Confirmatory Factor Analysis (CFA)

Confirmatory factor analysis (CFA) is a structural equation modeling technique that tests whether observed items measure a pre-specified set of latent factors as hypothesized.

확인적 요인분석(CFA)은 관측 문항들이 사전에 가정한 잠재요인 구조를 가설대로 측정하는지를 검정하는 구조방정식모형 기법이다.

How do I test whether my survey items fit a hypothesized factor structure?

설문 문항들이 가정한 요인 구조에 맞는지 어떻게 검정하나요?

Confirmatory factor analysis specifies in advance which items load on which latent factors and tests how well that model reproduces the observed covariances. It fits validating an established scale or a structure suggested by prior theory or exploratory analysis, and it supports convergent and discriminant validity checks.

When to use Confirmatory Factor Analysis (CFA)

• Validating the factor structure of an existing questionnaire
• Testing a measurement model before a structural equation model
• Checking measurement invariance across groups

When to use something else

• The factor structure is unknown: use exploratory factor analysis first
• You only need internal consistency of a single scale: use Cronbach's alpha or McDonald's omega

Assumptions and requirements

• A theory-based model specifying item–factor loadings
• Adequate sample size for stable estimates
• Multivariate normality for maximum likelihood, or a robust/ordinal estimator for Likert items
• Model identification (e.g., at least three items per factor)

What the analysis reports

• Chi-square test of model fit
• Fit indices (CFI, TLI, RMSEA, SRMR)
• Standardized factor loadings
• Composite reliability and average variance extracted
• Factor correlations and modification indices

How to report it

The [k]-factor model showed acceptable fit, χ²([df]) = [value], p = [value], CFI = [value], TLI = [value], RMSEA = [value], 90% CI [[lower], [upper]], SRMR = [value].

Related methods

• Exploratory Factor Analysis (EFA)
• Structural Equation Modeling (SEM)
• Measurement Invariance Testing

Run Confirmatory Factor Analysis (CFA) on Quorant