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Database Marketing
Factor Analysis
N. Kumar, Asst. Professor of
Marketing
Web Advertising
Objective:
Identify the profile of customers who visit your
website
Important information for advertisers who may
wish to use your advertising services
N. Kumar, Asst. Professor of
Marketing
Repositioning your Web Site
You may wish to learn of features that
consumers value when browsing thro’
websites
Analysis of consumer data may help
uncover different facets (dimensions) of
customers’ preferences
Can make a perceptual map to help form the
basis of your strategy
N. Kumar, Asst. Professor of
Marketing
How can Factor Analysis Help?
Often Factor Analysis can help summarize
the information in many variables into a few
underlying constructs/dimensions
Reduces the number of variables that you
have to deal with little loss of information
N. Kumar, Asst. Professor of
Marketing
Why Reduce Data?
Census Bureau – each zip code has more
than 200 pieces of information
Typical customer survey on attitudes,
lifestyles, opinions will probably have
responses to more than 100 questions
N. Kumar, Asst. Professor of
Marketing
Why Reduce Data … contd.
Too much data can be hard to absorb and
comprehend
Difficult to work with too much data
Even if you can get it to work results will be
distorted (multicollinearity problem) –
regression example
N. Kumar, Asst. Professor of
Marketing
What is Factor Analysis?
What is Factor Analysis?
Factor analysis is a MV technique which
analyzes the structure of the interrelationships
among a large number of variables
Can identify the separate dimensions of the
structure and can also determine the extent to
which each variable is explained by each
dimension
N. Kumar, Asst. Professor of
Marketing
Factor Analysis: Intuitive
Description
Factor Analysis summarizes information in Data by
reducing original set of “items”/attributes to a smaller set
of “factors”/“dimensions”/“constructs”
A Factor can be viewed as an “Index”:
Dow Jones Index -- summarizes the movement of
stock market
Consumer Price Index -- reflects prices of consumer
products and indicator of inflation
How to create such an “index” that appropriately
summarizes the data with the minimum loss of
information?
N. Kumar, Asst. Professor of
Marketing
Factor Analysis: Intuitive
Description (cont.)
How does Factor Analysis work?
Factor Analysis “constructs” factors/axes by
including original attributes with different weights
If the responses are rated almost identically for an
attribute, Factor Analysis gives much lower weight
If two attributes, say attributes #3 and #4, are highly
correlated i.e. stores which rate highly on attribute #3
are also rated high on #4, Factor Analysis treats #3
and #4 as measurements of the same underlying
construct
N. Kumar, Asst. Professor of
Marketing
Factor Analysis: e-admission
Data: Students’ scores on different subjects – say
Physics, Chemistry, Math, History, English and
French
Task at hand: to make an assessment about the
student’s ability to succeed in school given these
scores
Do we need to look at the scores on all subjects or
can we use a simplified heuristic?
N. Kumar, Asst. Professor of
Marketing
Single Factor Model
Suppose we could get something like this:
M = 0.8 I + Am
P = 0.7 I + Ap
C = 0.9 I + Ac
E = 0.6 I + Ae
H = 0.5 I + Ah
F = 0.65 I + Af
A’s denote aptitude specific to the subject
N. Kumar, Asst. Professor of
Marketing
Factor Analysis vs. Regression
Regression
Have data on I
Objective is to work out the weight on I
Factor Analysis
I is the underlying construct that we are trying
to work out
N. Kumar, Asst. Professor of
Marketing
Some Terminology
Communality – that which is common with
the variable and the underlying factor.
