• 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