Brand maps based on (dis)similarity data can be analyzed using Multi-Dimensional Scaling (MDS)
The city data (city
) contains information on distances
in miles between 10 major cities in the US. Distances for 45 (10 x 9 /
2) from-to city pairs are provided. These data are used to illustrate
that MDS can take simple data on distances (or on brand dissimilarities
as we will see) and create a 2-dimensional map that accurately depicts
the relative city (or brand) positions.
To load the city
data go to Data > Manage,
select examples
from the Load data of type
dropdown, and press the Load
button. Then select the
city
dataset. In Multivariate > Maps >
(Dis)similarity select from
as ID 1, to
as ID 2, and distance
as the Dissimilarity measure. After
the settings have been changed click the Estimate model
button or press CTRL-enter
(CMD-enter
on
macOS) to generate results.
The original distances are shown in (lower triangular) matrix form in the screenshot below. If the analysis is successful we expect cities that are close (e.g., Washington DC and New York) to also be located close together on the map. Cities that are far apart (e.g., Seattle and Miami) should also be positioned far apart in the map.
The basic measure of (lack of) fit for MDS is called
Stress
. If MDS cannot create a map that accurately
describes the original data this will result in high stress. Stress
values of .1 are generally considered fair, .05 is good, and .01 or
lower is excellent. High stress values indicate that a dimensionality of
three (or higher) is needed to accurately depict the available data. For
the city data the stress value is equal to .02 which is good. In the
Summary tab we also see the coordinates that will be used to
create the two-dimensional map shown in the Plot tab and the
recovered distances (i.e., how far the cities are apart in the
generated map).
In the screen shot from the Plot tab shown below the relative locations of Los Angeles, Boston, etc. look wrong. This is due to the fact the MDS program has no information on North, South, East and West. We can flip the plot to see if the map becomes easier to recognize and interpret.
To create the plot shown below click the check-boxes for
dimension 1
and dimension 2
. After
flipping the plot along both the horizontal and vertical axis
we see that the relative locations of the cities look quite good. Note
that this map is flat, i.e., there is no correction for the
curvature of the earth.
The following plot is based on similarity data for a set of
toothpaste brands (tpbrands
is available as one of the
example datasets). Respondents were asked the following question:
“Please rate the following pairs of toothpaste brands on the basis of
their similarity (1 = very similar, 7 = very dissimilar).” for all
pairwise combinations of 10 brands, i.e., 45 comparisons. MDS will try
to create a map that reproduces, as accurately as possible, the original
dissimilarities (or perceptual distances) provided by the 50
respondents. The original dissimilarity ratings are shown in (lower
triangular) matrix form in the figure below. From these data we can
already see that the respondents perceive some brands to be very similar
(e.g., Ultra Brite and Pepsodent have an average dissimilarity score of
1.11) and others to be very dissimilar (e.g., Crest and Sensodyne). The
stress value for a two-dimensional solution is reasonable (.058). As we
might expect, however, the original and recovered distances show that
the fit is not as good as for the city
data.
The coordinates shown in the Summary tab are used to plot the brands in two dimensions in the Plot tab. In the plot we see that Aqua Fresh and Colgate as well as Ultra Brite and Pepsodent are located very close together. This is consistent with the original data. Sensodyne and Crest, however, are positioned at opposite ends of the plot. Again, this is consistent with the original data and provides visual confirmation that MDS was able to create a plot that fits the data reasonably well.
From the plot a manager might conclude that the brands that are closest together in the map are perceived by consumers as close substitutes and, hence, close competitors in the minds of consumers in this market segment. A manager for Aqua Fresh or Macleans, in contrast, might focus less on Sensodyne when developing a competitive positioning plan for her brand. An important limitation of brand maps based on (dis)similarity data is that the axes are difficult to interpret. For example, why are Close-up and Crest located at opposite ends along the horizontal axes? The researcher could ask respondents to explain the meaning of the axes or else obtain additional attribute information for the brands and correlate/overlay these on the plot to facilitate interpretation. Such attribute data could, however, also be used to create a brand map without the need for (dis)similarity ratings (see Multivariate > Maps > Attributes).
Add code to
Report
> Rmd to (re)create the analysis by clicking the
icon on the bottom
left of your screen or by pressing ALT-enter
on your
keyboard.
For an overview of related R-functions used by Radiant to generate brand maps see Multivariate > Maps.
The key functions used in the mds
tool are
cmdscale
from the stats
package and
isoMDS
from the MASS
package.