Aaker, Kumar, Day Seventh Edition Instructor’s Presentation Slides Marketing Research Aaker, Kumar, Day Seventh Edition Instructor’s Presentation Slides

Discriminant and Canonical Analysis Chapter Twenty Discriminant and Canonical Analysis

Discriminant Analysis Used to classify individuals into one of two or more alternative groups on the basis of a set of measurements Used to identify which variable contribute to making classification Major Uses Prediction Description Marketing Research 7th Edition Aaker, Kumar, Day

Objectives Determining linear composites of the predictor variables to separate groups by measuring between groups variation relative to within-groups variation Developing procedures for assigning new objects, firms, or individuals, whose profiles, but not group identity, are known, to one of the two groups Testing whether significant differences exist between the two groups based on the group centroids Determining which variables account most in explaining inter-group differences Marketing Research 7th Edition Aaker, Kumar, Day

Discriminant Function zi = b1 xi1 + b2 xi2 + b3 xi3 + ... + bn xin Where z = discriminant score b = discriminant weights x = predictor (independent) variables In a particular group, each individual has a discriminant score (zi) Σ zi = centroid (group mean) I = individual Centroid Indicates most typical location of an individual from a particular group Marketing Research 7th Edition Aaker, Kumar, Day

Cut-off Score Criterion against which each individual’s discriminant score is judged to determine into which group the individual should be classified For equal group sizes Z cut-off = ZA + ZB 2 For unequal group size Z cut-off = NB ZA + NA ZB Na + nb Marketing Research 7th Edition Aaker, Kumar, Day

Determination of Significance Null Hypothesis In the population, the means of all discriminant function in all groups are equal Ho : μA = μB If Ho is rejected, interpret results Marketing Research 7th Edition Aaker, Kumar, Day

Interpretation Generally, predictors with relatively large standardized coefficients contribute more to the discriminating power of the function Canonical or discriminant loadings show the variance that the predictor shares with the function Marketing Research 7th Edition Aaker, Kumar, Day

Classification and Validation Holdout Method Use part of sample to construct classification rule Other subsample used for validation Uses classification matrix and hit ratio to evaluate groups classification Uses discriminant weights to generate discriminant scores for cases in subsample Marketing Research 7th Edition Aaker, Kumar, Day

Classification and Validation (Contd.) U-method of Cross Validation Uses all available data without serious bias in estimating error rates Estimated classification error rates P1 = m1 P2 = m2 n1 n2 m1 and m2 Number of sample observations mis-classified in G1 and G2 Marketing Research 7th Edition Aaker, Kumar, Day

Multiple Discriminant Analysis Number of possible discriminant functions = Min(p,m-1) Where M = number of groups P = number of predictor variables Marketing Research 7th Edition Aaker, Kumar, Day

Canonical Correlation Analysis Focuses on the relationship between one set of dependent variables and one set of independent variables Application Concept Marketing Research 7th Edition Aaker, Kumar, Day

Canonical Correlation Analysis (Contd.) Inputs Outputs Key Terms Canonical correlation, Canonical loadings, Canonical root, Canonical coefficients, Canonical cross-loadings Assumptions (least restrictive) Limitations From the interpretation Marketing Research 7th Edition Aaker, Kumar, Day