5. SEM | SPSS AMOS - What is Confirmatory Factor Analysis (CFA)? - Research Coach

Confirmatory Factor Analysis (CFA) is a statistical method for testing whether sets of observed items measure specific, unobserved constructs—and whether those constructs are distinct from one another. In practice, an unobserved construct such as “job satisfaction” is treated as a factor, measured by multiple indicators (for example, five or six survey items). CFA then evaluates how strongly each indicator reflects its intended factor and whether the measurement structure matches what the researcher specifies in advance.

CFA is often presented as a measurement model diagram. Unobserved constructs appear as circles or ovals, while observed indicators appear as rectangles. Single-headed arrows run from each factor to its indicators, representing the direct influence of the latent construct on the measured items. The estimated strength of each arrow is called a factor loading, which can be reported as unstandardized or standardized regression-style coefficients. These loadings are interpreted as evidence of how well the items represent the underlying construct.

Because indicators are never perfect, CFA includes error terms for each measurement. The unexplained portion of variance is captured by these errors, which can reflect random error (unpredictable fluctuations due to uncontrolled influences, often treated as “noise”) or systematic error (consistent over- or underestimation driven by bias). A key implication follows: assuming a single-indicator construct has no measurement error is typically unrealistic. CFA therefore relies on multiple items per construct to model measurement error more credibly.

CFA also accounts for relationships among latent constructs by estimating covariances. When multiple unobserved variables exist, the model includes two-headed arrows between them, allowing the analysis to estimate their covariance. Treating latent variables as exogenous and specifying their covariances is necessary; omitting required covariances can trigger software errors.

A major contrast is between CFA and Exploratory Factor Analysis (EFA). EFA is used for data reduction and for discovering which indicators belong to which constructs; it allows every indicator to load on multiple factors, which can produce cross-loadings and raise concerns about whether an item is a clean measure of a single construct. CFA, by contrast, starts with prior knowledge: the researcher specifies which indicators measure which factor, and indicators are restricted to load only on their designated construct—no cross-loading onto other factors.

Finally, CFA and EFA differ in how results are compared across samples. EFA often relies on correlation matrices and may be less straightforward for parameter comparison, while CFA uses covariance matrices and is generally better suited for cross-sample comparison. EFA may also involve rotation (such as rotated component matrices) to improve interpretability, whereas CFA does not depend on rotation because the item-to-construct mapping is predetermined. The session closes by pointing learners toward standard references for deeper study of CFA and related modeling concepts in SPSS AMOS.