EFA vs CFA: when to use exploratory or confirmatory factor analysis

What is the difference between EFA and CFA?

Both assume that something you can’t observe directly, such as job satisfaction, makes people answer a group of items in a similar way. The difference is who decides the structure. In EFA every item may load on every factor, and you interpret the pattern the software finds. In CFA you draw the model first (these five items measure Factor A, these four measure Factor B) and the software tells you how far the data depart from it.

Because EFA has no hypothesis to test, it can’t validate a scale by itself. Costello and Osborne (2005) are blunt about this: EFA is not designed to test hypotheses or theories, and once an instrument has been developed it is time to move to CFA. If your synopsis promises to “validate the instrument using EFA”, expect that line to be questioned.

Should you run EFA, CFA or both on your questionnaire?

It depends on where your items came from.

• Established scales used as published, in a similar population: CFA alone is normally enough.
• Scales adapted, shortened, translated into Hindi or Tamil, or given to a very different population (a Western burnout scale for ASHA workers, say): EFA first, then CFA on separate data.
• Items you wrote yourself: EFA, then CFA on separate data. No shortcut.

The mistake: EFA and CFA on the same respondents

This is the error I see most often in drafts. The scholar runs EFA on all 400 responses, drops the items that misbehave, then runs CFA on the same 400 and reports excellent fit as confirmation.

It confirms very little. The EFA shaped the model around that sample’s quirks, so the same sample fits it.

Split instead. Randomly divide your respondents in two (in SPSS, Data, Select Cases, Random sample of cases), run EFA on one half, fix the structure, and run CFA on the other half. If a half would be too small, collect a second sample for the CFA. Our sample size guide explains why “10 respondents per item” is only a rough check.

An illustrative case: a scholar writes 28 workload items for government-school teachers and gets 560 responses. She splits them 280 and 280. On the first half, principal axis factoring with promax suggests four factors; she drops two cross-loading items and one weak item after rereading their wording. She then tests the 25-item model in AMOS on the second half and reports everything from that half only.

How do you run EFA in SPSS, step by step?

SPSS will run EFA on its defaults. The defaults are the problem: principal components and eigenvalues over 1, and most theses then add varimax. Costello and Osborne found that combination in well over half the studies they surveyed and argued it is not the best choice.

1. 1

   Open the dialog

   Analyze, Dimension Reduction, Factor. Move in only the items of the scales you are examining.

2. 2

   Descriptives

   Tick KMO and Bartlett’s test of sphericity, and Anti-image if you want each item’s sampling adequacy.

3. 3

   Extraction

   Change Principal components to Principal axis factoring (or Maximum likelihood for near-normal data). Tick Scree plot.

4. 4

   Rotation

   Choose Promax or Direct Oblimin and leave kappa and delta at their defaults.

5. 5

   Options

   Sort by size and suppress coefficients below 0.30 so the matrix is readable on screen.

6. 6

   Rerun

   Fix the number of factors at your predicted number, then one fewer and one more, and compare the pattern matrices.

KMO and Bartlett’s test

The Kaiser-Meyer-Olkin (KMO) measure checks whether the partial correlations among your items are small, which is what you want if they share factors. The labels textbooks attach to it come from Henry Kaiser: in the 0.90s marvellous, 0.80s meritorious, 0.70s middling, 0.60s mediocre, 0.50s miserable, below 0.50 unacceptable. (Kaiser first gave that scale in a 1974 Psychometrika paper on a different index; the same year, Kaiser and Rice set 0.50 as the floor for sampling adequacy.) Check the anti-image diagonal too: an item below 0.50 there deserves a look before anything else.

Bartlett’s test checks whether the items correlate at all. With a few hundred respondents it is nearly always significant, so report it without reading much into it.

Principal axis factoring or principal components?

Principal components analysis (PCA) is strictly a data-reduction method, not factor analysis. It analyses all the variance in each item, error included, while factor analysis uses only the variance items share. Costello and Osborne’s comparison showed PCA inflating variance explained and loadings. Fabrigar and colleagues (1999) recommended maximum likelihood for reasonably normal data and principal axis factoring when normality is badly violated, which it often is with Likert items. If your supervisor insists on PCA, call it principal components in the thesis and don’t describe the components as latent factors.

