# Lecture 3: Exploratory Factor Analysis

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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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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