1. Marketing Research Aaker, Kumar, Day and Leone Tenth Edition Instructor’s Presentation Slides 1

2. Marketing Research 10th Edition http://www.drvkumar.com/mr10/ Chapter Twenty-one 2 Factor and Cluster Analysis

3. Marketing Research 10th Edition http://www.drvkumar.com/mr10/ Factor Analysis Combines questions or variables to create new factors Combines objects to create new groups Uses in Data Analysis ▫To identify underlying constructs in the data from the groupings of variables that emerge ▫To reduce the number of variables to a more manageable set 3

4. Marketing Research 10th Edition http://www.drvkumar.com/mr10/ Factor Analysis (Contd.) Methodology Principal Component Analysis ▫Summarizes information in a larger set of variables to a smaller set of factors Common Factor Analysis ▫Uncovers underlying dimensions surrounding the original variables 4

5. Marketing Research 10th Edition http://www.drvkumar.com/mr10/ Factor Analysis - Example 5

6. Marketing Research 10th Edition http://www.drvkumar.com/mr10/ Principal Component Analysis Since the objective of factor analysis is to represent each of the variables as a linear combination of a smaller set of factors, it is expressed as 6 X 1 = I 11 F 1 + I 12 F 2 + e 1 X 2 = I 21 F 1 + I 22 F 2 + e 2. X n = i n1 f 1 + i n2 f 2 + e n Where X 1,... X n represent standardized scores F 1,F 2 are the two standardized factor scores I 11, I n1,....I n2 are factor loadings e 1,...e n are error variances

7. Marketing Research 10th Edition http://www.drvkumar.com/mr10/ Export Data Set - Illustration 7 RespidWill(y1)Govt(y2)Train(x5)Size(x1)Exp(x6)Rev(x2)Years(x3) Prod(x4) 145149110005.56 234146110006.54 354154110006.07 423131030006.05 543150120006.57 654169110005.59......... 11543145120006.06 116 5 4 1 44 1 2000 5.811 11734146010007.03 11834154110007.04 11943149110006.57 12045154140006.57

8. Marketing Research 10th Edition http://www.drvkumar.com/mr10/ Description of Variables 8 Variable DescriptionCorresponding Name in Output Scale Values Willingness to Export (Y 1) Will1(definitely not interested) to 5 (definitely interested) Level of Interest in Seeking Govt Assistance (Y 2 ) Govt1(definitely not interested) to 5 (definitely interested) Employee Size (X 1 )SizeGreater than Zero Firm Revenue (X 2 )RevIn millions of dollars Years of Operation in the Domestic Market (X 3 ) YearsActual number of years Number of Products Currently Produced by the Firm (X 4 ) ProdActual number Training of Employees (X 5 )Train0 (no formal program) or 1 (existence of a formal program) Management Experience in International Operation (X 6) Exp0 (no experience) or 1 (presence of experience)

9. Marketing Research 10th Edition http://www.drvkumar.com/mr10/ Factors Factor ▫A variable or construct that is not directly observable but needs to be inferred from the input variables ▫All included factors (prior to rotation) must explain at least as much variance as an “average variable” Eigenvalue Criteria ▫Represents the amount of variance in the original variables that is associated with a factor ▫Sum of the square of the factor loadings of each variable on a factor represents the eigenvalue ▫Only factors with eigenvalues greater than 1.0 are retained 9

10. Marketing Research 10th Edition http://www.drvkumar.com/mr10/ How Many Factors - Criteria Scree Plot Criteria ▫A plot of the eigenvalues against the number of factors, in order of extraction. ▫The shape of the plot determines the number of factors 10

11. Marketing Research 10th Edition http://www.drvkumar.com/mr10/ How Many Factors: Criteria (Contd.) Percentage of Variance Criteria ▫The number of factors extracted is determined so that the cumulative percentage of variance extracted by the factors reaches a satisfactory level Significance Test Criteria ▫Statistical significance of the separate eigenvalues is determined, and only those factors that are statistically significant are retained 11

12. Marketing Research 10th Edition http://www.drvkumar.com/mr10/ Common Terms Factor Scores ▫Values of each factor underlying the variables Factor Loadings ▫Correlations between the factors and the original variables Communality ▫The amount of the variable variance that is explained by the factor 12

13. Marketing Research 10th Edition http://www.drvkumar.com/mr10/ Factor Rotations 13  Solutions generated by factor analysis for a data set.

