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

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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

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Factor analysis of cognitive abilities

• Verbal Reasoning
• Sentence completion
• Comprehension
• Cloze test

• Mathematical Spatial
• Spatial rotation
• Computation
• Find the figure

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Process

• Pre-analysis
• 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

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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

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Pre-analysis checks II

• Ratios Stable structure
• N (min 100)
• NP (21, 101)
• PM (41)
• NM (61)
• Social desirability
• Remove items correlating with social desirability

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Pre-analysis checksIII
Bartlett test of Sphericity
Matrix to be analysed
Identity matrix
V1 1 V2 0 1 V3 0 0 1 V4 0 0 0 1
V1 1 V2 .23 1V3 .31 .25 1 V4 .54 .32 .41 1
KMO greater than .5
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Communalities

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

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Number of factors to extract
Eigenvalues
2
Actual data (eigenvalues)
1
Random eigenvalues
Factors
1
n
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Rotation simple structure
FI FII FI FII Sentence .65 .34 .78 .14 Compreh
. .59 .28 .67 .09 Cloze .44 .71 .65 .10 Figure
.31 .62 .15 .70 Rotation .45 .65 .10 .78 Coputa
t. .53 .77 .17 .73
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Rotation - orthogonal
FI(a)
Verbal
Math/spatial
FII
(a)
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Rotate
FI(a)
Verbal
FI (b)
Math/spatial
FII
(a)
FII (b)
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Rotation - oblique
FI(a)
FII
(a)
Delta
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The basic factor model
Common factors
Loading
Verbal
Math/Spatial
Unique factors
Variables
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Naming and next steps

• Factor naming
• Re-captured Item Technique (RIT)
• Markers
• Raters
• Reliability validity

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Use abuses of EFA

• Uses
• IQ
• Personality psychometrics
• Education
• Psychophysiology
• Factorial validity
• Data reduction?
• Problems
• Garbage In Garbage Out (GIGO)