Exploratory Factor Analysis Using SPSS

Jul 1, 2024

Exploratory Factor Analysis Using SPSS

Overview

  • Focus: Exploratory factor analysis (EFA) using SPSS
  • Example Study: Based on a published study titled "Three-Factor Structure for Epistemic Belief Inventory: Cross Validation Study"
  • Data Source: Supporting data from the study; specifically, a sub-sample.

Sub-Sample Data

  • Original Data: 28-item epistemic belief inventory from 1785 Chilean high school students
  • Sub-sample: Simplified to 17 items from the original 28 to match the three-factor model in the study

Epistemic Belief Inventory (EBI) Content

  • Reflects beliefs about:
    • Nature of knowledge (e.g., "Most things worth knowing are easy to understand")
    • Nature of learning
    • Intelligence as fixed vs. malleable

Steps in Factor Analysis

  1. Check Factorability of the Matrix

    • Build a correlation matrix of the measured variables (items).
    • Must have sufficient correlations (ideally ≥ 0.30) and avoid issues with multi-collinearity and singularity.

  2. Determine Number of Factors

    • Use methods like Kaiser Criterion (eigenvalue > 1), screen plot, parallel analysis, and the MAP test.
    • Default in SPSS: Kaiser Criterion (eigenvalue > 1)
    • Parallel analysis and MAP test provide more reliable determinations.

  3. Perform Factor Extraction and Rotation

    • Extract the determined number of factors (e.g., 3 factors).
    • Rotate factors to improve interpretability.
    • Use orthogonal (e.g., Varimax) or oblique (e.g., Promax) rotations.

Factorability Checks

  • Correlation Matrix & Factorability
    • Examine correlation matrix for correlations ≥ 0.30.
    • Ensure determinant of correlation matrix > 0.0001.
    • KMO (Kaiser-Meyer-Olkin) Measure: Values > 0.50 are acceptable (classified from “marvelous” to “unacceptable”).
    • Sample value: 0.778 (middling yet acceptable).
    • Bartlett’s Test of Sphericity: P-value < .001 indicates that the matrix is not an identity matrix and factor analysis is appropriate.

Factor Extraction Techniques

  • Eigenvalue Cutoff: Retain factors with eigenvalue > 1 (though known to overestimate).
  • Screen Plot: Visual method where the “elbow” indicates the number of factors.
  • Parallel Analysis
    • Compare raw data eigenvalues with those from simulated data.
    • Retain factors where raw data eigenvalue > simulated eigenvalue.
  • MAP Test: Based on average squared partial correlations, choose the number of factors with the smallest value.

Practical Example With SPSS

  1. Selecting Items for Inclusion

    • Select specific items (
    • Items: ce1, ce2, ce3, ce4, etc

  2. Descriptive Statistics

    • Obtain means, standard deviations, zero-order correlations, determination, and the KMO/Bartlett's tests

  3. Factor Extraction and Rotation

    • Principal Axis Factoring (PAF) vs. Principal Components Analysis (PCA): PAF is recommended for EFA
    • Varimax (Orthogonal) vs. Promax (Oblique) Rotation
    • Rotated Factor Solution: Easier interpretation of factors

Output Analysis

  1. Communalities Table

    • Initial and extraction communalities indicate variance explained by factors.

  2. Eigenvalues & Variance Explained

    • Initial, extraction, and rotation sums of squared loadings give insight into variance explained.

  3. Factor Loadings

    • Use Pattern Matrix (especially with oblique rotation like Promax) for interpretation.
    • Loadings are similar to standardized regression coefficients in oblique rotations.

  4. Interpreting Factors

    • Items should load significantly on one factor and show near-zero loadings on others.
    • Decide a loading criterion (common thresholds: 0.30, 0.32, 0.40)

  5. Factor Names/Definitions

    • Factor 1: Belief in Fixed Ability and Quick Learning
    • Factor 2: Belief in Omniscient Authority
    • Factor 3: Belief in Simple and Certain Knowledge

  6. Structure and Pattern Matrices

    • Helps in understanding item-factor relationships

Conclusion

  • EFA involves checking the data's suitability, selecting extraction methods, choosing the number of factors, and interpreting the results.
  • Using SPSS: Ensure each step is followed carefully and appropriately based on data and analysis needs.
  • Additional Resources: Syntax files for SPSS provided for parallel analysis and MAP tests.