How to Report Confirmatory Factor Analysis Results in APA 7

You fit the model, lavaan (or Mplus, or AMOS) returns half a screen of indices, the loadings converge — and then you freeze in front of a blank page. Which fit indices do you report, exactly? Do you include the chi-square even though it came out significant? Standardized or unstandardized loadings? This guide answers those questions with a paragraph template and a table you can adapt directly to your manuscript.

Software does not change anything: a confirmatory factor analysis (CFA) is written up the same way in APA 7 whether you ran it in R with lavaan, in Mplus, in JASP or in AMOS. The output looks different in each program, but what the results section needs is identical: model specification, estimator and its justification, global fit indices, standardized loadings, and — if you respecified — what you changed and why.

What APA 7 requires in a CFA write-up

The 7th edition APA manual does not dedicate a section to CFA, but publication norms in psychology and psychometrics journals have consolidated a clear standard. A complete write-up includes, in this order: (1) the model you are testing and its theoretical justification; (2) the estimator used — ML, MLR or WLSMV — and why it fits your data; (3) global fit indices with their cutoffs; (4) the standardized loading table with significance; and (5) any model respecification, disclosed transparently. Skipping any of these is the fast lane to a "major revision."

The most common foundational error is the estimator. If your items are Likert-type with few categories (four or five points), treating them as continuous with classical maximum likelihood (ML) is no longer accepted in many Q1 journals: the correct choice is an estimator for ordinal variables, WLSMV (weighted least squares mean- and variance-adjusted). If the data are continuous but non-normal, use robust ML (MLR), which returns the Satorra-Bentler scaled chi-square. State the estimator and the reason, even briefly.

Which fit indices to report and with what cutoffs

Do not report the fifteen indices the program spits out: choose well and be consistent. The de facto standard, based on Hu and Bentler (1999), is to report one incremental index (CFI or TLI), one approximation-error index (RMSEA with its 90% confidence interval) and one residual index (SRMR). The chi-square is always reported, but it does not decide on its own: with large samples it is almost always significant even when the model is good, so do not reject the model just because p < .05.

One caveat worth internalizing: these values are indicative, not sacred thresholds. Marsh, Hau and Wen (2004) showed that applying Hu and Bentler's cutoffs as mechanical rules penalizes correct models under certain conditions. Report the set of indices, interpret them as a block, and if one lands in a gray zone, discuss it rather than hide it.

Results paragraph: template with real values

The following paragraph shows the standard format for a two-correlated-factor model. Statistical symbols are italicized and bracketed values are placeholders for your own results:

"A confirmatory factor analysis was conducted to test the [N]-factor structure of the [scale] using [robust maximum likelihood (MLR) / weighted least squares mean- and variance-adjusted (WLSMV)] estimation in [lavaan (R) / Mplus], appropriate for the [non-normal / ordinal] nature of the items. The hypothesized model showed [good / acceptable] fit to the data, χ²([df]) = [value], p [< .001 / = .xxx], χ²/df = [x.xx], CFI = [.xxx], TLI = [.xxx], RMSEA = [.xxx], 90% CI [.xxx, .xxx], SRMR = [.xxx]. All standardized factor loadings were statistically significant (p < .001) and ranged from [.xx] to [.xx], exceeding the [.40 / .50] threshold. The two factors, [Factor 1 Name] and [Factor 2 Name], correlated [r = .xx]. [If respecified: Based on modification indices and theoretical justification, the error terms of items [x] and [y], both worded in [negative / somatic] terms, were allowed to covary, improving fit without altering the factor structure.]"

Style points reviewers check: symbols (p, χ², r, β) are italicized; acronyms (CFI, RMSEA, WLSMV) and factor labels are not. Coefficients bounded between −1 and 1 (loadings, CFI, RMSEA, correlations) are written without a leading zero: .957, not 0.957.

The standardized loading table in APA 7 format

Here the number-one error is reporting unstandardized loadings (the items' original metric) instead of the completely standardized solution — std.all in lavaan, STDYX in Mplus — which is the interpretable, comparable one. The table should carry the standardized loading, its standard error or significance, and ideally each item's R² (proportion of variance explained by the factor).

Five common errors reviewers send back

After reviewing dozens of manuscripts with CFA, these are the problems that show up again and again:

1. Judging fit by chi-square alone. Either they reject a good model because χ² was significant (expected with large N), or they declare excellent fit without reporting RMSEA or SRMR. Always report the block of indices and reason about them together.

2. Reporting unstandardized loadings. Loadings in the original metric are neither interpretable nor comparable across items. The table must carry the completely standardized solution (std.all / STDYX). It is the error that fastest reveals an author copied the output without understanding it.

3. Omitting the RMSEA confidence interval. The point RMSEA says little without its 90% CI. An RMSEA of .06 with an interval of [.02, .10] signals huge uncertainty that can flip the conclusion. APA 7 explicitly values confidence intervals, and here they are required.

4. Respecifying the model blindly with modification indices. Freeing error correlations just because the modification index is high, with no theoretical justification, is data dredging. If you correlate errors, explain why it makes sense (near-identical wording, reverse phrasing, overlapping somatic content) and state that the final model is partly exploratory.

5. Ignoring Heywood cases. A standardized loading above 1, a negative error variance, or a between-factor correlation greater than 1 are signs that the model is misspecified or the sample is too small. Do not paper over them: diagnose and discuss them. A seasoned reviewer spots them in the first table.

Already ran the EFA? When the CFA comes in

CFA does not replace the exploratory analysis: it confirms it. If you are developing a new instrument or exploring its structure in a different population, the exploratory factor analysis comes first; CFA enters once you have a hypothesized structure — from a prior EFA or from theory — and want to test it. Many Q1 journals expect both: EFA on a calibration subsample and CFA on a validation subsample (cross-validation, typically with N > 400 to split the sample). If you are unsure whether to run CFA or principal component analysis, the difference is not cosmetic: I unpack it in CFA versus PCA.

Checklist before submitting the manuscript

Before hitting submit, verify that your results section includes: the tested model and its justification; the estimator (ML, MLR or WLSMV) with its reason; χ² with degrees of freedom and p value; the CFI/TLI block, RMSEA with 90% CI and SRMR; the standardized loading table with significance and, ideally, R²; between-factor correlations and composite reliability (omega); and, if you respecified, what you changed and on what theoretical grounds.

If your instrument is administered to more than one group (sex, country, time point) and you want to compare means or structures across them, the next step is measurement invariance: without it, comparing scores across groups is not defensible. And if you are preparing a full questionnaire validation — from EFA to CFA through reliability and invariance — my statistical consulting service covers the whole process. Details on the questionnaire validation page.