1 Cluster Analysis Objectives ADDRESS HETEROGENEITY Combine observations into groups or clusters such that groups formed are homogeneous (similar) within the group and heterogeneous (different) from other groups on some variables (?). When we don’t have “some variables”, we can still form groups using Multidimensional Scaling (MDS) Techniques. MDS - continuous Space Cluster - discrete groups Main Application in Marketing: Market Segmentation Data requirement ~ generally interval or ratio (ordinal and nominal ??) Steps Decide on measures of distance (similarity or dissimilarity) Hierarchical Cluster ~decide on how to combine observations Non-hierarchical cluster (K-means or quick cluster) Interpretation of clusters How many clusters Cluster validation

2 Cluster Analysis: Measures of Distance~ Similarity or Dissimilarity Two types of measures of distance ( or proximity, similarity) Direct ~ we shall use in MDS Indirect »Derived from original variables or factor scores Indirect Measures of distance Non-metric ~ we shall use in MDS Metric Data Euclidean Distance Minkowski Distance Mahalanobis Distance Distance between BMW and Ford Euclidean Minkowski Mahalanobis i=BMW j=Ford k = nos. variables v1 v2 ED

3 Cluster Analysis: Hierarchical Clustering Methods to combine observations Centroid Nearest Neighbor or single linkage Farthest-neighbor or complete linkage Average linkage Ward’s Centriod Method s1 s2 s3 s4 s5s6 distance Nearest neighbor Dendogram Data should be scaled?

4 Cluster Analysis: Non-Hierarchical Clustering K-Means Cluster/ Quick Cluster The data are divided into k-groups each group representing a cluster STEPS Select k initial cluster centroids, the number of cluster desired Assign each observation to the cluster to which it is closest Reassign or relocate each observation to one of the k clusters according to predetermined stopping rule Say we want 3 clusters and first 3 observations are centroids Change criterion: Continue if > 2% Which Clustering Method is Best? 1. Hierarchical ~ Which one to use? ~ Advantage: no prior knowledge of nos. of clusters, ~ Disadvantage: Once assigned, no reassignment 2. K-Means / Quick Cluster ~ require prior knowledge, how many clusters? Complementary: Run Hierarchical, decide on no of clusters, Run K -Means

5. Interpretation of Clusters Pseudo F

6 Cluster Analysis: Validation. S1 = assignment based on cluster on 1-14 cases S2 = assignment based on separate cluster Hit rate =112/151 =74% Cross-validation Example from Text

7 Latent Segments Model to Incorporate Heterogeneity

8 Introduction Customer segmentation - partition consumers into homogeneous groups that differ in purchasing behavior It provides information about consumer preferences and market structure at segment level Consumers with similar socio- demographics have different purchasing behavior Brand choice probabilities can be used to define both market segment and market structure Theoretical model: Multinomial logit Conceptual appeal being grounded in economic theory Analytical tractability and ease of econometric estimation Excellent Empirical performance

9 Kamakura and Russell (1989) propose and test latent segmentation. Number of applications and numerous citation, 200+ Discrete interpretation of continuous distribution. Number of useful applications in Marketing and other areas. In our own work used to determine size of price sensitive segment (25% to 35%).