Of course, the answer depends on what you mean by brand
image. But that is a more complicated
issue that we can address in another post.
For now, let’s agree on an operational definition and say that brand
image is measured by a series of ratings or a checklist associating attributes or
benefits with the brand. With this
definition, brand image is the pattern of associations endorsed by customers. We can simplify the data collection even more
by agreeing that our data will be brand image ratings, such as, “Windows 8 is
for work and play.”
Companies, like Microsoft, with a product portfolio seek
some degree of synergy from being able to provide a comprehensive solution
rather than a single product. They want
the “good” achieved with one product (e.g., Xbox Kinect) to transfer to the
brand first and then filter out to the other products it offers (e.g., MS
Office). Can statistical modeling
help? Can we collect brand ratings from
customers and model these connections between the product and the brand and then
between the brand and other products?
Getting concrete, if Windows 8 is seen as innovative, we
would expect customers to assume a confirmation bias and begin to see all
improvements in Microsoft products as additional instances of innovation. That is, customers begin to entertain the
hypothesis that Microsoft is getting innovative. For example, you hear about the new “big
data” capabilities in Excel 2013. Before
Windows 8, this information may not have generalized to the Microsoft
brand. But once the Microsoft "innovation
bucket” is opened by Windows 8, every improvement for every product is added
to the innovation reservoir and those productbrandproduct connections start
to be made. The distinction being proposed
is between brand cohesion where all the products mutually reinforce the brand
image and brand fragmentation where there is little synergy among the products
in the portfolio.
To be clear, I am not suggesting that we ever ask customers
to rate Microsoft. Brand image is a
latent construct that cannot be directly measured. Of course, there is nothing to stop us from asking customers to rate
Microsoft, but we have no idea what they are rating. Perhaps with a less wellknown company with
fewer products, we might believe that customers have no information except what
they have learned from using the company’s products. But this is not the case with Microsoft. What are customers thinking about when they
provide Microsoft ratings? We cannot just allow them
to fill in the “blanks” and make their own decision about what to include under
the Microsoft label. Do some respondents
focus on the corporate side of Microsoft appearing in the news and the business
reports? Are others thinking about
productivity software, or the operating system, or email and internet
explorer? Do gamers include Xbox? What products are businesses including under
the Microsoft heading? And by businesses,
do we mean owners, decision makers, or IT administers?
No, we must ask the complete brand image battery for some subset of
the different Microsoft products with which respondents are familiar.
Then, we infer brand image by measuring agreement across products. If each Microsoft product is rated
independently based only on the performance of that individual product, we will
not see sizeable correlations across different products. On the other hand, betweenproduct
correlations will increase in size to the extent that the attribution is to the
Microsoft brand and not the separate product (e.g., Excel is easy to use
because Microsoft makes all its products easy to use”). We are calling this effect brand cohesion,
and we are asking how Microsoft can use the release of Windows 8 to create
greater cohesion among its products.
It’s the Response Pattern and Not Individual Ratings
We are going to be looking at a correlation matrix. Often we will be examining a very large correlation
matrix with lots of ratings and lots of products. In order to keep it simple in this
introduction, let us suppose that we asked respondents to rate three different Microsoft
products on three different brand image items.
This would yield a 9x9 correlation matrix. Can we see an underlying structure that would
account for the pattern of correlations in this matrix?
For example, if we observed a correlation matrix like the
following one, we would conclude that there was no brand cohesion. The three ratings for the first Microsoft
product, labeled A, are highly correlated at 0.64, as are the three ratings for
Product B and the three ratings for Product C.
But there is no correlation between the same ratings for the different
products. Let the first rating be
innovative. Whatever the rating of
Product A’s innovation, it has no relationship with the innovation rating for
Product B or C. We cannot see any brand
cohesion for the Microsoft products because there is no relationship between
the ratings for different products.
A1