Formally, the square of the pattern loading
Unique/Specific Variance – that which is
unexplained by the factor(s)
N. Kumar, Asst. Professor of
Marketing
Input: Correlations
M
P
C
E
H
M
1
P
0.56
1
C
0.72
0.63
1
E
0.48
0.42
0.54
1
H
0.40
0.35
0.45
0.30
1
F
0.52
0.46
0.59
0.39
0.33
N. Kumar, Asst. Professor of
Marketing
F
1
Results
Variable Communality Unique
Variance
M
0.640
0.360
P
0.490
0.510
C
0.810
0.190
E
0.360
0.640
H
0.250
0.750
F
0.423
0.577
Total
2.973
3.027
N. Kumar, Asst. Professor of
Marketing
Pattern
Loading
0.8
0.7
0.9
0.6
0.5
0.65
Two-Factor Model
Suppose we could get something like this:
M = 0.8 Q + 0.2 V +Am P = 0.7 Q + 0.3 V + Ap
C = 0.6 Q + 0.3 V +Ac
E = 0.2 Q + 0.8 V + Ae
H = 0.15 Q + 0.82 V +Ah F = 0.25 Q + 0.85 V + Af
A’s denote aptitude specific to the subject
N. Kumar, Asst. Professor of
Marketing
Results:
Variable Q
V
M
P
C
E
H
F
Total
0.040
0.090
0.090
0.640
0.672
0.723
2.255
0.640
0.490
0.360
0.040
0.023
0.063
1.616
Unique
Variance
0.321
0.420
0.551
0.321
0.304
0.215
2.132
N. Kumar, Asst. Professor of
Marketing
Q
V
0.800
0.700
0.600
0.200
0.150
0.250
0.200
0.300
0.300
0.800
0.820
0.850
Results: 2
Variable Q
V
M
P
C
E
H
F
Total
0.234
0.118
0.071
0.130
0.170
0.126
0.849
0.445
0.462
0.378
0.549
0.526
0.659
3.019
Unique
Variance
0.321
0.420
0.551
0.321
0.304
0.215
2.132
N. Kumar, Asst. Professor of
Marketing
Q
V
0.667
0.680
0.615
0.741
0.725
0.812
-0.484
-0.343
-0.267
0.361
0.412
0.355
Factor Analysis: Basic Concepts
Each original item (variable) is expressed as a linear
combination of the underlying factors
Original
Items
Underlying
Factors
X1
X2
F1
X3
F2
N. Kumar, Asst. Professor of
Marketing
X4
Factor Analysis: Basic Concepts
(cont.)
Each Factor can be expressed as a linear combination of
the original items (variables)
Underlying
Factors
Original
Items
F1
X1
F2
X2
X3
N. Kumar, Asst. Professor of
Marketing
X4
Factor Analysis: Basic Concepts
(cont.)
Mathematical Model
Common Factors, F1, …, FM, can be expressed as linear
combinations of the original variables, X1, …, XN
F1 = r11X1 + r12X2 + … + r1NXN
……………………………………………..
……………………………………………..
FM = rM1X1 + rM2X2 + … + rMNXN
rij = factor loading coefficient of the ith variable on the
jth factor
N. Kumar, Asst. Professor of
Marketing
Factor Analysis: Basic Concepts
(cont.)
Key Words
Factor Loading: Correlation of a factor with the
original variable.
Communality: Variance of a variable summarized
by the underlying factors
Eigenvalue (latent root): Sum of squares of
loadings of each factor – just a measure of variance
e.g. the eigenvalue of factor 1, l1,
l1 = r112 + r122 + … + r1M2
N. Kumar, Asst. Professor of
Marketing
Factor Analysis: Basic Concepts
(cont.)
What does a Factor Analysis program do?
finds the factor loadings, ri1, ri2, … , riN, for each of the underlying
factors , F1, …, FM, to “best explain” the pattern of interdependence
among the original variables, X1, …, XN
How are Factor Loadings determined?
select the factor loadings, r11, r12, … , r1N, for the first factor so
that Factor 1 “explains” the largest portion of the total variance
select the factor loadings, r21, r22, … , r2N, for the second factor
so that Factor 2 “explains” the largest portion of the “residual”
variance, subject to Factor 2 being orthogonal to Factor 1
so on ...
N. Kumar, Asst. Professor of
Marketing
How many Factors do you Choose?