14. Marketing Research 10th Edition http://www.drvkumar.com/mr10/ Factor Rotations (Contd.) Varimax (orthogonal) rotation ▫Each factor tends to load high (1 or 1) on a smaller number of variables and low, or very low (close to zero), on other variables, to make interpretation of the resulting factors easier. ▫The variance explained by each unrotated factor is simply rearranged by the rotation, while the total variance explained by the rotated factors still remains the same. ▫The first rotated factor will no longer necessarily account for the maximum variance and the amount of variance each factor accounts for has to be recalculated. Promax (oblique) rotation ▫The factors are rotated for better interpretation, such that the orthogonality is not preserved anymore. 14

15. Marketing Research 10th Edition http://www.drvkumar.com/mr10/ Extraction using Principal Component Method - Unrotated Factor Loadings Factor Score Coefficient 15

16. Marketing Research 10th Edition http://www.drvkumar.com/mr10/ Extraction using Principal Component Method - Factor Rotation 16 Not significantly different from unrotated values

17. Marketing Research 10th Edition http://www.drvkumar.com/mr10/ Common Factor Analysis ▫The factor extraction procedure is similar to that of principal component analysis except for the input correlation matrix ▫Communalities or shared variance is inserted in the diagonal instead of unities in the original variable correlation matrix ▫The total amount of variance that can be explained by all the factors in common factor analysis is the sum of the diagonal elements in the correlation matrix ▫The output of common factor analysis depends on the amount of shared variance 17

18. Marketing Research 10th Edition http://www.drvkumar.com/mr10/ Common Factor Analysis – Results (Contd.) 18

19. Marketing Research 10th Edition http://www.drvkumar.com/mr10/ Common Factor Analysis - Results 19

20. Marketing Research 10th Edition http://www.drvkumar.com/mr10/ Common Factor Analysis – Results (Contd.) 20

21. Marketing Research 10th Edition http://www.drvkumar.com/mr10/ Cluster Analysis Technique for grouping individuals or objects into unknown groups. The typical criterion used in cluster analysis is distance between clusters or the error sum of squares. The input is any valid measure of similarity between objects, such as: ▫Correlations ▫Distance measures (Euclidean distance) ▫Association coefficients ▫The number of clusters or the level of clustering 21

22. Marketing Research 10th Edition http://www.drvkumar.com/mr10/ Steps in Cluster Analysis Define the problem Decide on the appropriate similarity measure Decide on how to group the objects Decide the number of clusters Interpret, describe, and validate the clusters 22

23. Marketing Research 10th Edition http://www.drvkumar.com/mr10/ Cluster Analysis (Contd.) Hierarchical Clustering ▫Can start with all objects in one cluster and divide and subdivide them until all objects are in their own single-object cluster ( ‘top-down’ or decision approach) ▫Can start with each object in its own single-object cluster and systematically combine clusters until all objects are in one cluster (‘bottom-up’ or agglomerative approach) Non-hierarchical Clustering ▫Permits objects to leave one cluster and join another as clusters are being formed ▫A cluster center is initially selected and all the objects within a pre-specified threshold distance are included in that cluster 23

24. Marketing Research 10th Edition http://www.drvkumar.com/mr10/ Hierarchical Clustering Single Linkage ▫Clustering criterion based on the shortest distance Complete Linkage ▫Clustering criterion based on the longest distance 24

