FACTOR ANALYSES
With In
Research Methology
By
NEERAV SHIVHARE
Factor Analysis
 Technique that serves to combine questions or
variables to create new factors
Purpose
 To identify unde...
Factor Analysis (Contd.)
Methodology
Two commonly employed factor analytic procedures
Principal Component Analysis
 Used ...
Factor Analysis (Contd.)
Principal Component Analysis
 The objective of factor analysis is to represent each of these var...
Factor Analysis (Contd.)
Factor
 A variable or construct that is not directly observable
but needs to be inferred from th...
Factor Analysis (Contd.)
Percentage of Variance Criteria
 The number of factors extracted is determined so that
the cumul...
Factor Analysis (Contd.)
Factor Scores
 Values of each factor underlying the variables
Factor Loadings
 Correlations bet...
Factor Analysis (Contd.)
Communality
 The amount of the variable variance that is explained
by the factor
Factor Rotation...
Factor Analysis (Contd.)
How Many Factors?
 Rule of Thumb
 All included factors (prior to rotation) must explain at leas...
Factor Analysis (Contd.)
Scree Plot Criteria
 Plot of the eigenvalues against the number of factors in
order of extractio...
Factor Analysis (Contd.)
Common Factor Analysis
 The factor extraction procedure is similar to that of
principal componen...
Marketing Research 8th Edition
Aaker,Kumar,Day
Cluster Analysis
 Technique that serves to combine objects to create new
g...
Marketing Research 8th Edition
Aaker,Kumar,Day
Cluster Analysis (Contd.)
Hierarchical Clustering
 Can start with all obje...
Marketing Research 8th Edition
Aaker,Kumar,Day
Hierarchical Clustering
Single Linkage
 Clustering criterion based on the ...
Marketing Research 8th Edition
Aaker,Kumar,Day
Hierarchical Clustering (Contd.)
Ward's Method
 Based on the loss of infor...
Marketing Research 8th Edition
Aaker,Kumar,Day
Non-hierarchical Clustering
Sequential Threshold
 Cluster center is select...
Number of Clusters
Determination of the appropriate number of clusters can be done
in one of the four ways
 The number of...
THANK YOU
SPECIAL THANKS TO
Prof.Pooja Jain
FOR CORAL SUPPORT.
THANK YOU
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Research Methology -Factor Analyses

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Research Methology -Factor Analyses

  1. 1. FACTOR ANALYSES With In Research Methology By NEERAV SHIVHARE
  2. 2. 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
  3. 3. 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
  4. 4. 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
  5. 5. 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.
  6. 6. 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
  7. 7. Factor Analysis (Contd.) Factor Scores  Values of each factor underlying the variables Factor Loadings  Correlations between the factors and the original variables
  8. 8. 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
  9. 9. 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
  10. 10. 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
  11. 11. 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
  12. 12. 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
  13. 13. 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
  14. 14. 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
  15. 15. 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)
  16. 16. 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
  17. 17. 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
  18. 18. THANK YOU SPECIAL THANKS TO Prof.Pooja Jain FOR CORAL SUPPORT. THANK YOU

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