approaches using the brand switching matrix to measure the brand substitutability. They are; (a) the approach using the probabilistic consumer behavior model (Carpenter & Lehmann, 1985;Tsurumi, 2005), (b) the approach using the log linear model (Colombo & Morrisson, 1989;Kannan & Wright, 1991;Novak, 1993), (c) the approach using the latent class model (Grover & Srinivasan, 1987;Jain, Bass, & Chen, 1990), (d) and the approach using multidimensional scaling (DeSarbo & Manrai, 1992;Harshman, Green, Wind, & Lundy, 1982;Okada, 1988Okada, , 1998. In (a) the approach using the probabilistic consumer behavior model, the marketing mix effect for the brand switching probability of consumers was estimated by the probabilistic consumer behavior model based on the multinomial logit model.…”

A Generalized Inner Product Model for the Analysis of Asymmetry

“…DEDICOM proposed by Harshman (1978Harshman ( , 1982 can be said to be a more general inner product model than the model proposed by Chino. DEDICOM decomposes observed similarity data into some combination of few basic underlying relationships.…”