Multi dimensional scaling

Multi dimensional Scaling (MDS) is a statistical technique used primarily in
marketing and the social sciences. It is a procedure for taking the
preferences and perceptions of respondents and representing them on a visual
grid. These grids, called perceptual maps are usually two dimensional, but
they can represent more than two. Potential customers are asked to compare
pairs of products and make judgements about their similarity. Whereas other
techniques (such as factor analysis, discriminant analysis, and conjoint
analysis) obtain underlying dimensions from responses to product attributes
identified by the researcher, MDS obtains the underlying dimensions from
respondentsÕ judgements about the similarity of products. This is an
important advantage. It does not depend on researchersÕ judgments. It does
not require a list of attributes to be shown to the respondents. The
underlying dimensions come from respondentsÕ judgements about pairs of
products. Because of these advantages, MDS is the most common technique used
in perceptual mapping.

Multidimensional Scaling Procedure

There are several steps in conducting MDS research:

  1. Formulating the problem - What brands do you want to compare? How many
     brands do you want to compare? More than 20 is cumbersome. Lets than 8
     (4 pairs) will not give valid results. What purpose is the study to be
     used for?
  2. Obtaining Input Data - Respondents are asked a series of questions. For
     each product pair they are asked to rate similarity (usually on a 7
     point Likert scale from very similar to very dissimilar). The first
     question could be for Coke/Pepsi for example, the next for Coke/Hires
     rootbeer, the next for Pepsi/Dr Pepper, the next for Dr Pepper/Hires
     rootbeer, etc. The number of questions is a function of the number of
     brands and can be calculated as Q = N (N - 1) / 2 where Q is the number
     of questions and N is the number of brands. This approach is referred
     to as the ÒPerception data : direct approachÓ. There are two other
     approaches. There is the ÒPerception data : derived approachÓ in which
     products are decomposed into attributes which are rated on a semantic
     differential scale. The other is the ÒPreference data approachÓ in
     which respondents are asked their preference rather than similarity.
  3. Running the MDS statistical program - Software for running the
     procedure is available in most of the better statistical applications
     programs. Often there is a choice between Metric MDS (which deals with
     interval or ratio level data), and Nonmetric MDS (which deals with
     ordinal data). The researchers must decide on the number of dimensions
     they want the computer to create. The more dimensions, the better the
     statistical fit, but the more difficult it is to interpret the results.
  4. Mapping the results and defining the dimensions - The statistical
     program (or a related module) will map the results. The map will plot
     each product (usually in two dimensional space). The proximity of
     products to each other indicate either how similar they are or how
     preferred they are, depending on which approach was used. The
     dimensions must be labelled by the researcher. This requires subjective
     judgement and is often very challenging. The results must be
     interpreted ( see perceptual mapping).
  5. Test the results for reliability and Validity - Compute R-squared to
     determine what proportion of variance of the scaled data can be
     accounted for by the MDS procedure. An R-square of .6 is considered the
     minimum acceptable level. Other possible tests are KruskalÕs Stress,
     split data tests, data stability tests (ie.: eliminating one brand),
     and test-retest reliability.

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