Discriminant AnalysisDiscriminant Analysis

DA is a technique for analyzing data DA is a technique for analyzing data when the criterion or dependent when the criterion or dependent variable is categorical and the variable is categorical and the predictor or independent variables predictor or independent variables are interval in nature.are interval in nature.

Discriminant AnalysisDiscriminant Analysis

DA is sometimes also calledDA is sometimes also called

Discriminant factor analysis Discriminant factor analysis Canonical discriminant analysisCanonical discriminant analysis

ObjectivesObjectives

Development of discriminant Development of discriminant functions functions

Examination of whether significant Examination of whether significant differences exist among the groups, differences exist among the groups, in terms of the predictor variables.in terms of the predictor variables.

Determination of which predictor Determination of which predictor variables contribute to most of the variables contribute to most of the intergroup differencesintergroup differences

Evaluation of the accuracy of Evaluation of the accuracy of classificationclassification

Multiple Discriminant Multiple Discriminant AnalysesAnalyses

Discriminant functionsDiscriminant functions

A function like multiple regression A function like multiple regression but different in the aspect that the but different in the aspect that the dependent variable is categorical.dependent variable is categorical.

Discriminant AnalysesDiscriminant Analyses

The The discriminant scorediscriminant score, or DA , or DA score, is the value resulting from score, is the value resulting from applying a discriminant function applying a discriminant function formula to the data for a given case. formula to the data for a given case.

Multiple Discriminant Multiple Discriminant AnalysesAnalyses

Discriminant coefficientsDiscriminant coefficients are the are the regression-like b coefficients in the regression-like b coefficients in the discriminant function, in the form D = discriminant function, in the form D = b1x1 + b2x2 + ... + bnxn + c, b1x1 + b2x2 + ... + bnxn + c,

where D is the latent variable formed by where D is the latent variable formed by the discriminant function, the b's are the discriminant function, the b's are discriminant coefficients, the x's are discriminant coefficients, the x's are predictor variables, and c is a constant. predictor variables, and c is a constant.

Multiple Discriminant Multiple Discriminant AnalysesAnalyses

The The structural discriminant function structural discriminant function coefficientscoefficients are partial coefficients, reflecting are partial coefficients, reflecting the unique contribution of each variable to the unique contribution of each variable to the classification of the criterion variable the classification of the criterion variable

The The standardized discriminant coefficientsstandardized discriminant coefficients, , like beta weights in regression, are used to like beta weights in regression, are used to assess the relative classifying importance of assess the relative classifying importance of the independent variables the independent variables

Discriminant AnalysesDiscriminant Analyses

Applications:Applications:

Market Research: Market Market Research: Market segmentationsegmentation

Financial Research: Default behaviorFinancial Research: Default behavior

Human resources: High performers Human resources: High performers