Week 10 Lecture Recording

Chapter 1: Introduction to Exploratory Factor Analysis (EFA)

Purpose of EFA
- Develop psychometric measures or questionnaires.
- Validate psychometric measures (function of Confirmatory Factor Analysis, CFA).
- Simplify data: factor extraction, rotation, and interpretation.
- Identify underlying patterns in psychological research.
Example of EFA Application
- Group of psychologists studying "criminal social identity" (CSI) through a series of questions.
- Process of factor analysis helps find meaningful patterns within the data by clustering related questions.
- Aim is to yield a more parsimonious set of questions that tap into specific aspects like centrality and affect.
EFA vs Principal Component Analysis (PCA)
- PCA: Data reduction technique that summarizes variance in the dataset; identifies principal components based on data variations.
- EFA: Identifies latent (unobserved) factors that explain the correlations between observed variables (e.g. CSI aspects).

Stages of EFA
- Extraction: Identify underlying factors.
- Rotation: Refine factor loadings; can be orthogonal or oblique.
- Final Interpretation: Assign meaning to the factors based on theoretical knowledge.
Example - 3 Personality Factors (Isaac’s Model)
- Extraversion/introversion: Measures sociability-related items.
- Neuroticism: Measures anxiety and emotional stability.
- Psychoticism: Measures unconventional traits.
Comparative Goals of EFA and PCA
- EFA aims to explain common variance with fewer factors.
- PCA aims to explain total variance using linear components.

Initial Considerations
- Sample size and correlation quality check. Focus on avoiding multicollinearity and singularity.
Commonality: The idea of shared and unique variance among variables.
Example Measurements
- Use of KMO test for sampling adequacy, Barlett's test of sphericity for significance, and determining commonality post-extraction.
Eigenvalues: Use in evaluating factors to retain; the rule is retaining factors with eigenvalues greater than 1.

Extraction Process: Determining how many factors best explain the covariation among variables.
Eigenvalues Explained
- Represent the strength of relationships between factors and items.
- Cumulative variance indicates the explained variance by the extracted factors.
Challenges in Determining Factor Count
- Utilizing scree plots as a visual determinant, looking for elbows in the plot.

Types of Rotations
- Orthogonal Rotation (e.g., Varimax): Assumes factors are uncorrelated.
- Oblique Rotation: Assumes factors may be correlated.
Visual Representations of Rotation Effects
- Facilitates clearer distinctions between loaded variables on factors.
Importance of Factor Loadings
- Helps determine the relationship of variables to the factors.

Summary of Steps in EFA
- Focus on extraction to find the right number of factors and aim for parsimony.
- Rotate to maximize loading clarity using oblique or orthogonal methods.
- Interpret and give meaningful names to factors based on psychological insights.
Practical Application
- Implement EFA in computer labs; learn the computation and interpretation of factor analyses.