Varimax or promax?

Varimax forces factors to be uncorrelated. Promax and direct oblimin let them correlate. The factors of one questionnaire nearly always correlate, so oblique rotation is the more realistic choice, and if they don’t, it gives almost the same answer as varimax anyway. Read the pattern matrix for loadings and report the factor correlation matrix.

How many factors should you keep, and which items should go?

Eigenvalue greater than 1 is SPSS’s default. Costello and Osborne report a broad consensus that it is among the least accurate methods; in their own simulations it kept too many factors in 36% of samples.

The scree plot (Cattell, 1966) needs judgement: keep the factors above the point where the curve flattens.

Parallel analysis (Horn, 1965) keeps only factors whose eigenvalues beat those from random data of the same size. Most methodologists prefer it. SPSS’s Factor dialog hasn’t traditionally offered it, so scholars use Brian O’Connor’s free SPSS syntax, fa.parallel in R’s psych package, or JASP. I’d report parallel analysis and the scree plot together, with theory as the tie-breaker.

Loadings, cross-loadings and deleting items

Costello and Osborne, following Tabachnick and Fidell, treat 0.32 as a minimum loading and call an item loading 0.32 or more on two factors a cross-loading. They also note that a factor with fewer than three items is weak and unstable. Many theses use 0.40 instead; state your cut-off and stick to it.

Delete one item at a time and rerun, since every loading shifts. Read the item before deleting it: cross-loaders are often double-barrelled or reverse-coded, problems the questionnaire design guide covers. Keep a deletion log.

How do you run CFA, and which fit indices should you report?

CFA needs a covariance-based SEM program: AMOS, where you draw the model, or lavaan’s cfa() function in R, which is free.

The cut-offs most theses cite come from Hu and Bentler (1999), whose simulations suggested values close to 0.95 for CFI and TLI, 0.06 for RMSEA and 0.08 for SRMR, judged in combination rather than one at a time.

These are guidelines, not pass marks. If fit is poor, resist the modification indices: adding correlated errors until CFI crosses 0.90 is exactly what examiners now question. Add one only when you can explain it, such as two items with near-identical wording.

What about SmartPLS?

PLS-SEM builds each construct as a weighted composite of its items, so its measurement model is not CFA in the covariance sense. Hair, Howard and Nitzl (2020) call it confirmatory composite analysis. If you use SmartPLS’s PLS algorithm, write “measurement model assessment”, not CFA, and don’t report CFI or RMSEA from it. See AMOS vs SmartPLS for choosing between them.

Convergent and discriminant validity

After fit come composite reliability, AVE (0.50 floor, from Fornell and Larcker, 1981) and discriminant validity, now usually HTMT (Henseler, Ringle and Sarstedt, 2015). Thresholds and fixes are in the reliability and validity guide.

What should you report for EFA and CFA in your thesis?

Put the measurement results before any hypothesis testing. Examiners won’t trust the paths if the measurement is shaky.

• Why you ran EFA, CFA or both, tied to where your scales came from.
• The sample for each analysis, and how you split it.
• EFA: KMO, Bartlett’s test (chi-square, df, p), extraction, rotation, and how you chose the number of factors.
• EFA: the full pattern matrix, communalities and factor correlations.
• Every deleted item, when, and why.
• CFA: software, estimator, standardised loadings, chi-square with df, CFI, TLI, RMSEA with its interval, SRMR, and any modification with its reason.
• CR, AVE and discriminant validity for each construct, from the CFA sample.

A workable EFA table: items in rows grouped by factor, pattern loadings and communalities, with eigenvalues and KMO at the foot. For CFA, one table each for loadings (with CR and AVE), fit and discriminant validity. Raw output goes in the appendix.

Once the measurement model holds, move to your structural questions: mediation and moderation for indirect or conditional effects, or the statistical test guide for the rest.