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# Research Methology -Factor Analyses

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• 1. FACTOR ANALYSES With In Research Methology By NEERAV SHIVHARE
• 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. 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. 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. 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. 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. Factor Analysis (Contd.) Factor Scores  Values of each factor underlying the variables Factor Loadings  Correlations between the factors and the original variables
• 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. THANK YOU SPECIAL THANKS TO Prof.Pooja Jain FOR CORAL SUPPORT. THANK YOU