Transcript Factor Analysis (Contd.)

Marketing Research
Aaker, Kumar, Day
Eighth Edition
Instructor’s Presentation Slides
Marketing Research 8th Edition
Aaker,Kumar,Day
Chapter Twenty One
Factor and Cluster Analysis
Marketing Research 8th Edition
Aaker,Kumar,Day
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 8th Edition
Aaker,Kumar,Day
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 8th Edition
Aaker,Kumar,Day
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 8th Edition
Aaker,Kumar,Day
Factor

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 8th Edition
Aaker,Kumar,Day
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 8th Edition
Aaker,Kumar,Day
Factor Analysis (Contd.)
Factor Scores

Values of each factor underlying the variables
Factor Loadings

Correlations between the factors and the
original variables
Marketing Research 8th Edition
Aaker,Kumar,Day
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 8th Edition
Aaker,Kumar,Day
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 8th Edition
Aaker,Kumar,Day
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 8th Edition
Aaker,Kumar,Day
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 8th Edition
Aaker,Kumar,Day
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 8th Edition
Aaker,Kumar,Day
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 8th Edition
Aaker,Kumar,Day
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 8th Edition
Aaker,Kumar,Day
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 8th Edition
Aaker,Kumar,Day
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 8th Edition
Aaker,Kumar,Day
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 8th Edition
Aaker,Kumar,Day