Individual Differences - Chapter 23 - Factor Analysis (EFA, extraction, rotation)

What is factor analysis used for?

To identify latent constructs (factors) and reduce data.

What is a factor loading?

Correlation between an item and a factor.

What is an eigenvalue?

Amount of variance in the dataset explained by a factor.

What is communality?

Percent of an item’s variance explained by all factors together.

When is EFA used?

When the factor structure (number/nature of factors) is unknown.

Orthogonal vs oblique rotation?

Orthogonal = factors uncorrelated; Oblique = factors allowed to correlate.

Why is a large sample important in EFA?

Prevents unstable or misleading factor solutions.

PCA vs PAF (principal axis factoring)?

PCA reduces data into components; PAF extracts shared variance (latent constructs).

What is Maximum Likelihood extraction?

Model-based extraction that estimates the factor structure with tests of fit.

Name three rules to decide number of factors.

Kaiser >1 rule; scree plot; parallel analysis (Monte Carlo).

Which retention rule is most accurate and why?

Parallel analysis — keeps factors whose real eigenvalues exceed random-data eigenvalues.

Why might Kaiser’s >1 rule be weak?

Tends to overestimate the number of factors.

What’s a limitation of the scree plot?

Subjective “elbow” judgement.

How has factor analysis been used in personality?

Cattell’s 16PF; Costa & McCrae’s Big Five.

Why is PCA criticised for measurement models?

Doesn’t model latent constructs — it’s data reduction only.

Give an example of parallel analysis in scale design.

Academic vindictiveness scale → Monte Carlo supported 2 factors (attitudes + behaviours).