Marketing Research

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Marketing Research

• Aaker, Kumar, Day
• Seventh Edition
• Instructors Presentation Slides

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Chapter Twenty-One

• Factor and Cluster Analysis

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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

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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

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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

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Factor Analysis (Contd.)

• Factor
• 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.

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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

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Factor Analysis (Contd.)

• Factor Scores
• Values of each factor underlying the variables
• Factor Loadings
• Correlations between the factors and the original
  variables

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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

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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

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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

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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

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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

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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

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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

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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)

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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

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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