1. Lecture 3: Exploratory Factor Analysis
Aims & Objectives
To describe the basic factor model
Understand pre-analysis checks, extraction & rotation
To describe the basic process of conducting a EFA, and
To show when and where EFA is most appropriately use

2. Basic principle of EFA
EFA tries to explain a set of correlations among variables in terms of a set of smaller common factors and zero cross loadings

3. Factor analysis of cognitive abilities
Verbal Reasoning
Sentence completion
Comprehension
Cloze test
Mathematical & Spatial
Spatial rotation
Computation
Find the figure

4. Process Pre-analysis Extraction Rotation Collect data of the 6 test
Sample size, N of items, Social desirability
Create correlation matrix
Extraction
How many factors?
Rotation
How to best view the solution

5. Pre-analysis checks: I
Scaling
Likert-type
Dichotomous use Phi
% correct
Item selection
Theory, a-priori structure (marker variables)
Sampling
To the population where the results are to be generalised

6. Pre-analysis checks: II
Ratios & Stable structure
N (min = 100)
N:P (2:1, 10:1)
P:M (4:1)
N:M (6:1)
Social desirability
Remove items correlating with social desirability

7. Sentence
Compre
Cloze
Rotation
Comput
Figure 1
Compre.
.55
.65
.70
.17
.10
.25
.28
.18
.60
.22
.35
.33
.77
.58

8. Pre-analysis checks:III
Bartlett test of Sphericity
Matrix to be analysed
Identity matrix
V1 1
V2 0 1 V V
V1 1
V V V
KMO greater than .5

9. Communalities The shared variance of a variable with a factor
Initially need to estimate these.
Largest column r in the diagonal
SMC

10. Number of factors to extract
Eigenvalues 2
Actual data (eigenvalues) 1
Random eigenvalues
Factors 1 n

11. Rotation & simple structure
FI FII FI FII
Sentence
Compreh
Cloze
Figure
Rotation
Coputat

12. Rotation - orthogonal
FI(a)
Verbal
Math/spatial
FII
(a)

13. Rotate
FI(a)
Verbal
FI (b)
Math/spatial
FII
(a)
FII (b)

14. Rotation - oblique
FI(a)
FII
(a)
Delta

15. The basic factor model Common factors Loading Verbal Math/Spatial
Unique factors
Variables

16. Naming and next steps Factor naming Reliability & validity
Re-captured Item Technique (RIT)
Markers
Raters
Reliability & validity

17. Use & abuses of EFA Uses Problems IQ Personality & psychometrics
Education
Psychophysiology
Factorial validity
Data reduction?
Problems
Garbage In Garbage Out (GIGO)