This document provides an overview of exploratory factor analysis (EFA). It explains that EFA is a statistical technique used to uncover the underlying structure of a set of variables and reduce them to a smaller set of factors. The key steps of EFA involve extracting factors from the variables, determining the number of factors to retain, and interpreting the factors, which may require rotating the factors to improve interpretation. Factor loadings and rotations like varimax and oblimin are important statistical outputs that aid in interpretation. The goal of EFA is to identify the latent constructs influencing the variables.

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

6. Exploratory factor analysis –
equations? (just set of regressions)
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I2
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I1
Factor
I
Factor
II
E
E
E
E
Factors=unob
served (latent
variables, that
we try to
identify
observed
(manifest)

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)
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Factor
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Factor
II
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E
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Factor
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Factor
II
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E
E
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