Multidimensional Scaling (Mds). The Next

¶ … multidimensional scaling (MDS). The next section compares MDS with factor analysis and cluster analysis. The third section identifies actual applications of MDS in the marketing research literature and the last section is devoted to a hypothetical situation in which MDS is used in a snack food market.

What is Multidimensional Scaling?

According to Young (1985), multidimensional scaling was introduced as an aid to understanding people's judgments about the similarity of members of a set of objects. In marketing applications, MDS is a technique for assessing and visually representing the preferences and perceptions of consumers. Potential customers are asked to compare pairs of products and make judgments about them. Discriminant analysis is a statistical technique used in marketing and the social sciences. ...Conjoint analysis, also called multiattribute compositional models, is a statistical technique that originated in mathematical psychology. ... The judgments can be as simple as "prefer a to B," "A is more like B. than C," or a rating of 5 given to product a on an "appealingness" scale of 1 to 7, where a, B, and C. are three products in a larger set of products.

The aggregated judgments (e.g., percentage of times preferred, average appeal rating) for each product are shown as points in space, usually two- but sometimes three-dimensional. (More than three dimensions makes for difficulty in interpreting.) the objective of MDS is to place points in multidimensional space so that the distances between points reflect as closely as possible the subjective distances obtained by surveying subjects.

An important issue in MDS is dimensionality. Normally, MDS is used to provide a perceptual map of a complex set of relationships that can be scanned at a glance. Dimensions are item attributes that seem to order the items in the map along a continuum. Borgatti's (1997) example of MDS applied to dog breeds is illustrative. Borgatti proposed that an MDS of perceived similarities among breeds of dogs might show a clear ordering of dogs by size. At the same time, an independent ordering of dogs by perceived viciousness might be observed. This ordering might be perpendicular to the size dimension, or it might cut a sharper (less that ninety degree) angle.

The underlying dimensions are thought to "explain" the perceived similarity between items. In his dog example, Borgatti stated that two dogs are seen as similar because they have similar scores or locations on the identified dimensions. That is, the observed similarity between a Doberman and a German Shepherd is explained by their being perceived as nearly equally vicious and about the same size. The implicit logic of how similarity judgments are made is that items have attributes (such as size, viciousness, speed, thickness of fur, etc.) in varying degrees, and the similarity between them is due to their similarity across all attributes.

Garson (2009) pointed out that the labeling of axes in MDS is just as subjective as in factor analysis. Subjects and/or experts "eyeball" the MDS perceptual maps (scatterplots) and infer dimension labels. Where labeling is subjective and sometimes debatable, there is some objectivity to deciding on the number of dimensions. The "Stress Test" is the name given to the most commonly used statistical test of goodness of fit for a given number of dimensions. Garson noted that the statistic is the ordinary phi.

Garson (2009) cautioned that, while MDS makes fewer assumptions than factor analysis, some guidelines must be adhered to when applying the method. They include the following:

1. Include all relevant objects (products or items) in the preference comparisons on which the MDS is based. Omission of relevant items can drastically alter MDS results, as can inclusion of irrelevant items.

2. Do not allow more dimensions than objects. If there are more dimensions than objects, the MDS solution will be unstable and goodness of fit measures will be inflated. Garson's rule of thumb is that "the research design should provide for four times as many objects as dimensions, plus 1 (thus 5 objects for a 1-dimensional solution, 9 for 2-dimensional, etc.).

3. Make sure that the objects being compared/voted upon/ranked share one or more meaningful dimensions so that meaningful comparisons are possible.

4. Be aware that dimensions may change over time for the same individuals. There are some problems or questions where the market researcher might wish to examine changes over time.

5. Insure that missing values comprise only a small percentage of total cases. Large numbers of missing values can lead to misleadingly low estimates of stress. (Low values of stress indicate a good fit. Larger values of stress signal a poorer fit.)

6. Likewise, insure there are few ties. A large number of ties can also lead to misleadingly low estimates of stress.

7. Insure that there is variability in the raw data. Although MDS does not assume any particular data distribution, some variance in the data is necessary for meaningful results.

How does MDS Differ from Factor Analysis and Cluster Analysis?

In marketing applications of factor analysis, the investigator obtains underlying dimensions from responses to product attributes identified by the researcher. MDS obtains the underlying dimensions from respondents' judgments about the similarity of products. MDS does not depend on researchers' judgments. Not does it require a list of attributes to be shown to the respondents. The underlying dimensions come from respondents' judgments about pairs of products. Moreover, unlike factor analysis, MDS does not require assumptions of linearity, metricity, or multivariate normality, so sometimes it is preferred over factor analysis even for objective data.

If the raw data are metric or dichotomous, factor analysis or cluster analysis would be more efficient for the researcher's problem. On the other hand, MDS has relaxed data distribution assumptions and is robust with smaller sample size than is factor analysis, so there are instances where the researcher might prefer MDS even for objective data (Garson, 2009).

The major difference between MDS and cluster analysis is that multidimensional scaling identifies underlying dimensions, while cluster analysis identifies clusters. Thus, if a market researcher wished to group customers based on their preferences and had no need to identify underlying dimensions; he or she would probably choose cluster analysis.

How is MDS Used by Companies to Address Business Problems?

Cooper (1983) reviewed MDS in marketing research and found applications as diverse as (a) assessing how a given brand of coffee relates to other brands, (b) rating the appeal of different breakfast bakery items, (c) relating individuals' degree of concern over ecology to laundry detergent ratings, (d) evaluating law enforcement officers' judgments of the severity of different kinds of drug abuse, and (e) determining the effect, in a before an after design, of aggressive marketing's on attitudes toward a cigarette brand. These are by no means the only applications, but an indication of their variety. Applications are limited only by the creativity of the market researchers and managers.

How Might MDS Be Used in a Snack Food Market?

The following is a hypothetical situation. CW, a manufacturer of candy bars, has decided to put a new candy bar on the market. He wants to insure that it is a strong competitor with other more established candy bars. So CW hires a market research organization (MRO) to advise him on where to direct his efforts. He already knows that a good portion of candy bar buyers are in the age range 12-19 years old, so he informs MRO that that is who should be the subjects of the research.