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CHAPTER 18
MULTIVARIATE ANALYSIS
Marketing Research, 2nd Edition
Alan T. Shao
Copyright © 2002 by South-Western
PPT-1
What the Experts Say
…I’ve never considered myself a ‘quant jock,’ for
reasons probably due to genetic ancestry. I find it
difficult to get excited about the inner workings of
optimization algorithms or exploring the sensitivity of
[multivariate] ANOVA to violations in the
independence assumption, for example. Rather, my
interest in the various multivariate tools arises from
their usefulness as a means for examining
phenomena that do interest me.
--Rob Kleine, A Seminar in Multivariate
Statistics,
http://www.gentleye.com/research/
multivar/index.html, September 23, 2000.
Marketing Research, 2nd Edition
Alan T. Shao
Copyright © 2002 by South-Western
PPT-2
Learning Objectives
 Discuss the basics of multivariate statistical analyses
 Explain which technique is appropriate given the type
of variables involved
 Describe the usefulness of multivariate statistics
Marketing Research, 2nd Edition
Alan T. Shao
Copyright © 2002 by South-Western
PPT-3
Get This!
Fore! Golfers Benefit from Conjoint Analysis
 Every golfer has two things in common. They’re all
looking to drive the ball farther and to hit it with
more accuracy.
 Sawtooth Technologies, a well-known company
providing software for research data collection and
analysis, uses conjoint analysis to examine the extent
to which average driving distance, average ball life,
and price are concerns of golfers when selecting their
golf balls.
Marketing Research, 2nd Edition
Alan T. Shao
Copyright © 2002 by South-Western
PPT-4
Get This!
Fore! Golfers Benefit from Conjoint Analysis –
cont’d
 Conjoint analysis encompasses three critical steps:
– Collecting trade-offs
– Estimating buyer value systems
– Making choice predictions
The trade-offs might deal with paying a little extra for a
ball that travels farther. A golfer might value a long drive
more than a highly durable ball. And a choice prediction
might be that a golfer prefers the long-life ball over the
distance ball since it has the larger total value. All of
these findings would be based on computations from
conjoint analysis.
Marketing Research, 2nd Edition
Alan T. Shao
Copyright © 2002 by South-Western
PPT-5
Now Ask Yourself
 Does conjoint analysis make intuitive sense to you?
If so, why is it needed?
 What other multivariate techniques are available to
researchers?
 Do I need to be a statistical expert to understand
multivariate statistical analysis?
Marketing Research, 2nd Edition
Alan T. Shao
Copyright © 2002 by South-Western
PPT-6
Multivariate Statistical Analysis




Multivariate Statistics: Investigates more than two variables at a
time.
Many times, multivariate techniques are a means of performing in one
analysis what used to take multiple analyses using univariate
techniques.
The techniques can be used to summarize data and reduce the number
of variables necessary to describe the data.
Several of the more common multivariate techniques:
– Multiple Regression Analysis
– Multiple Discriminate Analysis
– Factor Analysis
– Cluster Analysis
– Multidimensional Scaling
– Conjoint Analysis
Marketing Research, 2nd Edition
Alan T. Shao
Copyright © 2002 by South-Western
PPT-7
Multiple Regression Analysis
 The premise behind multiple regression analysis is
consistent with that of simple regression analysis: to
determine the association or relationship between
dependent and independent variables.
 In multiple regression analysis, more than two variables
are included in examinations.
 The dependent and independent variables must be
interval-scaled to use this technique.
 The general form of the multiple regression model is as
follows:
Y   0  1 X 1   2 X 2  ...   n X n
where  0 = Y intercept of the regression model
1 ,  2 ... n = slope of the regression model
Marketing Research, 2nd Edition
Alan T. Shao
Copyright © 2002 by South-Western
PPT-8
Multiple Regression Analysis – cont’d
or the computed multiple regression model is
Yc  a  b1 X 1  b2 X 2  ...  bn X n
where Yc  computed value of the dependent variable
a = y intercept when x equals zero
b1 and b2 ...bn  partial regression coefficients
X 1 , X 2 ,..., X n  independent variables
 Partial Regression Coefficient: Denotes the change in the
computed value, Yc , per one unit change in X 1 when all other
independent variables are held constant.
