Confirmatory Factor Analysis (CFA)
Test a measurement model you already have — loadings, fit, AVE and CR — in your browser, then export your data to SPSS/.sav or AMOS, and the model syntax to R (lavaan).
What it is
Confirmatory factor analysis (CFA) tests whether your items measure the latent constructs you expect. You specify which items load on which factor before you look at the data. CFA then checks how well that structure fits the observed covariances. It is a measurement model: it does not yet test relationships between constructs, only whether each construct is measured well. CFA is the standard first step before structural equation modeling, because a structural model is only trustworthy if the measures behind it are sound.
When to use it
- You have a hypothesized factor structure — you know which items belong to which construct.
- You are validating a published scale on a new sample, language or population.
- You need to report convergent and discriminant validity before testing a structural model.
- A reviewer asked for a measurement model with fit indices, loadings, AVE and CR.
When not to use it
- You do not yet know how many factors exist, or which items go where — run exploratory factor analysis (EFA) first.
- You only need internal consistency for a single scale — a reliability coefficient such as omega or CR alone may be enough.
Assumptions
- Multivariate normality of the indicators (or use a robust estimator such as MLR when items are non-normal).
- Continuous indicators, or ordinal indicators treated with a categorical estimator (WLSMV) for Likert items with few categories.
- An adequate sample size — a common rule of thumb is 5–10 cases per estimated parameter, and ideally N ≥ 200.
- The model is identified — each latent factor needs a fixed scale (a marker item or fixed variance).
- Each factor has at least three indicators; a factor with only two is under-identified on its own. Three to six items per factor is the usual range. When you develop a new scale, Hinkin (1998) suggests four to six items per construct in the final scale, and writing about twice as many items at the start, so that weak items can be dropped.
- No major specification errors, such as omitted cross-loadings or correlated errors that belong in the model.
Thresholds & cutoffs
| Criterion | Rule of thumb | Source |
|---|---|---|
| CFI | ≥ .95 good, ≥ .90 acceptable | Hu & Bentler (1999; https://doi.org/10.1080/10705519909540118) |
| TLI | ≥ .95 good, ≥ .90 acceptable | Hu & Bentler (1999) |
| RMSEA | ≤ .06 good, ≤ .08 acceptable | Hu & Bentler (1999); Browne & Cudeck (1993) |
| SRMR | ≤ .08 | Hu & Bentler (1999) |
| Standardized loading | ≥ .70 ideal, ≥ .50 tolerable | Hair et al. (2019) |
| AVE | ≥ .50 (convergent validity) | Fornell & Larcker (1981; https://doi.org/10.2307/3151312) |
| CR / ω | ≥ .70 (composite reliability or McDonald's omega; preferred over alpha for CFA models) | Hair et al. (2019); McDonald (1999) |
How to report it in APA
The measurement model fit the data well, χ²(df) = X.XX, CFI = .9X, TLI = .9X, RMSEA = .0X, 90% CI [.0X, .0X], SRMR = .0X. All standardized loadings exceeded .70 and were significant (p < .001). Composite reliability (or McDonald's omega) ranged from .XX to .XX and average variance extracted (AVE) from .XX to .XX, supporting convergent validity.
How Explonia runs it
Explonia runs CFA in the browser on the data you collect or upload. You pick the items for each latent construct, and Explonia estimates the model and shows fit indices, standardized loadings, AVE and CR with the thresholds applied for you. It also drafts an 'Article description' — a plain APA paragraph of the results that you read, check and edit before it goes in your paper. You can export your data to SPSS (.sav) or AMOS, and the model syntax to R (lavaan), to reproduce or extend the analysis.
Frequently asked questions
What is a good CFI value for CFA?
CFI ≥ .95 is considered good fit and ≥ .90 is usually acceptable (Hu & Bentler, 1999). Treat these as guidelines, not strict pass/fail rules — they were derived under specific conditions and can mislead with complex models or non-normal data (Marsh, Hau & Wen, 2004). Always report CFI together with RMSEA and SRMR; no single index decides fit on its own.
CFA or EFA — which do I run first?
Use EFA to discover how many factors exist when you do not know the structure. Use CFA to confirm a structure you already hypothesize. If you are unsure, see our EFA vs CFA comparison.
How large should my sample be for CFA?
A common guideline is 5–10 cases per estimated parameter, and many methodologists suggest N ≥ 200 for stable estimates. Complex models with many indicators need more.
My items are 5-point Likert — does normality matter?
Likert items are rarely normally distributed. Use a robust estimator (MLR) or a categorical estimator (WLSMV) for ordinal items with few categories rather than default maximum likelihood.
Last updated: September 2026
Run CFA on your own data
Collect or upload your data, run the analysis in your browser, and get a draft APA paragraph you can edit. Free to start. No credit card.
Start free