Discriminant Analysis

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Discriminant Analysis

• Similar to Regression, except that criterion (or
  dependent variable) is categorical rather than
  continuous.
• -used to identify boundaries between groups of
  objects

For example (a) does a person have the disease
or not (b) Is someone a good credit risk or
not? (c) Should a student be admitted to college?
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Benefits of Discriminant Analysis

• Similar to regression
• What predictor variables are related to the
  criterion (dependent variable)
• Predict values on the criterion variable when
  given new values on the predictor variable

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A cartoon of Discriminant Analysis showing the
Discriminant Function
Cutoff score to discriminate groups
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Cluster Analysis

• Set of techniques used to partition a set of
  objects (people) into relatively homogenous
  subsets based on similarity.
• Example Applications
• Psychology classifying individuals into types
• Regional Analysis classifying cities into
  typology based on demographic and fiscal
  variables
• Marketing research classifying individuals into
  clusters

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Goal of Cluster Analysis
Identify a few groups so that individuals /
objects in a group are more similar than objects
outside a group. Reduce the set of n objects to
less than n groups. Thus it is a data reduction
technique
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Similarity to Factor Analysis
Factor Analysis and Cluster Analysis are both
data reduction techniques. Goal of Factor
Analysis is to reduce original set of variables
to smaller set of factors. Goal of Cluster
Analysis is to form groups from the people or
objects, thus reducing original number of
elements to fewer groups. Factor Analysis can be
seen as a clustering technique than is focused on
the columns of data matrix, rather than the rows.
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Similarity to Discriminant ANalysis
In Discriminant Analysis, groups are know a
priori I.e., all the observations are supposed
to be correctly classified at the outset.
Objective of analysis is to predict that
classification from the predictor
variables. Cluster Analysis is used when the
natural clusterings are not known. The objective
is to discover is there are any natural
groups. In cluster analysis, one begins with
groups that are undifferentiated, and tries to
form groups and subgroups.
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Types of Data
Ratings of n objects on p properties
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Distance Data
Distance of n objects from each other (can use
categorical data, when you just know if two
objects are in the same group)
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