Create brand maps based on attribute data to provide a rich visual summary of large numeric tables
To load the retailers
data go to Data >
Manage, select examples
from the
Load data of type
dropdown, and press the Load
button. Then select the retailers
dataset. The data set
contains information on consumer evaluations for a set of retailers in
the Chicago area on 7 attributes. In addition to attribute evaluations
the dataset contains preference ratings on a scale from 1-9 for each
retailer from two predefined consumer segments.
Select the retailer
variable as the Brand
attribute. This is simply a list of retailer names/labels. Then select
the variables good_value
through cluttered
in
the Attributes
box. Choose the segment1
and
segment2
variables in the Preferences
box.
After the settings have been changed click the Estimate
button or press CTRL-enter
(CMD-enter
on mac)
to generate results.
The variables in the Attributes
box will be analyzed
using factor analysis and the output is provided in the Summary
tab. We will start with a 2-dimensional solution. The first table shows
the factor scores for the brands. In essence these are a weighted
average of the original attribute data, where the weights are the factor
loadings. In other words, the factor scores are (two) variables created
by factor analysis to summarize the information contained in the
original 7 attributes. The second table of numbers shows the factors
loadings. These represent the correlations between the original
attributes and the derived factor scores.
We are also provided with information on how much of the information contained in the attributes is captured by the two derived factors. The first factor captures 56.4% and factor two captures 42% of the variation in the original data. Together the factors cover 98.4% of the variation, i.e., the information loss from reducing the dimensionality of the data from 7 attributes to two factors is only 1.6%. Adding a third factor will increase the captured variance only slightly but will make the interpretation of the map(s) more difficult. Therefore we will focus on the 2-dimension brand map.
The preference correlations indicate how strongly the preference
scores provided by respondents are linked to the uncovered factor
scores. The preferences for Segment 2
seems very strongly
positively correlated with factor 2 so we might expect to see the
preference arrow for this segment pointing almost straight up. The
communalities indicate how much of the variation in the segment
preferences can be explained by the two factors. The number are
excellent (i.e., 97.5% for Segment 1 and 91.5% for Segment 2). We can
infer from these numbers that the attributes selected in the study
reflect consumers preferences well, a key feature of useful brand
mapping research. Choosing attributes that are not linked to customer
preferences leads to brand maps that will be of limited value to a
manager.
The final table shows the attribute communalities. These numbers indicate how much of the variation in the attributes data can be explained by the two factors. The cumulative variance mentioned earlier is an overall measure across attributes. However, we are also interested to see if each of the individual attributes is well represented by the two factors. The numbers in this example are excellent across the board (i.e., all over 90%).
It is useful to start with a map showing only brand locations. Create the map in the Plot tab by checking the ‘Brands’ box. The graph is a scatter plot of the scores for factor 1 (the horizontal axis) and factor 2 (the vertical axis). In other words the scores for a brand on factor 1 and factor 2 are the coordinates for that brand in the map. The retailer names are used to label each point.
We can create a brand map with both the brand locations (again, using
the factor scores) and the attribute arrows (using the factor loadings)
by checking both the ‘Brands’ and ‘Attributes’ boxes. The orientation of
the arrows is determined by the degree of correlation between attribute
and factors, i.e., the factor loadings. The attribute
Service
has a strong positive loading on factor 1 and so it
points, mostly, in the direction in which factor 1 increases in value
(i.e., to the right). Since the correlation of Service
with
factor 2 is, slightly, positive the arrow points up rather than down. In
contrast, the attribute Convenience
has a strong positive
loading on factor 2 and so it points, mostly, in the direction in which
factor 2 increases in value (i.e., up). Since it’s correlation with
factor 1 is, slightly, positive the arrow points to the right rather
than to the left. The length of the arrows is proportional to the
communalities reported in the Summary tab. The higher the
communality, the longer the arrow. If an attribute is not well
summarized in the derived factors it’s communality will be low and the
arrow in the brand map for that attribute will be short.
Finally, we can add the preference information to the map by checking the ‘Preferences’ box. The orientation of the segment preference arrows is determined by the correlation between the factor scores and the preference scores. Since the preferences for the retailers expressed by respondents assigned to segment 2 are highly correlated with factor 2 the arrow points almost straight up. The negative correlations of the preference scores for segment 1 with both factor 1 and factor 2 ensure the arrow will point down and to the left.
In the plot we see that Whole foods and Cub foods are perceived as more comparable on the attributes for which we have data than, for example, Whole foods and Wal-Mart. From the plot a manager might conclude that the brands that are closest together in the map are perceived as close substitutes and, hence, close competitors in the minds of consumers.
An important limitation of a map without attribute information, e.g., based on (dis)similarity data, is that it is difficult to interpret why brands are located close together or far apart. By adding the attribute arrows to the map, as shown above, our understanding of the brand positions in the maps is significantly enhanced. For example, Jewel and Dominick’s are positioned higher in the map because they are perceived to offer consumers higher levels of convenience. Similarly, Cub foods, and particularly Whole foods, offer higher levels of customer service and quality products. We can also infer which available attributes are most strongly linked to consumer preferences. Segment 2 is primarily concerned with Convenience which may explain the higher preference scores for Jewel and Dominick’s. Similarly, Segment 2 cares most about Good value and very little for Assortment. This segment prefers to shop at Treasure Island and Wal-Mart.
Attribute-based perceptual maps are calculated using Principal
Components Analysis (PCA). The correlation matrix used as input for PCA
can currently be calculated only for variables of type
numeric
, integer
, and date
.
Preference information, however, can be of type numeric
,
integer
, date
, and factor
. When
preference variables of type {factor} are included, correlations between
the factor scores and preference data will be calculated using
polycor::hetcor
. The {factor} variables will be treated as
(ordinal) categorical variables and all other variables will be treated
as continuous.
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 prmap
tool are
cor
and cov
from the stats
package and principal
from the psych
package.