• Buy!!!• What’s best for me?• Which brand to buy?• What Style? Color?
• Sell!!!• What matters to customers?• Where are we positioned
relative to competitors?
Business CustomerComplex products, such as a cars, have dozens of criteria to consider.
Perceptual Map: Automobile
Understand Customers
SurveyAttribute Ratings
Factor Analysis
PerceptualMap
R
AnalyticApproach
ResearchObjectives
Get Data
AnalysisSoftware
Reporting
Project Plan
Surveys
• Exploratory: no guiding hypotheses• Confirmatory: set of hypotheses that form the
conceptual basis
Factor Analysis
Q Rate on a scale of 1-Low to 9-High(randomized list)
Shopper#1 NewBMW
1971 Olds 442 Conv.
1 Initial Price 9 3 42 Style 7 8 93 # of Miles on Car 7 9 44 Reliability 7 6 25 Color 5 7 96 Comfort 6 7 57 Horsepower 2 6 98 Safety 6 7 19 Financing Terms 7 5 2
10 Country Origin 1 7 711 Drive Type (Front, 4WD) 4 4 612 Miles Per Gallon (MPG) 6 7 513 Warranty Coverage 4 5 2
Survey: Attribute Ratings
Many more features, options….
Q Rate on a sale of 1- 91 Initial Price
2 Style
3 # of Miles on Car
4 Reliability
5 Color
6 Comfort
7 Horsepower
8 Safety
9 Financing Terms
10 Country Origin
11 Drive Type (Front, 4WD)
12 Miles Per Gallon (MPG)
13 Warranty Coverage
Survey: Attribute Ratings1 2 3 4 5 6 7 8 9 1
011
12
13
cor(data, digits=2)
Correlation Matrix
install.packages("corrgram")library(corrgram)corrgram(data)
Factor Analysis / Variable Reduction
Correlation Matrix
Correlated variables are grouped together and separated from other variables with low or no correlation
Factor Analysis
F1
Factor Analysis
F2 FN….F3
F1
b’s Factor Loadings
Factor Analysis
F2 FN….F3
Psych Package – includes FA
Psych Package – falibrary(psych)rmodel <- fa(r = corMat, nfactors = 3, rotate = “none", fm = "pa")
Psych Package
Each variable (circle) loads on both
factors and there is no clarity about
separating the variables into different
factors, to give the factors useful
names.
Factor 2
Factor 1
RotationRotations Courtesy of Professor Paul Berger
17
“CLASSIC CASE”
After rotationof ~450
NOW, all variables are loading on one factor and not at all the other; This is an overly “dramatic” case.
• Not Correlated Orthogonal• Varimax = Orthogonal Rotation
RotationRotations Courtesy of Professor Paul Berger
Psych Package – falibrary(psych)rmodel <- fa(r = corMat, nfactors = 3, rotate = "oblimin", fm = "pa")
Principal Components Analysis
Psych Package – principallibrary(psych)fit <- principal(ratings6, nfactors=4, rotate=“null")
Modelmodel <- princomp(data, cor=TRUE)summary(model) biplot(model)
Psych Package – principallibrary(psych)fit <- principal(ratings6, nfactors=4, rotate="varimax“)
corrgram(ratings6[,(1,2,9,12,3,4,6,8,10,5,11,7,13)])
Orthogonal /No Correlation
Psych Package – principalplot(fit)
Output
# scree plotplot(fit,type="lines")
3 Factor vs. 4 Factor
3 Factor vs. 4 Factor
StyleComfortColorUpgrade PackagesReliabilitySafetyCountry OriginHorsepowerNice DashMiles Per GallonInitial Price# of Miles on CarFinancing Options
Aaahh!!!Factor
Money
Perceptual Map
Factor Loadings
Brand Ratings
Weights
Average
Variance
Which One?Which Car?
Price$$$
$
Sweet!!!BORING
Aaaah factor…
Component Matrixa
.714 -7.61E-02 .327
.539 .226 -.145
.796 -3.02E-02 .338
.789 6.734E-02 -.379
.712 .107 -.499
.747 -2.02E-02 -.205
6.412E-03 .795 -4.87E-02
-.130 .841 3.175E-02
.675 -4.47E-02 .512
-5.09E-02 .701 .251
.791 1.682E-02 6.907E-02
D01
D02
D03
D04
D05
D06
D07
D08
D09
D10
D11
1 2 3
Component
3 components extracted.a.
Factor Analysis Recap
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