Marketing Research, 2nd Edition
Alan T. Shao
Copyright © 2002 by South-Western
PPT-9
Multiple Regression Analysis – cont’d
 The association between the dependent and independent
variables is referred to as the coefficient of multiple
2
determination, denoted by R . It is interpreted in a similar
manner as we did when we referred to bivariate data. The
coefficient of multiple determination R 2 is computed as
follows:
R2 
RSS
ESS
 1
TSS
TSS
where TSS = total sum of squares
=  (Y  Y )
2
RSS = regression sum of squares
=  (Yc  Y ) 2
ESS = error sum of squares
=
Marketing Research, 2nd Edition
Alan T. Shao
Copyright © 2002 by South-Western
 (Y  Y )
2
c
PPT-10
Multiple Discriminant Analysis (MDA)
 Multiple Discriminant Analysis (MDA): The appropriate tool
for predicting the membership of observations in two or more
groups.
 Similar to multiple regression analysis except different types of
variables are involved.
 Appropriate if the dependent variable is nominal, categorical,
or multichotomous and the independent variables are interval
data.
 When two classifications are being examined, it is referred to
as a two-group discriminant analysis. When three or more
classifications are identified, then multiple discriminant
analysis is used.
Marketing Research, 2nd Edition
Alan T. Shao
Copyright © 2002 by South-Western
PPT-11
Multiple Discriminant Analysis (MDA) –
cont’d
 MDA is useful in situations where the total sample can be divided
into groups, based on a dependent variable characterizing several
known classes. The intent of this technique is twofold:
– To understand group differences.
– To predict the likelihood that a variable will belong to a
particular group, based on several independent variables.
 The linear combination is known as the discriminant function, and
is derived from the following equation:
Z  b1 X 1  b2 X 2  b3 X 3  ...  bn X n
where
Marketing Research, 2nd Edition
Alan T. Shao
Copyright © 2002 by South-Western
Z
= discriminant score
bi
= discriminant weight for variable i
Xi
= independent variable i
PPT-12
Multiple Discriminant Analysis (MDA) 
cont’d
 By averaging the discriminant scores for all the
individuals within a certain group, we create a group
mean, also referred to as a centroid.
 An important function of discriminant analysis is to
create a classification matrix, which shows the
number of correctly and incorrectly classified cases.
 The total number of properly classified cases divided
by the total number of cases is used to determine the
hit ratio—the percentage of properly classified cases.
Marketing Research, 2nd Edition
Alan T. Shao
Copyright © 2002 by South-Western
PPT-13
Factor Analysis
 MDA identifies groups of attributes on which individual
objects differ. Factor analysis groups attributes that are
alike.
 This technique can be used to examine interrelationships
among many variables and to explain these variables in
terms of their common underlying and unobservable
dimensions (called “factors”).
 Marketing researchers use factor analysis to reduce the
information contained in several original variables into a
smaller, more manageable set of variables while losing as
little information as possible.
Marketing Research, 2nd Edition
Alan T. Shao
Copyright © 2002 by South-Western
PPT-14
Factor Analysis – cont’d
 While there is no distinction between dependent and
independent variables when using this analysis technique,
data must be gathered from interval scales.
 The factor model that is used for calculations is:
Fi  Wi X 1  Wi X 2  Wi X 3  ...  Wi X k
where
Fi = estimate of the ith factor
Wi = weight or factor score coefficient
k = number of variables
Marketing Research, 2nd Edition
Alan T. Shao
Copyright © 2002 by South-Western
PPT-15
Cluster Analysis
 Cluster Analysis: Involves grouping data into “clusters” such
that elements in the same group are similar to each other and
elements in different groups are as different as possible.
 It is a statistical method that classifies or segments a sample
into homogeneous classes.
 Marketers often use cluster analysis to identify market
segments—groups of consumers with relatively similar needs.
They also use the technique to design products and establish
brands, target direct mail, make decisions about customer
conversion and retention, and decide on marketing cost levels.
Marketing Research, 2nd Edition
Alan T. Shao
Copyright © 2002 by South-Western
PPT-16
Cluster Analysis – cont’d
 Unlike factor analysis, which seeks to identify constructs that
underlie several variables, cluster analysis seeks to identify
constructs that underlie objects. Like factor analysis, though, in
order to use cluster analysis, interval scales must be used
during data gathering.
