EFA in Practice: Choosing the Number of Factors, Interpreting Cross-Loadings, and Removing Items

1. Objectives and prerequisites for EFA

EFA seeks latent factors that explain covariance among observed variables. Software sees associations; researchers must supply conceptual meaning, item content and the analytical rationale. Without an expected-content map and retention criteria, deletion can become a search for an attractive matrix (Finch et al., 2016).

EFA suits uncertain structures, newly developed scales or substantially adapted measures. CFA usually better addresses testing a prespecified model. Do not claim both exploration and confirmation on the same sample.

• Define each construct and its content domain.
• Check coding, reversed items, out-of-range values and missingness.
• Identify continuous, ordinal and binary variables.
• Plan factor-count selection before inspecting loadings.
• Provide an independent validation sample or acknowledge its absence.

2. EFA, PCA and CFA answer different questions

PCA derives components from total variance to reduce data. Common factor analysis models shared variance and better suits inference about latent structure. CFA tests a prespecified measurement model. Selecting Principal Components in SPSS is therefore not another way of performing EFA (Fabrigar et al., 1999; Watkins, 2018).

Principal axis factoring (PAF) is a common practical choice for common factors with imperfectly normal data. Maximum likelihood supports tests and CIs under suitable assumptions. Do not choose extraction merely because it is the software default.

3. Step 1: inspect data before correlations

Check category frequencies, missingness, reversed items, skewness, kurtosis and nearly duplicate pairs. Almost identical wording may create a method factor. A variable with insufficient variation cannot inform the structure.

KMO and Bartlett support initial assessment but do not establish a correct model. High KMO can coexist with an incorrect factor count or redundant items. Bartlett is often significant in large samples. Also inspect the determinant, correlation matrix, communalities and residuals (Watkins, 2018).

• Reverse-code correctly before analysis.
• Check unused categories and sparse frequency cells.
• Describe missing-data treatment; do not automatically mean-impute.
• Identify near-perfect correlations and repeated wording.
• Do not rely solely on KMO and Bartlett.

4. Step 2: Pearson or polychoric correlations for Likert data

Pearson uses observed scores and is often chosen for items with many categories, moderate distributions and approximately continuous treatment. Polychoric correlations estimate associations between latent continuous variables underlying ordinal responses. Consider them with fewer categories, skewness or concentrated responses (Flora & Curran, 2004).

Not every Likert item requires polychoric correlations. Consider category count, distribution, sample size and sparse cross-tabulations. Polychoric estimates can be unstable with small samples or many empty cells. Report the matrix analyzed rather than only naming SPSS.

5. Step 3: select the factor count before deleting items

Eigenvalues greater than 1 can retain too many or too few factors. Scree plots help but involve judgment. Parallel analysis compares observed with random-data eigenvalues; MAP seeks the component count minimizing average partial correlations. Combine these methods with theory and interpretability (O'Connor, 2000; Watkins, 2018).

Ordinal parallel analysis should use an appropriate matrix and simulation. Garrido et al. (2013) show that ordinal characteristics matter. Do not automatically generalize Pearson-based results to every Likert distribution.

• Run parallel analysis appropriate to the data.
• Inspect the scree plot and neighboring solutions.
• Use MAP as complementary evidence where suitable.
• Compare the factor count with the content map.
• Do not fix the count merely to match earlier research.

6. Step 4: choose extraction and rotation

For latent structure, choose PAF or an appropriate common-factor estimator. Rotation aids interpretation but cannot repair an inappropriate correlation matrix or factor count.

Social science constructs often correlate, making Direct Oblimin or Promax reasonable starting points. Varimax constrains factor correlations to 0. Use orthogonal rotation only when theory and data support independence (Fabrigar et al., 1999; Finch et al., 2016).

7. Step 5: pattern, structure and factor-correlation matrices

With oblique rotation, pattern coefficients describe each factor’s unique contribution to an item conditional on other factors. Structure coefficients are item–factor correlations and may be high because factors correlate. Prioritize the pattern matrix for primary and cross-loadings while using the structure matrix for context (Finch et al., 2016).

The factor-correlation matrix describes relationships between factors. Very high correlations can signal indistinct constructs or overextraction. Do not switch to Varimax merely to hide cross-loadings.

8. Step 6: inspect four item-level signals

Low communality indicates little item variance explained by retained factors. A low primary loading indicates a weak association. Cross-loadings indicate contributions to several factors. Content mismatch means an item no longer represents the intended domain despite attractive loadings.

Loadings of 0.30, 0.40 or 0.50 and loading differences of 0.20 are heuristics. Requirements depend on sample size, stability, indicator count, item quality and objectives. Do not turn a reference point into an automatic deletion rule (Costello & Osborne, 2005).

9. Step 7: handle cross-loadings without chasing an attractive matrix

For each cross-loading item, review wording, reverse coding, reference object, recall period and level of abstraction. An item may genuinely bridge concepts, be ambiguous or reflect wording effects. Combine pattern loadings, communality, content and coverage consequences.

If removing an item, remove one justified item per iteration and rerun factor-count selection, extraction, rotation and loadings. The new solution may reorder the problems. Do not preselect many deletions from one run.

10. SPSS practice: Pearson, PAF and oblique rotation

11. Ordinal EFA when Pearson is insufficient

For few-category or strongly skewed items, obtain polychoric correlations in suitable software. R offers psych::polychoric and fa.parallel or equivalents; FACTOR supports ordinal analysis and parallel analysis. Check sparse-cell, non-positive-definite-matrix and Heywood warnings.

Run parallel analysis on the appropriate ordinal matrix, extract common factors using a suitable estimator and rotate obliquely. Compare with Pearson results for sensitivity. Report substantial changes in factor count or item placement rather than selecting only the favorable solution.

12. Hypothetical example: EFA of 18 Likert items

These numbers are constructed illustrations, not empirical results. An 18-item, five-category scale was administered to 420 people. Two items were strongly skewed and one response category was rare. Polychoric parallel analysis suggested three factors, whereas Pearson eigenvalues > 1 suggested four. The scree plot and theory supported three.

The team fitted common factors with oblique rotation. Q07 had pattern loadings of 0.31 on F1 and 0.29 on F2, a difference of 0.02; cognitive review showed combined professional and emotional support content. It was earmarked for rewriting rather than reassigned. Q14 had communality 0.18 and duplicated Q13, justifying removal. Rerunning yielded primary loadings of 0.52 to 0.83 and factor correlations of 0.28 to 0.47.

13. Ten common mistakes

14. Read the final solution before naming factors

Name a factor from the shared content of its strongly loading items, not one standout item. Check sufficient quality indicators, consistent abstraction and a label no broader than the evidence. If factors differ only in wording, consider a method factor.

Explained variance is not the sole criterion. A stable, meaningful solution preserving content may be preferable despite lower variance explained. Report deleted items and imperfect retained items with reasons.

15. APA 7 reporting template and checklist

• State the EFA objective and why PCA or CFA was not chosen.
• Describe the sample, missingness, distributions and reverse coding.
• Identify Pearson, polychoric or other correlations.
• State extraction or estimator.
• Explain communality estimation.
• Describe parallel analysis, MAP, scree and theory.
• State and justify rotation.
• Report the complete pattern matrix.
• Report structure matrices when substantially different.
• Report factor correlations.
• Document each deletion iteration and content rationale.
• Do not hide low coefficients in the analysis record.
• Explain factor naming.
• Describe CFA or independent validation plans.
• Identify hypothetical examples when values are not empirical.