Multidimensional Scaling
Multidimensional
scaling (MDS) is a series of techniques that helps the analyst to identify key
dimensions underlying respondents’ evaluations of objects. It is often used in
Marketing to identify key dimensions underlying customer evaluations of products,
services or companies.
Once
the data is in hand, multidimensional scaling can help determine:
• What
dimensions respondents use when evaluating objects
• How
many dimensions they may use in a particular situation
• The
relative importance of each dimension, and
• How the
objects are related perceptually
The
purpose of MDS is to transform consumer judgments of similarity or preference
(eg. preference for stores or brands) into distances represented in
multidimensional space.
The
resulting perceptual maps show the relative positioning of all objects. Multidimensional
scaling is based on the comparison of objects.
Any
object (product, service, image, etc.) can be thought of as having both
perceived and objective dimensions. For example, a firm may see their new model
of lawnmower as having two color options (red versus green) and a 24-inch
blade. These are the objective dimensions. Customers may or may not see these attributes. Customers may
also perceive the lawnmower as expensive-looking or fragile, and these are the perceived dimensions.
• The
dimensions perceived by customers may not coincide with (or even include) the objective
dimensions assumed by the researcher.
• The
evaluations of the dimensions may not be independent and may not agree. For example,
one soft drink may be judged sweeter than another because the first has a
fruitier aroma, although both contain the same amount of sugar.
Steps for Designing Multidimensional
Scaling
Step 1: Objectives of Multidimensional Scaling
Perceptual
mapping, and multidimensional scaling in particular, is most appropriate for
achieving two objectives:
1.
As an exploratory technique to identify unrecognized dimensions affecting behavior
2.
As a means of obtaining comparative evaluations of objects when the specific
bases of comparison are unknown or undefinable
The
strength of perceptual mapping is its ability to infer dimensions without the
need for defined attributes. In a simple analogy, it is like providing the
dependent variable (similarity among objects) and figuring out what the
independent variables (perceptual dimension) must be.
The
researcher must define a multidimensional scaling analysis through three key
decisions: selecting the objects that will be evaluated, deciding whether similarities
or preference is to be analyzed and choosing whether the analysis will be
performed at the group or individual level.
Identification of All Relevant Objects to Be Evaluated
The
most basic, but important, issue in perceptual mapping is the definition of the
objects to be evaluated. The researcher must ensure that all “relevant” firms,
products/services or other objects be included, and that no “irrelevant”
objects are included, because perceptual mapping is a technique of relative
positioning.
Similarity versus Preference Data
To
this point we have discussed perceptual mapping and MDS mainly in terms of similarity data. In
providing preference data, the respondent applies “good-bad” assessments, where we assume
that differing combinations of perceived attributes are valued more highly than
others. Both bases of comparison can be used to develop perceptual maps, but
with differing interpretations.
Aggregate versus Disaggregate Analysis
In
considering similarities or preference data, we are taking respondent’s
perceptions of different stimuli / treatments and creating outputs of the
proximity of these treatments in t dimensional space. The researcher can
generate this output on a subject-by-subject basis (producing as many maps as
subjects), known as disaggregate analysis.
Aggregate analysis.
If
the focus is on an understanding of the overall evaluations of objects and the
dimensions employed in those evaluations, an aggregate analysis is the most
appropriate. But if the objective is to understand variation among individuals,
then a disaggregate approach is the most helpful.
Step 2: Research Design of MDS
Perceptual
mapping techniques can be classified by the nature of the responses obtained
from the individual concerning the object.
One
type, the decomposition method, measures only the overall impression or evaluation of an
object and then attempts to derive spatial positions in multidimensional space
reflecting these perceptions. The compositional method is an alternative method
in which a defined set of attributes is considered in developing the similarity
between objects.
Decompositional
techniques are typically associated with multidimensional scaling and so our
focus will be primarily on these methods.
Similarities Data
When
collecting similarities data, the researcher is trying to determine which items
are the most similar to each other and which are the most dissimilar. Three
procedures commonly used to obtain respondents’ perceptions of similarities are
outlined below
Comparison of Paired Objects:
By
far the most widely used method of obtaining similarity judgments, the respondent
is asked simply to rank or rate the similarity of all pairs of objects.
Confusion Data:
The pairing (or “confusing”) of stimulus I with stimulus J is
taken to indicate similarity. Also known as subjective
clustering, the typical procedure for gathering these
data is to place the objects whose similarity is to be measured (eg. ten candy
bars) on small cards, either descriptively or with pictures. The respondent is
asked to sort the cards into stacks so that all the cards in a stack represent similar
candy bars. The data result in an aggregate similarities matrix similar to a
cross-tabulation table.
Preference Data
Preference
implies that stimuli should be judged in terms of dominance relationships –
that is, stimuli are ordered in terms of the preference for some property.
Direct Ranking:
Each
respondent ranks the objects from most preferred to least preferred, as in the
following example: Rank from most preferred (1) to least preferred (4)
_____
Candy Bar A
_____
Candy Bar B
_____
Candy Bar C
_____
Candy Bar D
Paired Comparisons: A
respondent is presented with all possible pairs and asked to indicate which
member of each pair is preferred, as in this example:
Please
circle the preferred candy bar in each pair:
A
B
A
C
A
D
B
C
B
D
C
D
Preference
data allows the researcher to view the location of objects in a perceptual map
where difference implies differences in preference.
If
there are n elements to compare then we have n*(n-1)/2 pairs to compare
Ashitosh Mohite
14012
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