25. Marketing Research 10th Edition http://www.drvkumar.com/mr10/ Hierarchical Clustering (Contd.) Average Linkage ▫Clustering criterion based on the average distance Ward's Method ▫Based on the loss of information resulting from grouping of the objects into clusters (minimize within cluster variation) 25

26. Marketing Research 10th Edition http://www.drvkumar.com/mr10/ Hierarchical Clustering (Contd.) Centroid Method ▫Based on the distance between the group centroids (the point whose coordinates are the means of all the observations in the cluster) 26

27. Marketing Research 10th Edition http://www.drvkumar.com/mr10/ Hierarchical Cluster Analysis - Example 27

28. Marketing Research 10th Edition http://www.drvkumar.com/mr10/ Hierarchical Cluster Analysis (Contd.) 28 A dendrogram for hierarchical clustering of bank data

29. Marketing Research 10th Edition http://www.drvkumar.com/mr10/ Hierarchical Cluster Analysis (Contd.) 29

30. Marketing Research 10th Edition http://www.drvkumar.com/mr10/ Non-hierarchical Clustering Sequential Threshold ▫Cluster center is selected and all objects within a pre-specified threshold value are grouped Parallel Threshold ▫Several cluster centers are selected and objects within threshold level are assigned to the nearest center Optimizing ▫Objects can be later reassigned to clusters on the basis of optimizing some overall criterion measure 30

31. Marketing Research 10th Edition http://www.drvkumar.com/mr10/ Export Data – K-means Clustering Results 31 Size/10 Revenue/1000

32. Marketing Research 10th Edition http://www.drvkumar.com/mr10/ Export Data – K-means Clustering Results (contd.) 32

33. Marketing Research 10th Edition http://www.drvkumar.com/mr10/ Nonhierarchical Cluster Analysis - Example 33

34. Marketing Research 10th Edition http://www.drvkumar.com/mr10/ Nonhierarchical Cluster Analysis – Example (Contd.) 34

35. Marketing Research 10th Edition http://www.drvkumar.com/mr10/ Nonhierarchical Cluster Analysis – Example (Contd.) 35

36. Marketing Research 10th Edition http://www.drvkumar.com/mr10/ Nonhierarchical Cluster Analysis – Example (Contd.) 36

37. Marketing Research 10th Edition http://www.drvkumar.com/mr10/ Criteria for Determining the Number of Clusters ▫Number of clusters is specified by the analyst for theoretical or practical reasons. ▫Level of clustering with respect to clustering criterion is specified. ▫Determine the number of clusters from the pattern of clusters generated. The distances between clusters or error variability measure at successive steps can be used to decide the number of clusters (from the plot of error sum of squares with the number of clusters). ▫The ratio of total within-group variance to between group variance is plotted against the number of clusters and the point at which an elbow occurs indicates the number of clusters. 37

38. Marketing Research 10th Edition http://www.drvkumar.com/mr10/ Methods to Validate a Cluster Analysis Solution Apply two or more different clustering approaches to same data or use different distance measures and compare the results. Split the data randomly into two halves and perform clustering on each half and then examine the average profile values of each cluster across sub samples. Delete various columns (variables) from the original data, compute dissimilarity measures across remaining variables and compare these results with the results obtained using full set. Using simulation procedures create a data set with the properties matching the overall properties of the original data but containing no clusters. Use the same clustering method on both original and the artificial data and compare the results. 38

39. Marketing Research 10th Edition http://www.drvkumar.com/mr10/ Assumptions and Limitations of Cluster Analysis Assumptions ▫The basic measure of similarity on which the clustering is based is a valid measure of the similarity between the objects. ▫There is theoretical justification for structuring the objects into clusters Limitations ▫It is difficult to evaluate the quality of the clustering ▫It is difficult to know exactly which clusters are very similar and which objects are difficult to assign. ▫It is difficult to select a clustering criterion and program on any basis other than availability. 39