Chapter 17
Overview of Multivariate
Analysis Methods
MULTIVARIATE ANALYSIS
statistical techniques used when there are multiple
measurements of each element/concept and the
variables are analyzed simultaneously.
These techniques are important in marketing
research because most business problems are
multidimensional and can only be understood when
multivariate techniques are used.
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Classification of Multivariate Methods
We’ve already discussed ANOVA, MANOVA, Correlation,
Multiple Regression, and Perceptual Mapping.
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Summary of Multivariate Methods
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DEPENDENCE VS INTERDEPENDENCE METHODS
Dependence – multivariate
Interdependence – multivariate
techniques appropriate when
statistical techniques in which a
one or more of the variables
set of interdependent
can be identified as
relationships is examined – The
dependent variables and the
goal is grouping variables in
remaining as independent
some way.
variables.
Examples: multiple
regression analysis,
discriminant analysis,
ANOVA and MANOVA
Examples: factor analysis,
cluster analysis, and
multidimensional scaling.
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FACTOR ANALYSIS
. . . used to summarize information contained in a large
number of variables into a smaller number of subsets or
factors.
Purpose – to simplify the data.
Dependent and independent variables are analyzed
separately, not together.
All variables being examined are analyzed together – to
identify underlying factors.
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FACTOR ANALYSIS PROCESS
Examine factor loadings
& percentage of variance
Steps
Decide on number of
factors
Interpret & name factors
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Factor Loadings are correlations between the
variables and the new composite factor.
These are the starting point for interpreting
factor analysis.
They measure the importance of each
variable relative to each composite factor.
Like correlations, factor loadings range
from +1.0 to –1.0
Factor loadings are calculated between all
factors and each of the original variables.
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CLUSTER ANALYSIS
classifies objects into relatively homogeneous
groups based on the set of variables analyzed.
classifies or segments objects into groups that
are similar within groups and as different as
possible across groups.
identifies natural groupings or
segments among many variables,
does NOT include a dependent variable.
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CLUSTER ANALYSIS
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SPSS DIALOG BOX FOR CLUSTER ANALYSIS
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CLUSTER ANALYSIS COEFFICIENTS
Coefficients
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NEW CLUSTER VARIABLE
New
cluster
variable
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DISCRIMINANT ANALYSIS
It’s a dependence technique used for
predicting group membership on the basis of
two or more independent variables.
Dependent variable – nonmetric or
categorical (nominal or ordinal).
Independent variables – metric (interval or
ratio), but non-metric (nominal) dummy
variables are possible.
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DISCRIMINANT ANALYSIS
Develops a linear combination of
independent variables and uses it to
predict group membership.
Characteristics
Predicts categorical dependent variable
based on group differences using a
combination of independent variables.
Discriminant function – a linear
combination of independent variables
that bests discriminates between the
dependent variable groups.
15
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DISCRIMINANT ANALYSIS
Discriminant
Function
Coefficients
Estimates of the
discriminatory power
of a particular
independent
variable.
Multipliers of
variables in the
discriminant function
when variables are in
the original units of
measurement.
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DISCRIMINANT ANALYSIS
.
The prediction is referred
to as the hit ratio.
.
Shows the number of correctly and
incorrectly classified cases .
Classification (Prediction) Matrix –
shows whether the estimated discriminant
function is a good predictor.
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DISCRIMINANT ANALYSIS
SCATTER PLOT
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SPSS DIALOG BOX FOR
DISCRIMINANT ANALYSIS
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SPSS DISCRIMINANT
ANALYSIS OUTPUT
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SPSS DISCRIMINANT ANALYSIS
OUTPUT CONTINUED
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Sample Conjoint Survey Profiles
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Importance Calculations for
Restaurant Data
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Conjoint Part-Worth Estimates for
Restaurant Survey
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