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Chapter XIX. Factor Analysis. Chapter Outline 1) Overview 2) Basic Concept 3) Factor Analysis Model 4) Statistics Associated with Factor Analysis. 5) Conducting Factor Analysis i. Problem Formulation ii. Construction of the Correlation Matrix
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Chapter XIX Factor Analysis
Chapter Outline 1) Overview 2) Basic Concept 3) Factor Analysis Model 4) Statistics Associated with Factor Analysis
5) Conducting Factor Analysis i. Problem Formulation ii. Construction of the Correlation Matrix iii. Method of Factor Analysis iv. Number of of Factors v. Rotation of Factors vi. Interpretation of Factors vii. Factor Scores viii.Selection of Surrogate Variables ix. Model Fit
6) Applications of Common Factor Analysis 7) Internet and Computer Applications 8) Focus on Burke 9) Summary 10) Key Terms and Concepts 11) Acronyms
Problem formulation Construction of the Correlation Matrix Method of Factor Analysis Determination of Number of Factors Rotation of Factors Interpretation of Factors Conducting Factor Analysis Fig 19.1 Selection of Surrogate variables Calculation of Factor Scores Determination of Model Fit
Correlation Matrix Table 19.2
Results of Principal Components Analysis Table 19.3 • Barlett test of sphericity • Approx. Chi-Square = 111.314 • df = 15 • Significance = .00000 • Kaiser-Meyer-Olkin measure of sampling adequacy = .660
Table 19.2 Contd. The lower left triangle contains the reproduced correlation matrix; the diagonal, the communities; the upper right triangle, the residuals between the observed correlations and the reproduced correlations.
Screen Plot Fig. 19.2 3.0 2.5 2.0 Eigenvalue 1.5 1.0 0.5 0.0 2 3 4 5 6 1 Component Number
Factor Loading Plot Fig. 19.3 Rotated Component Matrix Component Variable 1 2 V1 0.962 -2.66E-02 V2 -5.72E-02 .848 V3 0.934 -.146 V4 -9.83E-02 .854 V5 -.933 -8.40E-02 V6 8.337E-02 0.885 Component Plot in Rotated Space Component 1 1.0 0.5 0.0 -.5 -1.0 V4 V6 V2 V1 Component 2 V5 V3 1.0 0.5 0.0 -.5 -1.0
Results of Common Factor Analysis Table 19.4 • Barlett test of sphericity • Approx. Chi-Square = 111.314 • df = 15 • Significance = .00000 • Kaiser-Meyer-Olkin measure of sampling adequacy = .660
Table 19.4 Contd. The lower left triangle contains the reproduced correlation matrix; the diagonal, the communities; the upper right triangle, the residuals between the observed correlations and the reproduced correlations.
Driving Nuts For Beetles RIP 19.1 Generally, with time, consumer needs and tastes change. Consumer preferences for automobiles need to be continually tracked to identify changing demands and specifications. However, there is one car that is quite an exception - the Volkswagen Beetle. More than 21 million have been built since it was introduced in 1938. Surveys have been conducted in different countries to determine the reasons why people purchase Beetles. Principal components analyses of the variables measuring the reasons for owning Beetles have consistently revealed one dominant factor - fanatical loyalty. The company has long wished its natural death but without any effect. This noisy and cramped "bug" has inspired devotion in drivers.
RIP 19.1 Contd. Now old bugs are being sought everywhere. "The Japanese are going absolutely nuts for Beetles," says Jack Finn, a recycler of old Beetles in West Palm Beach, Florida. Beetles are still made in Mexico, but they cannot be exported to US or Europe because of safety and emission standards. Because of faithful loyalty for the "bug", VW has repositioned the beetle as a new shiny VW Passat, a premium quality car which gives an image of sophistication and class as opposed to the old one which symbolized low-priced brand.
Factors Predicting Unethical Marketing Research Practices RIP 19.2 A survey of 420 marketing professionals was conducted to identify organizational variables that determine the incidence of unethical marketing research practices. These marketing professionals were asked to provide evaluations of the incidence of fifteen marketing research practices that have been found to pose ethical problems. They also provided responses on several other scales, including an 11 item scale pertaining to the extent to which ethical problems plagued the organization, and what top management's actions were toward ethical situations. The commonly used method of principal components analysis with varimax rotation indicated that these 11 items could be represented by two factors. Contd.
RIP 19.1 Contd. Factor Analysis of Ethical Problems and Top Management Action Scale Extent of Ethical Problems within Top Management the organization actions on ethics (factor 1) (factor 2) 1. Successful executives in my company make rivals look bad in the eyes of important people in my company. 0.66 2. Peer executives in my company often engage in behaviors that I consider unethical. 0.68 3. There are opportunities for peer executives in my company to engage in unethical behavior. 0.43 4. Successful executives in my company take credit for the ideas & accomplishment of others. 0.81 5. In order to succeed in my company, it is often necessary to compromise one's ethics. 0.66 6. Successful executives in my company are generally more unethical than unsuccessful executives. 0.64 7. Successful executives in my company look for a "scapegoat" when they feel they may by associated with failure. 0.78
Factor Analysis of Ethical Problems and Top Management Action Scale Extent of Ethical Problems within Top Management the organization actions on ethics (factor 1) (factor 2) 8. Successful executives in my company withhold information that is detrimental to their self-interest. 0.68 9. Top management in my company has let it be known in no uncertain terms that unethical behaviors will not be tolerated. 0.73 10. If an executive in my company engages in unethical behavior resulting in personal gain (rather than corporate gain), he/she will be promptly reprimanded. 0.80 11. If an executive in my company engages in unethical behavior resulting in corporate gain, he/she will be promptly reprimanded. 0.78 Eigenvalue 5.06 1.17 % of Variance Explained 46% 11% Coefficient Alpha 0.87 0.75 To simplify the table, only varimax-rotated loading of .40 or greater are reported. Each was rated on a five-point scale with 1 = "strongly agree" and 5 = "strongly disagree” RIP 19.1 Contd.
RIP 19.1 Contd. Factor Analysis of Ethical Problems and Top Management Action Scale The first factor could be interpreted as the incidence of unethical practices, while the second factor denotes top management actions related to unethical practices. The two factors together account for more than half the variation in the data with the first factor being dominant. These two factors were then used along with four other variables as predictors in a multiple regression. The results indicated that they were the two best predictors of unethical marketing research practices.
