Confirmatory Factor Analysis (CFA) is a statistical technique used to test and confirm the factor structure of a set of observed variables based on a hypothesized model. Unlike Exploratory Factor Analysis (EFA), which aims to explore and uncover the underlying structure of a dataset, CFA is used to evaluate whether a pre-specified factor model fits the data well.

Here’s how confirmatory factor analysis works:

1. Hypothesized Model Specification:
   • Before conducting CFA, researchers specify a theoretical model that represents the relationships among observed variables and underlying latent factors. This model includes the number of factors, the variables associated with each factor, and the direction and strength of the relationships (factor loadings) between the factors and the observed variables.
2. Model Testing:
   • Using CFA, researchers test the fit of the hypothesized model to the observed data. The goal is to evaluate whether the observed data are consistent with the expected relationships specified in the model.
3. Fit Indices and Assessment:
   • Researchers use various fit indices to assess the goodness of fit of the model to the data. Common fit indices include the Comparative Fit Index (CFI), Tucker-Lewis Index (TLI), Root Mean Square Error of Approximation (RMSEA), and Standardized Root Mean Square Residual (SRMR). These indices provide information about how well the hypothesized model reproduces the observed covariance matrix.
4. Model Modification:
   • If the initial model does not fit the data well based on fit indices, researchers may modify the model by adding or removing paths, allowing for correlated errors, or altering the factor structure. This iterative process continues until an acceptable fit to the data is achieved.
5. Interpretation:
   • Once a satisfactory model is identified, researchers interpret the results in terms of the relationships between the latent factors and the observed variables. Factor loadings indicate the strength and direction of the relationship between each observed variable and its corresponding latent factor.

Confirmatory factor analysis is commonly used in social sciences, psychology, education, and health sciences to test theoretical models and validate the underlying factor structure of constructs measured by multiple observed variables. It provides a rigorous method for evaluating the fit of hypothesized models to empirical data and for assessing the validity of measurement instruments.

You can find videos demonstrating how to do these techniques using SPSS here: https://www.youtube.com/playlist?list=PLtx0cY9iho28Iw0o97hVjao2NB-LLd9wT