1. Discriminant Analysis
By Rama Krishna Kompella

2. Discriminant Analysis
• Discriminant Analysis may be used for two
objectives:
– Either we want to assess the adequacy of
classification, given the group memberships of the
objects under study; or
– we wish to assign objects to one of a number of
(known) groups of objects.
• Discriminant Analysis may thus have a
descriptive or a predictive objective

3. Discriminant analysis
• Discriminant analysis is used to analyze relationships
between a non-metric dependent variable and metric or
dichotomous independent variables.
• Discriminant analysis attempts to use the independent
variables to distinguish among the groups or categories
of the dependent variable.
• The usefulness of a discriminant model is based upon its
accuracy rate, or ability to predict the known group
memberships in the categories of the dependent
variable.

4. Discriminant scores
• Discriminant analysis works by creating a new variable
called the discriminant function score which is used to
predict to which group a case belongs.
• The discriminant function is similar to a regression
equation in which the independent variables are
multiplied by coefficients and summed to produce a
score.

5. Number of functions
• If the dependent variable defines two groups, one statistically
significant discriminant function is required to distinguish the
groups; if the dependent variable defines three groups, two
statistically significant discriminant functions are required to
distinguish among the three groups; etc.
• If a discriminant function is able to distinguish among groups,
it must have a strong relationship to at least one of the
independent variables.
• The number of possible discriminant functions in an analysis
is limited to the smaller of the number of independent
variables or one less than the number of groups defined by
the dependent variable.

6. Discriminant Function
Zi = b1 X1 + b2 X2 + b3 X3 + ... + bn Xn
Where Z = discriminant score
b = discriminant weights
X = predictor (independent) variables
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7. Determination of Significance
• Null Hypothesis: In the population, the group means the
discriminant function are equal
Ho : μ A = μ B
• Generally, predictors with relatively large standardized
coefficients contribute more to the discriminating power
of the function
• Discriminant loadings show the variance that the
predictor shares with the function
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8. Uses of Discriminant Analysis
• Product research – Distinguish between heavy, medium,
and light users of a product in terms of their
consumption habits and lifestyles
• Perception/Image research – Distinguish between
customers who exhibit favorable perceptions of a store
or company and those who do not
• Advertising research – Identify how market segments
differ in media consumption habits
• Direct marketing – Identify the characteristics of
consumers who will respond to a direct marketing
campaign and those who will not

9. Steps in Discriminant Analysis
1. Form groups
2. Estimate discriminant function
3. Determine significance of function and variables
4. Interpret the discriminant function
5. Perform classification and validation
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10. Example
X2
Back Yard Burger
Income ($)
Customers
Other Fast-Food
Restaurants
X1
Lifestyle-Eating Nutritious Meals

11. Classification of Multivariate Methods
Dependence One Number of None Interdependence
Methods Dependent Variables Methods
(Nonmetric) (Metric)
Dependent Variable Interval • Factor Analysis
Nominal
Level of Measurement or Ratio • Cluster Analysis
• Perceptual Mapping
Ordinal
• Multiple Regression
• Discriminant • ANOVA
Analysis • Spearman’s Rank • MANOVA
• Conjoint Correlation • Conjoint

12. Questions?