Factor Analysis

What Is Factor Analysis?

Factor analysis is a technique for identifying underlying, unobservable "factors" (latent variables) that explain the correlations among observed variables. It is most commonly used to develop and validate questionnaires and psychological scales.

• ●Example: A 20-item anxiety questionnaire might measure three underlying dimensions: social anxiety, generalized worry, and panic symptoms.
• ●EFA (Exploratory Factor Analysis): Discovers factor structure from data without pre-specified structure. Used in scale development.
• ●CFA (Confirmatory Factor Analysis): Tests whether a pre-specified factor structure fits the data. Used in scale validation and SEM.

Steps in Exploratory Factor Analysis

1. 1.Sample size: Minimum 5–10 participants per variable, and absolute minimum N = 100–200.
2. 2.Factorability: Check if correlation matrix is suitable. Bartlett's test should be significant; KMO should be ≥ 0.6.
3. 3.Extraction method: Principal Axis Factoring (PAF) for psychometric scales; Maximum Likelihood (ML) if normality holds.
4. 4.Number of factors: Use parallel analysis (most accurate), scree plot (look for the elbow), or factors with eigenvalue > 1 (Kaiser criterion — overly liberal).
5. 5.Rotation: Oblique rotation (Promax, Oblimin) if factors may correlate — common in psychology. Orthogonal (Varimax) if factors are assumed independent.
6. 6.Interpret factor loadings: ≥ 0.40 is typically considered a meaningful loading.

Interpreting Factor Loadings

Factor loadings represent the correlation between each observed variable and the latent factor. High loadings indicate that the variable is a good indicator of that factor.

• ●|loading| ≥ 0.70: Excellent indicator
• ●|loading| ≥ 0.50: Good indicator
• ●|loading| ≥ 0.40: Acceptable indicator (minimum threshold in many guidelines)
• ●Cross-loadings > 0.30 on two factors: The item is ambiguous and may need to be dropped or reworded
• ●Communality (h²): Proportion of item variance explained by all factors. h² < 0.30 suggests the item is poorly measured by the solution.

Internal Consistency: Cronbach's Alpha

After establishing factor structure, assess internal consistency with Cronbach's alpha (α), which measures how well items in a scale correlate with each other.

• ●α ≥ 0.90: Excellent (but may indicate redundancy — items too similar)
• ●α ≥ 0.80: Good
• ●α ≥ 0.70: Acceptable
• ●α < 0.60: Questionable — consider removing items with low item-total correlations