Confirmatory Factor Analysis
Confirmatory Factor Analysis (CFA) is a statistical technique used in the field of psychometrics to verify the factor structure of a set of observed variables. Unlike exploratory factor analysis, which allows the data itself to reveal the underlying structure, CFA tests a pre-specified factor model to see how well it fits the observed data.
History
The development of Confirmatory Factor Analysis is closely tied to the evolution of Structural Equation Modeling (SEM). Jöreskog was a seminal figure in formalizing the method as a way to validate factor structures suggested by exploratory factor analysis or theoretical constructs.
Key Concepts
Factors: Factors are latent variables that explain the correlations or covariances among observed variables.
- Factor Loadings: Factor loadings are the coefficients that indicate the relationship between each observed variable and the underlying factor.
- Error Terms: Error terms account for the variability in observed variables not explained by the factors.
- Model Specification: In CFA, researchers must a priori specify which observed variables are related to which factors. This is typically based on theoretical considerations or previous research.
- Model Estimation: Various methods can be used for estimating the model parameters, such as maximum likelihood, generalized least squares, or weighted least squares.
Model Evaluation
- Goodness-of-Fit: Several goodness-of-fit indices exist to evaluate how well the model fits the data, including Chi-square, Root Mean Square Error of Approximation (RMSEA), Comparative Fit Index (CFI), and Tucker-Lewis Index (TLI).
- Modification Indices: Modification indices can be inspected to identify paths or constraints that, if changed, would improve the model fit.
Applications
- Psychology: CFA is widely used in psychology to confirm the validity of constructs like intelligence, self-esteem, and many others.
- Business: In business, CFA can be used to validate the structure of customer satisfaction surveys, organizational climate scales, and more.
- Healthcare: In healthcare, it is often employed to validate measurement instruments such as health-related quality of life scales.
- Software Tools: Several statistical software packages can perform CFA, including SPSS Amos, Mplus, and R packages like lavaan.
Limitations
- Requires large sample sizes for stable and reliable estimates.
- It is confirmatory in nature, meaning it doesn't allow for the discovery of unexpected or novel structures in the data.
- Assumes linear relationships between factors and observed variables.