Look at the Eigen Values of the Factors
If K of P factors have an eigen value > 1
then K factors will do a pretty good job
Scree plot helpful
N. Kumar, Asst. Professor of
Marketing
Scree Plot: Selection of # of Factors
6
5
4
“elbow”
3
2
1
2
4
6
8
N. Kumar, Asst. Professor of
Marketing
10
Factor Analysis:
Geometric Interpretation
Error
F1
x1
F2
N. Kumar, Asst. Professor of
Marketing
Illustrative Example: Measurement of
Department Store Image
Description of the Research Study:
To compare the images of 5 department stores in
Chicago area -- Marshal Fields, Lord & Taylor, J.C.
Penny, T.J. Maxx and Filene’s Basement
Focus Group studies revealed several words used by
respondents to describe a department store
e.g. spacious/cluttered, convenient, decor, etc.
Survey questionnaire used to rate the department
stores using 7 point scale
N. Kumar, Asst. Professor of
Marketing
Portion of Items Used to Measure Department
Store Image
1. Convenient place to shop
 q q q q q q
Inconvenient place to shop
2. Fast check out
q q q q q q q
Slow checkout
3. Store is clean
q q q q q q q
Store is dirty
4. Store is not well organized
q q q q q q q
Store is well organized
5. Store is messy, cluttered
q q q q q q q
Store is neat, uncluttered
6. Convenient store hours
q q q q q q q
Inconvenient store hours
7. Store is far from home,
school or work
q q q q q q q
Store is close to home, school, or
home
8. Store has bad atmosphere
q q q q q q q
Store has good atmosphere
9. Attractive decor inside
q q q q q q q
Unattractive decor inside
10. Store is spacious
q q q q q q q
Store is crowded
N. Kumar, Asst. Professor of
Marketing
Department Store Image Measurement:
Input Data
Respondents
…
…
…
Store 1
Store 2
Store 3
…
…
…
Store 4
Store 5
Attribute 1
…
Attribute 10
N. Kumar, Asst. Professor of
Marketing
Pair-wise Correlations among the Items Used
to Measure Department Store Image
X1
X2
X3
X4
X5
X6
X7
X1
X2
X3
X4
X5
X6
X7
X8
X9
1.00
0.79
0.41
0.26
0.12
0.89
0.87
0.37
0.32
0.18
1.00
0.32
0.21
0.20
0.90
0.83
0.31
0.35
0.23
1.00
0.80
0.76
0.34
0.40
0.82
0.78
0.72
1.00
0.75
0.30
0.28
0.78
0.81
0.80
1.00
0.11
0.23
0.74
0.77
0.83
1.00
0.78
0.30
0.39
0.16
1.00
0.29
0.26
0.17
1.00
0.82
0.78
1.00
0.77
X8
X9
X10
X10
1.00
N. Kumar, Asst. Professor of
Marketing
Principal Components Analysis for the Department
Store Image Data :
Variance Explained by Each Factor
Factor
(Latent Root)
Factor 1
Factor 2
Factor 3
Factor 4
Factor 5
Factor 6
Factor 7
Factor 8
Factor 9
Factor 10
Variance
Explained
5.725
2.761
0.366
0.357
0.243
0.212
0.132
0.123
0.079
0.001
N. Kumar, Asst. Professor of
Marketing
Scree Plot: Selection of # of Factors
6
5
4
“elbow”
3
2
1
2
4
6
8
N. Kumar, Asst. Professor of
Marketing
10
Unrotated Factor Loading Matrix for Department
Store Image Data Using Two Factors
Factor
Variable
1
2
3
4
5
6
7
8
9
10
1
0.633
0.621
0.872
0.833
0.774
0.626
0.619
0.859
0.865
0.790
2
0.707
0.695
-0.241
-0.366
-0.469
0.719
0.683
-0.303
-0.293
-0.454
Eigenvalue or latent root
5.725
2.761
Achieved
Communality
.900
0.869
0.819
0.828
0.818
0.908
0.850
0.829
0.835
0.831
©1991 T he Dryden Press. All rights reserved
N. Kumar, Asst. Professor of
Marketing
Factor Loading Matrix for Department Store Image
Data after Rotation of the Two Using Varimax
Factor
Variable
1
2
3
4
5
6
7
8
9
10
1
0.150
0.147
0.864
0.899
0.904
0.138
0.151
0.886
0.887
0.910
Eigenvalue or latent root
4.859
2
0.937
0.920
0.269
0.142
0.024
0.942
0.909
0.209
0.221
0.045
Achieved
Communality
0.900
0.869
0.819
0.828
0.818
0.908
0.850
0.829
0.865
0.831
3.628
©1991 T he Dryden Press. All rights reserved.
