Discriminant Analysis

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Discriminant Analysis
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Discriminant Analysis
Discriminant analysis is a versatile statistical
method often used by market researchers
to classify observations into two or more groups
or categories. In other words, discriminant
analysis is used to assign objects to one group
among a number of known groups. In order to
perform any kind of discriminant analysis, you
must first have a sample within these known
groups.
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When To Use Discriminant Analysis?
By performing discriminant analysis, researchers
are able to address classification problems in
which two or more groups, clusters, or
populations are known up front, and one or more
new observations are placed into one of the
known classifications based on measured
characteristics. Discriminant analysis is also
used to investigate how variables contribute to
group separation, and to what degree. For this
reason, its often leveraged to compliment the
findings of cluster analysis.
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Market researchers are continuously faced with
situations in which their goal is to obtain a
better understanding of how groups (customers,
age cohorts, etc.) or items (brands, ideas,
etc.), differ in terms of a set of explanatory
or independent variables. These situations are
where discriminant analysis serves as a powerful
research and analysis tool.
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Descriptive discriminant analysis
Descriptive discriminant analysis is used when
researchers want to assess the adequacy
of classification, given the group memberships of
the object under study.
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Predictive discriminant analysis
Predictive discriminant analysis is used when
researchers want to assign objects to one of a
number of known groups of objects.
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Researchers overcome Type I error.
In discriminant analysis, the intercorrelation
of variables is addressed by partitioning
correlations between independent
variables. When discriminant analysis uses one
independent variable to rationalize differences
between the groups, the remaining variables are
amended so that any difference that is apparent
between groups is not due to correlation that
the other independent variables have with the
first variable. For this reason, discriminant
analysis only addresses the unduplicated variance
between groups.
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Benefits of Discriminant Analysis

• Discriminant analysis can be closely compared to
  regression analysis for the ways in which it
• identifies the degree to which objects adhere to
  the specifications of certain groups.
• Discriminant analysis is also commonly used by
  marketers to develop perceptual maps.

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There are seemingly endless ways to implement
discriminant analysis for market research and
business purposes. By conducting this method of
data analysis, researchers are able to obtain a
much stronger grasp on the products and services
they provide, and how these offerings stack up
against varying topics and areas of interest.
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Discriminant Analysis Procedure
Step 1 Collect training data Step 2 Prior
Probabilities Step 3 Bartlett's test Step 4
Estimate the parameters of the conditional
probability density functions Step 5 Compute
discriminant functions Step 6 Use cross
validation to estimate misclassification
probabilities Step 7 Classify observations with
unknown group memberships
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