Factor Analysis Explained: EFA vs. CFA, Rotation, and Factor Loadings

Factor analysis uncovers the small number of latent factors behind many measured items. It splits into exploratory factor analysis (EFA), which discovers the structure, and confirmatory factor analysis (CFA), which tests a theoretically specified structure. The procedure runs from suitability checks through extraction, rotation, and naming.

What Is Factor Analysis?

Factor analysis groups many interrelated items into a few latent factors, revealing the structure and validity of a measurement instrument. It is central to developing and validating survey scales.

What Is the Difference Between EFA and CFA?

Exploratory factor analysis (EFA) is used when the factor structure is not fixed in advance and you want to discover it from the data, while confirmatory factor analysis (CFA) tests whether a structure hypothesized from theory or prior research fits the data. EFA belongs to the early stage of scale development, CFA to the validation stage.

How Do You Run a Factor Analysis?

Work from suitability checks through to naming the factors.

Step 1: Check Suitability

Confirm the data are suitable for factoring using the KMO measure (0.6 or above recommended) and a significant Bartlett's test of sphericity.

Step 2: Extract Factors and Decide How Many

Extract factors with principal component analysis or common factor analysis, and decide the number of factors by considering eigenvalues (above 1), the scree plot, and cumulative variance explained together.

Step 3: Rotate the Factors

Rotate to make the solution interpretable. Use orthogonal rotation (Varimax) if you assume the factors are independent, and oblique rotation (Oblimin) if you allow them to correlate.

Step 4: Name the Factors

Name each factor from the shared meaning of the items that load highly on it.

What Is an Acceptable Factor Loading?

A factor loading indicates how strongly an item belongs to a factor, and the usual cutoff is 0.4 to 0.5 or above. Cross-loading items that load similarly on two factors should be considered for removal.

Summary

Factor analysis discovers latent structure with EFA and validates it with CFA. Check suitability (KMO and Bartlett's test) first, then settle the structure using the number of factors, rotation, and loading cutoffs. Internal consistency of the items continues with Cronbach's alpha, and causal relationships among latent variables with structural equation modeling.