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

2. Factor and Cluster Analysis
Chapter Twenty-One
Factor and Cluster Analysis

3. Factor Analysis
Technique that serves to combine questions or variables to create new factors
Purpose
To identify underlying constructs in the data
To reduce the number of variables to a more manageable set
Marketing Research 7th Edition
Aaker, Kumar, Day

4. Factor Analysis (Contd.)
Methodology
Two commonly employed factor analytic procedures
Principal Component Analysis
Used when the need is to summarize information in a larger set of variables to a smaller set of factors
Common Factor Analysis
Used to uncover underlying dimensions surrounding the original variables
Marketing Research 7th Edition
Aaker, Kumar, Day

5. Factor Analysis (Contd.)
Principal Component Analysis
The objective of factor analysis is to represent each of these variables as a linear combination of a smaller set of factors
This can be represented as
X1 = I11F1 + I12F2 + e1
X2 = I21F1 + I22F2 + e2 .
Xn = in1f1 + in2f2 + en
Where
X1, ... xn represent standardized scores
F1,F2 are the two standardized factor scores
I11, i12,....I52 are factor loadings
E1,...E5 are error variances
Marketing Research 7th Edition
Aaker, Kumar, Day

6. Factor Analysis (Contd.)
A variable or construct that is not directly observable but needs to be inferred from the input variables
Eigenvalue Criteria
Represents the amount of variance in the original variables that is associated with a factor
Scree Plot Criteria
A plot of the eigenvalues against the number of factors, in order of extraction.
Marketing Research 7th Edition
Aaker, Kumar, Day

7. Factor Analysis (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
Marketing Research 7th Edition
Aaker, Kumar, Day

8. Factor Analysis (Contd.)
Factor Scores
Values of each factor underlying the variables
Factor Loadings
Correlations between the factors and the original variables
Marketing Research 7th Edition
Aaker, Kumar, Day

9. Factor Analysis (Contd.)
Communality
The amount of the variable variance that is explained by the factor
Factor Rotation
Factor analysis can generate several solutions for any data set. Each solution is termed a particular factor rotation and is generated by a particular factor rotation scheme
Marketing Research 7th Edition
Aaker, Kumar, Day

10. Factor Analysis (Contd.)
How Many Factors?
Rule of Thumb
All included factors (prior to rotation) must explain at least as much variance as an "average variable"
Eigenvalues Criteria
Eigenvalue represents the amount of variance in the original variables associated with a factor
Sum of the square of the factor loadings of each variable on a factor represents the eigen value
Only factors with eigenvalues greater than 1.0 are retained
Marketing Research 7th Edition
Aaker, Kumar, Day

11. Factor Analysis (Contd.)
Scree Plot Criteria
Plot of the eigenvalues against the number of factors in order of extraction
The shape of the plot determines the number of factors
Percentage of Variance Criteria
Number of factors extracted is determined when the cumulative percentage of variance extracted by the factors reaches a satisfactory level
Marketing Research 7th Edition
Aaker, Kumar, Day

12. Factor Analysis (Contd.)
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
Marketing Research 7th Edition
Aaker, Kumar, Day

13. Cluster Analysis
Technique that serves to combine objects to create new groups
Used to group variables, objects or people
The input is any valid measure of correlations between objects, such as
Correlations
Distance measures (Euclidean distance)
Association coefficients
Also, the number of clusters or the level of clustering can be input
Marketing Research 7th Edition
Aaker, Kumar, Day

14. 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
Non-hierarchical Approach
Permits objects to leave one cluster and join another as clusters are being formed
Marketing Research 7th Edition
Aaker, Kumar, Day

15. Hierarchical Clustering
Single Linkage
Clustering criterion based on the shortest distance
Complete Linkage
Clustering criterion based on the longest distance
Average Linkage
Clustering criterion based on the average distance
Marketing Research 7th Edition
Aaker, Kumar, Day

16. Hierarchical Clustering (Contd.)
Ward's Method
Based on the loss of information resulting from grouping of the objects into clusters (minimize within cluster variation)
Centroid Method
Based on the distance between the group centroids (the centroid is the point whose coordinates are the means of all the observations in the cluster)
Marketing Research 7th Edition
Aaker, Kumar, Day

17. Non-hierarchical Clustering
Sequential Threshold
Cluster center is selected and all objects within a prespecified threshold is grouped
Parallel Threshold
Several cluster centers are selected and objects within threshold level are assigned to the nearest center
Optimizing
Modifies the other two methods in that the objects can be later reassigned to clusters on the basis of optimizing some overall criterion measure
Marketing Research 7th Edition
Aaker, Kumar, Day

18. Number of Clusters
Determination of the Appropriate Number of Clusters Can Be Done in One of the Four Ways
The number of clusters can be specified by the analyst in advance
The levels of clustering can be specified by the analyst in advance
The number of clusters can be determined from the pattern of clusters generated in the program
The ratio of within-group variance and the between-group variance an be plotted against the number of clusters. The point at which a sharp bend occurs indicates the number of clusters
Marketing Research 7th Edition
Aaker, Kumar, Day