1. EXPLORATORY FACTOR ANALYSIS (EFA)
P. Soukup

2. What is EFA?
a statistical method used to uncover the underlying structure of a relatively large set of variables
Example: intelligence
Mainly for phenomenons that can not be measured directly (other examples?)

3. Some pictures instead of equations

4. Exploratory factor analysis:

5. Exploratory factor analysis:
observed (manifest)
Factors=unobserved (latent variables, that we try to identify

6. Exploratory factor analysis – equations? (just set of regressions)
observed (manifest)
Factors=unobserved (latent variables, that we try to identify

7. Steps? 1. big set of manifest variables
2. we try to extract small number of latent variables (factors)
Many questions:
1. How to extract factors?
2. How many factors?
3. How to interpret factors?.....

8. Exploratory and confirmatory (EFA) factor analysis (CFA)
CAN YOU SEE SOME DIFFERENCE?

9. Assumptions about data
set of related continous (cardinal) variables (how we can measure relationship?)
Expectation about some hidden dimension (factor) behind data

10. Statistical „test“ for assumptions
Bartlett’s test (stat. sig. result=EFA can be useful)
KMO (value>0.5) – this is not formal test just criteria
Example in SPSS

11. Steps? 1. Extraction of factors (first solution)
2. Decision about nr. of factors
3. Interpretation: if complicated try rotate factors

12. Extraction techniques

13. Possible approaches Principal components (PC):
the first factor accounts for as much common variance as possible, then the second factor next most variance, and so on
mostly used
does not offer confidence intervals and significance tests
Maximum likelihood (ML):
the best choice when data are normally distributed
permits statistical significance testing
rarely used
Example in SPSS

14. Basic results in SPSS Percentage of expl. variance
Factor loadings – i.e. correlation of factor and manifest variables (main tool for interpretation)

15. How to select nr. of factors
Many approaches:
Minimum level of explained variance
Kaiser's eigenvalue-greater-than-one rule
Cattell's scree plot
Example in SPSS
Problem: Different reccomendations

16. Interpretation of factors
Factor loadings are the key
Correlation between factor and manifest variable
Interpretation: try to find what the items have in common= meaning of the factor
Example in SPSS
Problem: Impossible to find interpretation
Solution: Rotation of factors

17. Rotation of factors Orthogonal rotation: factors are uncorrelated
Mostly used technique is varimax
Problem: for many constructs we expect they are related
Oblique rotation:
Factors are related
Mostly used technique is direct oblimin
More complicated (more outputs including correlation matrix for factors)
Example in SPSS

18. Saving of factors (factor scores)
Factor score = value of factor for every unit in my data set
Continous variable
Can be used for next analysis
Replace original (manifest variables)
Example in SPSS