multivariate analysis: factor analysis

1. Multivariate Analysis: Factor Analysis

2. Marketing Research Factor Analysis Basic function is to identify groups of variables that are related Main purposes in marketing research: to identify underlying constructs in the data Using Common Factor Analysis to reduce the number of variables to a more manageable subset Using Principal Components Analysis

3. Factor Analysis Factor analysis is not about making predictions from variables—it is about finding relationships between whole sets of variables, and finding the strength of those relationships

4. Marketing Research So … Most Common Procedures Common factor analysis Used when we want uncover the underlying dimensions surrounding the original variables (1st purpose) Principal components analysis Used when the objective is to reduce a large set variables into a smaller number of factors (2nd purpose)

5. Marketing Research Factor, Loading, Eigenvalue Factor: A variable (or construct) that is not directly observable but needs to be inferred from the input variables Factor Loading: A “correlation coefficient” showing the importance of each variable in defining the factor Eigenvalue: Represents the variance in the original variables that is explained by a factor (standardized so that the avg. variable has an eigenvalue = 1.0)

6. Marketing Research Factor Loadings for Coffee

7. Marketing Research Factor, Loading: Instant Tomato Sauce200 respondents evaluated Instant Tomato Sauce on 5 attributes. A correlation matrix was calculated, then this matrix was factor analyzed.

8. Marketing Research Factor Rotation Factor analysis can generate several solutions (loadings & factor scores) for any data set each solution is called a “factor rotation” each time the factors are rotated the pattern of loadings changes geometrically, rotation simply means that the axes are rotated Varimax rotation--each factor tends to load high on some variables and low on others makes factor interpretation easier

9. Factor Analysis: Key Terms

10. Marketing Research Lifestyle Factors

11. Marketing Research Lifestyle Factors

12. Marketing Research How Many Factors? It is possible to keep generating factors until there are as many factors as there are original variables Methods, Rules of thumb Percentage of Variance Criterion All included factors must explain at least as much variance as an “average variable” (eigenvalue = 1.0) Scree Plot Criterion A scree plot is a plot of the eigenvalues against the number of factors Look for a large drop in the variance explained between two factors

13. Marketing Research Scree Plot

14. Marketing Research Example #1 : Sheldon’s Constitutional Psychology Took dozens of measures of people’s physique Height, weight Limb, torso length ratios Observed 50 representative traits: anxious vs not anxious cautious vs not cautious orderly vs not orderly

15. Marketing Research Example #1: Sheldon’s Constitutional Psychology Sheldon felt some attributes should go together … which go together? Ambitious, energetic, spontaneous, restless Absentminded, calm, cruel, dull 3 factors for the 50 traits emerged Relaxation, love of comfort & eating, amiability, etc. Assertiveness; love of adventure, exercise, & risks; dominance & power, etc. Restraint, love of privacy, mental intensity, etc. Sheldon finally examined distribution of factors by body type

16. Marketing Research

17. Marketing Research Example #1: Sheldon’s Constitutional Psychology

18. Marketing Research Example #1: Sheldon’s Constitutional Psychology

19. Marketing Research Relaxation, love of comfort & eating, amiability, etc. Example #1: Sheldon’s Constitutional Psychology

20. Marketing Research Factor Analysis to Reduce # Var’s Perhaps we have a battery of questions measuring … life styles attribute importances Factor analysis helps present the data in an understandable form

21. Marketing Research Reducing Number of Variables Example #2 Motorcycle Psychographics ….

22. Marketing Research 69 Variables ? 15 FactorsShown for Hard Core Segment

23. Marketing Research Example #3: Fast Food20 “Importance” Variables ? 6 Factors

24. Marketing Research Attribute Importance Factor Scores byFast Food Frequency Quartiles

25. Example 4: Parenting Styles3 batteries 16 total questions, 1781 respondents

26. Identifying the number of factors

27. Name That Factor….

28. Marketing Research Terms Factor: a concept underlying other related variables Correlation matrix: the intercorrelations between variables Factor loading: the strength of association between a variable and its factor Labeling of factors: selecting the phrase best describing the factor Factor scores: the score or variable value for a respondent on a factor

29. Marketing Research Assumptions The most important assumption is that there are factors that do in reality underlie the variables and that the variables indeed completely and adequately represent these factors.  In practical terms, this assumption means that the list of variables should be complete, in that among them each factor is measured at least once and hopefully several times from several different perspectives. 

30. Marketing Research Limitations The greatest limitation is that factor analysis is a highly, subjective process.  The determination of the number of factors and the interpretation of the factors. A related limitation is that there are really no statistical tests regularly employed in factor analysis.  As a result, it is sometimes difficult to know if the results are merely an accident or do reflect something meaningful. Consequently a standard procedure of factor analysis should be to divide the sample randomly into two or more groups and independently run a factor analysis with each group.  If the same factors emerge in each analysis, then confidence that the results do not represent a statistical accident is increased.