Performing Exploratory Factor Analysis (EFA) and Confirmatory Factor Analysis (CFA) involves several systematic steps. Here's a detailed guide for each:
How to Perform Exploratory Factor Analysis (EFA)
Prepare the Data:Collect Data: Ensure you have a sufficiently large dataset. Check for Suitability: Use the Kaiser-Meyer-Olkin (KMO) test and Bartlett’s Test of Sphericity to determine if your data is suitable for factor analysis. Select the Number of Factors:Eigenvalues: Use the Kaiser criterion (eigenvalues > 1). Scree Plot: Examine the scree plot to identify the point where the eigenvalues level off. Parallel Analysis: Compare the eigenvalues with those obtained from random data. Extract the Factors:Methods: Common methods include Principal Axis Factoring (PAF) or Maximum Likelihood (ML). Software: Use statistical software like SPSS, R (using the psych package), or SAS. Rotate the Factors:Orthogonal Rotation: Varimax rotation for uncorrelated factors. Oblique Rotation: Promax or Oblimin for correlated factors. Interpretation: Identify and label the factors based on the rotated factor loadings. Interpret the Results:Factor Loadings: Examine loadings to understand which variables correlate strongly with which factors. Communalities: Check communalities to understand the variance explained by the factors. How to Perform Confirmatory Factor Analysis (CFA)
Specify the Model:Theory-Driven: Define the number of factors and the loadings of observed variables on these factors based on theoretical expectations or previous research. Path Diagram: Draw a path diagram to visualize the model. Collect and Prepare Data:Sample Size: Ensure a large enough sample, typically a minimum of 200 observations or 5-10 times the number of parameters. Data Cleaning: Check for missing data and outliers. Estimate the Model:Software: Use software like AMOS, LISREL, Mplus, or R (using the lavaan package). Fit the Model: Use the software to estimate the parameters of the specified model. Assess Model Fit:Fit Indices: Evaluate fit indices such as Chi-Square (χ²), Root Mean Square Error of Approximation (RMSEA), Comparative Fit Index (CFI), and Tucker-Lewis Index (TLI). Modification Indices: Check modification indices to identify potential improvements to the model. Refine the Model:Modification: Make theoretical justifiable adjustments based on modification indices. Re-Estimation: Re-estimate the model after modifications. Interpret the Results:Factor Loadings: Examine standardized factor loadings to understand relationships between observed variables and latent factors. Residuals: Analyze residuals to ensure the model is capturing the data well. Example using R for EFA and CFA
EFA Example (Using psych package)
# Install and load the psych package
install.packages("psych")
library(psych)
# Sample data
data
