What is Confirmatory Factor Analysis (CFA)?
Confirmatory factor analysis (CFA) is a statistical method that tests whether a set of observed variables fits a predetermined factor structure. It falls under the broader umbrella of factor analysis. Unlike exploratory factor analysis (EFA), which searches for patterns without strong assumptions, researchers use CFA when they want to confirm a specific theoretical model. Their goal is to assess how well the observed data support a model in which variables are associated with specific unobserved, or latent, factors defined by prior research or theory.
In confirmatory factor analysis, researchers specify in advance the number of factors, the variables that load onto each factor, and the relationships among factors based on existing theory or past research. The model is then tested using statistical techniques to evaluate how well the observed data fit the proposed structure. Because of this, CFA imposes tight restrictions on the analysis: variables are only allowed to load onto preassigned factors, cross-loadings are often set to zero, and factor correlations are typically constrained according to the theoretical framework.
CFA is often used in psychology, education, and social science research to validate survey instruments, personality scales, or theoretical models of behavior. It provides a rigorous way to test whether a conceptual model is supported by the data.
Learn in-depth: Factor Analysis Guide.
CFA Example
In a real-world example, researchers in a 2010 study used confirmatory factor analysis to test three competing models (seven-, five-, and three-factor structures) of the Academic Motivation Scale (AMS) using data from over 2,000 business students across three universities. They also examined whether the factor structure remained consistent across male and female students and between undergraduate and MBA students. The CFA results supported the original seven-factor model, with adequate model fit for most groups—though the fit was weaker for the MBA subgroup. Internal consistency was acceptable across all subscales, but the expected correlation pattern between subscales was only partially supported.
Findings like these—where a model shows partial but not complete support—are valuable in scientific research. They point to areas where theories may need refinement or where measurement tools could be improved. CFA allows researchers to rigorously test and revise conceptual frameworks, helping theories evolve based on real-world data.
Citation:
Smith, K., Davy, J., & Rosenberg, D. (2010). An examination of the validity of the Academic Motivation Scale with a United States business student sample. Psychological Reports, 106(2), 323–341.