A2

A3

B1

B2

B3

C1

C2

C3


A1

1.00

0.64

0.64

0.00

0.00

0.00

0.00

0.00

0.00

A2

0.64

1.00

0.64

0.00

0.00

0.00

0.00

0.00

0.00

A3

0.64

0.64

1.00

0.00

0.00

0.00

0.00

0.00

0.00

B1

0.00

0.00

0.00

1.00

0.64

0.64

0.00

0.00

0.00

B2

0.00

0.00

0.00

0.64

1.00

0.64

0.00

0.00

0.00

B3

0.00

0.00

0.00

0.64

0.64

1.00

0.00

0.00

0.00

C1

0.00

0.00

0.00

0.00

0.00

0.00

1.00

0.64

0.64

C2

0.00

0.00

0.00

0.00

0.00

0.00

0.64

1.00

0.64

C3

0.00

0.00

0.00

0.00

0.00

0.00

0.64

0.64

1.00

A second hypothetical correlation matrix, shown below, looks
a lot more like what we typically see in brand image research. The withinproduct correlations (in the boxes
along the diagonal) are uniformly higher than the other correlations. Product C has the highest values with r
values of 0.77, 0.72, and 0.69. The
other two products also have substantial withinproduct correlations. We also want to look at the correlations
among the same rating across different products. In order to see these values in the
correlation matrix, I have used different colors. Only the ratings for the first attribute (A1,
B1, and C1) are uniformly higher than the other correlations between different
rating items for different products.
These correlations are in red and have values of 0.48, 0.48 and 0.47.
A1