N. Kumar, Asst. Professor of
Marketing
Procedure for Conducting a
Factor Analysis
Data Collection
Step 1
Run Factor Analysis
Step 2
Determine the Number of Factors
N. Kumar, Asst. Professor of
Marketing
Step 3
Procedure for Conducting a
Factor Analysis
Rotate Factors
Step 4
Interpret Factors
Step 5
Calculate Factor
Score
Step 6
Do Other Stuff
Step 7
N. Kumar, Asst. Professor of
Marketing
Product Differentiation &
Positioning Strategy
Product Differentiation: creation of tangible or
intangible differences on one or two key dimensions
between a brand/product and its main competitors
Example: Toyota Corolla and Chevy Prizm are
physically nearly identical cars and yet the Corolla
is perceived to be superior to the Prizm
Product Positioning: set of strategies that firms develop
and implement to ensure that these perceptual differences
occupy a distinct and important position in customers’
minds
Example: KFC differentiates its chicken meal by
using its unique blend of spices and cooking
processes
N. Kumar, Asst. Professor of
Marketing
Product Positioning &
Perceptual Maps
Information Needed for Positioning Strategy:
Understanding of the dimensions along which target
customers perceive brands in a category and how these
customers perceive our offering relative to competition
How do our customers (current or potential) view
our brand?
Which brands do those customers perceive to be our
closest competitors?
What product and company attributes seem to be
most responsible for these perceived differences?
 Competitive Market Structure
Assessment of how well or poorly our offerings are
positioned in the market
N. Kumar, Asst. Professor of
Marketing
Product Positioning &
Perceptual Maps (cont.)
Managerial Decisions & Action:
Critical elements of a differential strategy/action plan
What should we do to get our target customer
segment(s) to perceive our offering as different?
Based on customer perceptions, which target
segment(s) are most attractive?
How should we position our new product with
respect to our existing products?
What product name is most closely associated with
attributes our target segment perceives to be
desirable
 Perceptual Map facilitate differentiation &
positioning decisions
N. Kumar, Asst. Professor of
Marketing
Application Summary: Data Reduction
Identifying underlying dimensions, or FACTORS, that
explain the correlation among a set of variables
e.g. a set of lifestyle statements may be used to measure
the psychographic profiles of consumers
M<N
Psychographic
Factors
Statement 1
…………….
…………….
Statement N
Life-style Statements
N. Kumar, Asst. Professor of
Marketing
Psychographic
Profiles
Application Summary: Product
Positioning/Introduction
Understanding customer preferences
What dimensions to differentiate on to be
successful – implications for repositioning or
introduction strategy
N. Kumar, Asst. Professor of
Marketing
Web Advertising
Understanding the profile of customers
Conduct a survey
Analyze the data – extract the factors
Interpret the factors – score the customers
Can even draw a perceptual map of customers
in the factor space
N. Kumar, Asst. Professor of
Marketing
Repositioning your Web Site
To learn of features that consumers value when
browsing thro’ websites – conduct a survey
Factor analyze the data to uncover the underlying
factors that influence customers’ preferences –
interpret the factors
How score on these dimensions relative to your
competition - perceptual map to help form the
basis of your strategy
N. Kumar, Asst. Professor of
Marketing