 While cluster analysis is similar to factor analysis in that it is
often used to reduce complexity in a data set, factor analysis is
concerned with reducing the number of variables; cluster
analysis tries to reduce the number of objects (e.g., individuals,
products, advertisements).
 Cluster analysis differs from discriminant analysis in that
cluster analysis actually creates groups of like items, whereas
discriminant analysis assigns elements to groups that were
defined beforehand.
Marketing Research, 2nd Edition
Alan T. Shao
Copyright © 2002 by South-Western
PPT-17
Multidimensional Scaling
 Multidimensional Scaling: (a.k.a., perceptual
mapping) Is a technique used to identify important
dimensions underlying respondents’ evaluations of
test objects.
 The objective is to convert judgments of similarity or
preference into distances represented in
multidimensional space.
 Allows the researcher to illustrate relationships
within data using pictures (a spatial representation of
data) rather than only numbers.
Marketing Research, 2nd Edition
Alan T. Shao
Copyright © 2002 by South-Western
PPT-18
Multidimensional Scaling – cont’d
 There is no distinction between dependent and
independent variables.
 Marketing researchers tend to use multidimensional
scaling techniques to identify important dimensions
underlying customer evaluations of products,
services, or companies.
Marketing Research, 2nd Edition
Alan T. Shao
Copyright © 2002 by South-Western
PPT-19
Conjoint Analysis
 Conjoint Analysis: Provides information about the
relative importance respondents place on individual
attributes when choosing from multiple products or
brands.
 Appropriate tool for nominal independent variables and
an ordinal dependent variable.
 Conjoint analysis estimates the value of each attribute
based on the choices respondents make along product
concepts that are systematically differed. So respondents’
preferences toward the attributes are inferred from their
choices rather than from self-reporting.
Marketing Research, 2nd Edition
Alan T. Shao
Copyright © 2002 by South-Western
PPT-20
Conjoint Analysis – cont’d
 This technique is built on the assumption that consumers
make complex decisions based not on one factor at a time
but on several factors “jointly” (hence the term conjoint).
Consumers make trade-offs in their decisions that will create
the most satisfaction.
 Conjoint analysis predicts what products and services
consumers will select and evaluates the weight people give
to various factors that underlie their decisions.
 Utility: Is the number that represents the value consumers
place on an attribute.
 Conjoint analysis creates a part-worth function that
describes the utility respondents give to the levels of each
attribute.
Marketing Research, 2nd Edition
Alan T. Shao
Copyright © 2002 by South-Western
PPT-21
Choosing the Appropriate Test
Multivariate Tests According To Scaled Data
Multivariate Test
Independent
Variable
Dependent
Variable
Multiple Regression
Interval
Interval
Multiple Discriminant Analysis
Interval
Nominal
Factor Analysis
Interval
Interval
Cluster Analysis
--
--
Multidimensional Scaling
Conjoint Analysis
Marketing Research, 2nd Edition
Alan T. Shao
Copyright © 2002 by South-Western
Ordinal or Interval Ordinal or Interval
Nominal
Ordinal
PPT-22
Decision Time!
You are a marketing manager of a mid-sized company, and
your marketing researcher has recently returned from a twoday seminar on multivariate statistics. He starts using some of
the techniques he learned, but you feel that the research
results he presents you with contradict your knowledge of the
market.
What are you going to do? Confront him and admit that you
do not know anything about multivariate statistics, but you
are uncomfortable with the research results?
Or do you educate yourself before confronting him? Is it your
responsibility to learn statistical techniques?
Marketing Research, 2nd Edition
Alan T. Shao
Copyright © 2002 by South-Western
PPT-23
Net Impact
 The Internet:
– Will not help researchers with statistical analyses.
– Can lend qualitative support for the research
findings obtained from the quantitative analyses.
– Can inform researchers about advancements made
in statistical analyses through published
manuscripts, clipboards, and chat groups.
Marketing Research, 2nd Edition
Alan T. Shao
Copyright © 2002 by South-Western
PPT-24
Chapter 18
End of Presentation
Marketing Research, 2nd Edition
Alan T. Shao
Copyright © 2002 by South-Western
PPT-25