A2

A3

B1

B2

B3

C1

C2

C3


A1

1.00

0.59

0.53

0.48

0.41

0.34

0.48

0.41

0.34

A2

0.59

1.00

0.49

0.41

0.35

0.29

0.41

0.35

0.29

A3

0.53

0.49

1.00

0.35

0.30

0.25

0.34

0.29

0.24

B1

0.48

0.41

0.35

1.00

0.67

0.61

0.47

0.40

0.33

B2

0.41

0.35

0.30

0.67

1.00

0.58

0.40

0.34

0.28

B3

0.34

0.29

0.25

0.61

0.58

1.00

0.33

0.28

0.24

C1

0.48

0.41

0.34

0.47

0.40

0.33

1.00

0.77

0.72

C2

0.41

0.35

0.29

0.40

0.34

0.28

0.77

1.00

0.69

C3

0.34

0.29

0.24

0.33

0.28

0.24

0.72

0.69

1.00

If you found the above description hard to follow, you are
not alone. It is difficult to see the
pattern even with a small 9x9 correlation matrix. Usually, we would run a factor analysis to
uncover and display the underlying structure.
Although everyone uses factor analysis now, much of the early work came
from psychometricians studying intelligence.
I note this only because we need to borrow another factor analytic model
from psychometrics in order to separate the effects of brand and product.
Borrowing Some Statistical Tools from a Psychometric Neighbor
We can agree that there are just too many correlations to
examine without a factor analytic model to uncover the underlying
structure. But, the underlying structure
that we are proposing has a very specific set of constraints. We need to run a bifactor model because we
believe that these correlations are the outcome of two independent components:
a general brand effect impacting all the ratings and separate more specific
product effects isolated to each product.
If you wish to learn more, I have written two earlier posts describing
the bifactor model in more detail:Halo Effects and Multicollinearity: Separating the General from the Specific
Structural Equation Modeling: Separating the General from the Specific (Part II)
Hopefully, the following diagram will clear up any confusion.
If the bifactor model works, then the path coefficients in
this diagram ought to reflect what we observed in the correlation matrix. There are three specific product factors (F1*,
F2*, and F3*) and one general brand latent variable (g). The path coefficients for Product C are
consistently higher than the path coefficients for Product B, which in turn,
are consistently higher than the path coefficients for Product A. This is what we found in the product blocks
along the main diagonal of our second correlation matrix. The Product A intercorrelations are in the
0.50’s. The Product B intercorrelations
tend to be in the 0.60’s (one exception at 0.58). The Product C intercorrelations range from
0.69 to 0.77. In addition, the general
brand effect (labeled “g”) is responsible for some level of correlation
among all the ratings. In fact, it is
the only reason why ratings from different products are correlated. These path coefficients from the g latent
variable seem to be larger for the ratings of the first item, as we noted when
we looked at the correlation matrix (these were the higher correlations in
red).
We can use the bifactor model to assess the contribution of the brand and the product to the observed correlations. These product specific paths account for some portion of the
observed correlations within a product.
For instance, the observed correlation between C2 and C3 is 0.69. The portion that is due to Product C is calculated
by multiplying their path coefficients or 0.63 x 0.63 = 0.40. The remaining portion can be attributed to
the general brand effect. Again, we
multiply the path coefficients, this time from g, and find 0.58 x 0.50 = 0.29
due to the brand. Assuming a correct
model specification, we have been able to decompose the observed 0.69
correlation between the two ratings into a 0.29 component from the brand and a
0.40 component from the product.
How can Microsoft use these findings to improve its brand
image?
1. The path coefficients from the generalized brand
latent variable (the gcoefficients) tell Microsoft if its brand image is cohesive
or fragmented. The higher the
coefficients we find, the more cohesive the brand.
In our diagram we see gcoefficients ranging from 0.50 to 0.67. Like all factor analyses, these path
coefficients are factor loadings (i.e., correlations between the latent brand
variable and the observed ratings), and you are free to judge their magnitude as
you would any other factor loading.
2.
The path coefficients from each product latent
variable provide Microsoft with similar information about the products. High product path coefficients indicate a
cohesive product. It is not always the
case that we find the high degree of product separation that we found in this
example. Sometimes we have more or fewer
latent variables than products. Many
times there are multiple path coefficients heading into each rating item, and
the diagram looks more like an entangled web rather than the nice separation we find in
our diagram.
3.
Finally, we can use
the path coefficients to identify where Microsoft ought to concentrate its
effort to improve its brand image. We are looking for productspecific image attributes that have strong connections to the general brand. The strategy is to change the perceptions of those productspecific attributes and have those improvements work their way back and enhance the brand image. Over time, the boosted brand image will encourage a more positive evaluation of all Microsoft products. This is synergy.
Summary: Using
the bifactor model, we have been able to decompose the correlation matrix of customer
ratings into brand and product components.
The higher the path coefficients from the general brand latent variable,
the more cohesive the brand. The higher
the path coefficients from each separate product latent variable, the more
cohesive the product. Thus, Microsoft
products that are less integrated into the brand will have lower path
coefficients from g. We do not see this
pattern with this hypothetical data. The average of the path
coefficients from g to each of the ratings is approximately the same for all
three products.
However, we do see some differences in the gcoefficients
for the three ratings. Across the three
products, the first rating has the largest gcoefficient. If this first rating item measured
innovation, for example, we would argue that innovation is more central to the
brand image and where we might get our best return, all less being equal. That is, improving the innovation perception
for Product C would work its way backward to the general brand perception and
thus increase all the ratings for all the products proportional to their gcoefficients.Finally, you can see the advantages of using the bifactor modeling approach. We are able to make specific recommendations about individual ratings for each product in Microsoft’s portfolio. Where should Microsoft focus its efforts? They should focus on those ratings with the highest centrality – a measure from network analysis indicating the ability of that rating to have the most impact on the greatest number of other ratings.
Appendix (R code to run this analysis)
library(psych)
loadings < matrix(c(
.70, .40, .00, .00,
.60, .43, .00, .00,
.50, .45, .00, .00,
.69, .00, .50, .00,
.59, .00, .53, .00,
.49, .00, .55, .00,
.68, .00, .00, .60,
.58, .00, .00, .63,
.48, .00, .00, .65),
nrow=9,ncol=4, byrow=TRUE)
cor_matrix<loadings %*% t(loadings)
diag(cor_matrix)<1
cor_matrix
R<data.frame(cor_matrix)
names(R)<c("A1","A2","A3","B1","B2","B3","C1","C2","C3")
R
m<omega(R)
m
omega.diagram(m, digits=2, main="Bifactor Structure Underlying Brand Image")