T18 discriminant analysis
Click here to load reader
-
Upload
kompellark -
Category
Technology
-
view
1.703 -
download
0
Transcript of T18 discriminant analysis
Discriminant Analysis
By Rama Krishna Kompella
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
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.
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.
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.
http://www.drvkumar.com/mr9/ 6
Discriminant Function
Zi = b1 X1 + b2 X2 + b3 X3 + ... + bn Xn
Where Z = discriminant score
b = discriminant weights
X = predictor (independent) variables
http://www.drvkumar.com/mr9/ 7
Determination of Significance
• Null Hypothesis: In the population, the group means the discriminant function are equal
Ho : μA = μB
• 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
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
http://www.drvkumar.com/mr9/ 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
Example
Back Yard BurgerCustomers
Other Fast-FoodRestaurants
X2
X1
Lifestyle-Eating Nutritious Meals
Inco
me
($)
Classification of Multivariate Methods
Nominal
• Discriminant Analysis• Conjoint
Dependent VariableLevel of Measurement
Ordinal
• Spearman’s Rank Correlation
DependenceMethods
Number of Dependent Variables
Intervalor Ratio
• Multiple Regression• ANOVA• MANOVA• Conjoint
InterdependenceMethods
• Factor Analysis• Cluster Analysis• Perceptual Mapping
One None
(Metric)(Nonmetric)
Questions?