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Factor Analysis Optional Session

Factor Analysis. 2. What is Factor Analysis. Data Reduction TechniqueA factor is a weighted sum of the variablesThe goal is to summarize the information in a larger number of correlated variables into a smaller number of factors that are not correlated with each other.In contrast to Regression,

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Factor Analysis Optional Session

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    1. Factor Analysis 1 Factor Analysis (Optional Session)

    2. Factor Analysis 2 What is Factor Analysis Data Reduction Technique A factor is a weighted sum of the variables The goal is to summarize the information in a larger number of correlated variables into a smaller number of factors that are not correlated with each other. In contrast to Regression, there is no dependent variable. We just look at the correlations between variables to summarize.

    3. Factor Analysis 3 Graphical Intuition: Factor Analysis works when data are correlated

    4. Factor Analysis 4 Graphical Intuition: Factor Analysis will not work when variables are uncorrelated

    5. Factor Analysis 5 When to do Factor Analysis in business research? Applications Eliminating Multicollinearity problems in Regression Measuring managerially useful constructs Intelligence, Leadership Skills, Customer satisfaction Useful in constructing perceptual maps of products that are useful in positioning studies

    6. Factor Analysis 6 Perceptual Map… Example

    7. Factor Analysis 7 Applying Factor Analysis: Evaluating MBA Applications Suppose school believes success of future managers depends on Intelligence Teamwork and Leadership skills

    8. Factor Analysis 8 Applying Factor Analysis: Evaluating MBA Applications Variables available GPA GMAT score Scholarships, fellowships won Evidence of Communications skills Prior Job Experience Organizational Experience Other extra curricular achievements

    9. Factor Analysis 9 Data…

    10. Factor Analysis 10 Quick and dirty sense of the data: Looking at the correlation matrix

    11. Factor Analysis 11 First Step: Do Principal Component Analysis (PCA) to select # of factors PCA uses the correlation matrix of the data and constructs factors Factors If there are n variables we will have n factors First factor will explain most variance, second next, and so on… Variance Explained by Factors With standardized variables each variable has a variance of 1, so the total variance in n variables is n Each factor will have an associated eigen-value which is the amount of variance explained by that factor

    12. Factor Analysis 12 SPSS Output of PCA: Eigen Analysis

    13. Factor Analysis 13 SPSS Output of PCA: Scree Plot

    14. Factor Analysis 14 Second Step: Do Factor Analysis with number of factors selected from Step 1 First interpret resulting factors Use factor loadings to interpret factors If it is not interpretable use rotation options until we get something that can be interpreted Look at factor equations and factor scores Score plots will be useful

    15. Factor Analysis 15 Why not Unrotated Factor Loadings? Variable’s correlation with the factors

    16. Factor Analysis 16 Interpreting Factors: Looking at Loading Plot without Rotations

    17. Factor Analysis 17 Rotated Factor Loadings: Variable’s correlation with the factors

    18. Factor Analysis 18 Interpreting Factors: Looking at Loading Plot with Rotation

    19. Factor Analysis 19 Naming Factors Apriori, theory based selection of variables Should be easy to name factors Otherwise use managerial intuition

    20. Factor Analysis 20 How did applicants score on Intelligence and Leadership Factors

    21. Factor Analysis 21 Which Applicants to select for Haas: The Score Plot

    22. Factor Analysis 22 Step 1: Choosing number of factors to extract from data Do Factor Analysis In SPSS select Analyze>Data Reduction>Factor… Select “Extraction”, select “Principle Component Analysis” Select the variables you want to factor analyze in Variables box Select “Correlation” as the data that will be analyzed; this will mean that the data will be standardized and therefore each variable will have equal effect. Ask for Scree Plot (using Graphs button) which graphs the amount of variance explained by each factor

    23. Factor Analysis 23 Step 2: Performing Factor Analysis with # of factors from Step 1 Do Factor Analysis Number of Factors to extract should be from Step 1 Try “None” rotation for a start (else try Varimax or others if it doesn’t work) In Graphs: select loading plot and score plot In Storage: in the scores box store the factor scores by selecting 2 variables

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