Multivariate Data Analysis

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Chapter 15

• Multivariate Data Analysis

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• Interdependence Techniques
• Factor Analysis
• Technique in which researchers look for a small
  number of factors that could explain the
  correlation between a large number of variables
• Cluster Analysis
• Variables are placed in subgroups or clusters
• Multidimensional Scaling
• It encompasses a set of computational procedures
  that can summarize an input matrix of
  associations between variables or objects in two
  dimensional space

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• Dependence Techniques
• Discriminant Analysis
• To find a linear combination of independent
  variables that makes the mean scores across
  categories of the dependent variable on this
  linear combination m different
• Conjoint Analysis
• Deals with the joint effects of two or more
  independent variables on the ordering of a
  dependent variable

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• Factor Analysis
• Look for small set of factors to explain
  correlation
• between a large set of variables
• Used for data reduction and transformation
• Used in personality scales, identification of
  key
• product attributes, etc.

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Factor Analysis (contd) Factor A variable or
a construct that is not directly observable but
needs to be inferred from input
variables Eigenvalue Amount of variance in
the original variables that are associated with
the factor
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Factor Analysis (contd) Scree Plot Plot of
eigenvalues against number of factors. For
factors with large eigenvalues this plot has a
steep slope . Percentage of Variance Criteria
The number of factors extracted is determined
so that the cumulative percentage of variance
extracted by the variance reaches a
satisfactory level. Factor Score Value of
each factor for all respondents
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• Disadvantages of Factor Analysis
• Subjective
• Does not make use of any standard
• statistical tests

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• Cluster Analysis
• Group objects into clusters based on the
• attributes they possess.
• Objects that are similar placed in one group
• Groups have minimum within-group variability
  and
• maximum between-group variability.

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• Multi-dimensional Scaling
• Creates a matrix associations between
  variables
• Used by marketers to study relationships
  among objects, consumer perceptions, brand
  preferences, and preferred product attributes.

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• Discriminant Analysis
• Objective is to find a linear combination of
• independent variables that make the mean scores
• across categories of dependent variables on
  this linear combination maximally different.
• Used to classify objects into two or more
• alternative groups on the basis of a set of
• measurements

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• Conjoint Analysis
• Measure joint effects of two or more
  independent variables on the ordering of a
  dependent variable
• Quantitative measure of relative importance of
  one attribute over another