Opening the CFA output for the first time is always a tense moment. Did CFI clear 0.90? Is RMSEA under 0.08? Your eyes go straight to those numbers. Clearing the thresholds brings relief; falling short leaves you stuck. But the reason it feels so daunting is not really the numbers themselves. It is that there is little guidance on how to judge a given situation and what to do about it.
This article covers the thresholds and the judgment logic behind three fit indices — CFI, RMSEA, and SRMR — and then walks through five situations researchers run into often.
CFI, RMSEA, SRMR — what each index tells you
CFA fit is not judged from a single number. You have to look at indices that measure different things together.
CFI (Comparative Fit Index) indicates how much better the researcher's model is compared with a fully misspecified independence model. It ranges from 0 to 1, and the thresholds proposed by Hu & Bentler (1999) are ≥ 0.90 (acceptable) and ≥ 0.95 (excellent). It tends to be judged more strictly as the sample grows, so once the sample exceeds 500, aiming for ≥ 0.95 is the safer course.
RMSEA (Root Mean Square Error of Approximation) indicates how well the model approximates the population covariance structure. Smaller is better, and Browne & Cudeck's (1993) thresholds are ≤ 0.08 (acceptable) and ≤ 0.06 (excellent). RMSEA is estimated unstably in models with low degrees of freedom — that is, when there are few items or the factors are simple. Reporting the 90% confidence interval alongside it is the standard practice.
SRMR (Standardized Root Mean Square Residual) is the standardized difference between the observed and model-implied covariances. The Hu & Bentler (1999) threshold is ≤ 0.08. It is less well known than CFI or RMSEA, but it is useful for catching models that have leaned too heavily on modification indices.
| Index | Acceptable | Excellent | Source |
|---|---|---|---|
| CFI | ≥ 0.90 | ≥ 0.95 | Hu & Bentler (1999) |
| RMSEA | ≤ 0.08 | ≤ 0.06 | Browne & Cudeck (1993) |
| SRMR | ≤ 0.08 | — | Hu & Bentler (1999) |
When reporting the three indices together, it is common to present CFI and RMSEA as the primary indices and SRMR as a supporting one.
Case-by-case judgment — five situations
Case 1. CFI falls short but RMSEA clears the threshold
CFI 0.88, RMSEA 0.065, SRMR 0.071. How should you read a result like this?
Because CFI and RMSEA measure fit in different ways, they often point in different directions. In this situation, look first at why CFI is low. CFI is sensitive to sample size. When the sample is small — 200 or below — CFI tends to be estimated lower than it actually is. If RMSEA and SRMR both clear their thresholds and there is an error covariance with a theoretical rationale among the modification indices, the realistic move is to revise that path in a limited way and report again.
If only RMSEA looks good while CFI stays persistently low, it may be a signal that the model is failing to capture a particular factor relationship. In that case, returning to the EFA results to re-examine the factor structure itself is better than piling on modification indices.
Case 2. RMSEA falls short but CFI clears the threshold
CFI 0.94, RMSEA 0.095, SRMR 0.063. This is the opposite direction.
RMSEA is a degrees-of-freedom-based index. In complex models with many items and several factors, RMSEA tends to come out stricter than CFI. Conversely, in simple models with low degrees of freedom, RMSEA can come out excessively low. If CFI is 0.94 at an RMSEA of around 0.09, the priority is to present the model's theoretical validity and the SRMR result together while checking whether the upper bound of the 90% confidence interval for RMSEA exceeds 0.10. If that upper bound does not stray far beyond 0.10, you can describe it as a limitation and still treat the model as within submittable range.
Case 3. Several modification indices applied — where do you stop?
A modification index (MI) indicates how much chi-square drops when a particular path is added. Adding a path with a high MI raises CFI and lowers RMSEA. The problem is that this can go on indefinitely.
The principle for applying modification indices is that the theoretical rationale comes first. Adding a path solely because "the MI value is large" is overfitting to the data. When you allow an error covariance between items within the same factor, you should be able to give a theoretical account that the two items share structurally similar wording.
As a practical guide, many view exceeding three error-covariance modifications in the same model as a signal that the model itself needs reconsideration. If SRMR does not improve much after the modifications, it is a warning that the modifications are drifting away from genuine fit improvement and toward manipulating the numbers.
If you have applied modification indices, you must state so in the methods section. Without describing how many error covariances you added and why, it is hard to escape a reviewer's objection.
Case 4. The sample is large, so chi-square is always significant
The CFA results table also reports the chi-square test. But once the sample passes 300, chi-square comes out significant almost every time. With a sample of 1,000, chi-square shows p < .001 even when the model fits substantively well.
This is not a flaw. Chi-square is a test designed to respond sensitively to sample size. With large samples, some researchers use the chi-square/degrees-of-freedom ratio (χ²/df) as a supporting indicator, but there is no agreed-upon threshold for this ratio. In large-sample studies, it is methodologically appropriate to treat CFI, RMSEA, and SRMR as the primary basis for judgment rather than chi-square significance. The standard wording in a paper is something like "owing to the effect of sample size, chi-square was significant, but CFI, RMSEA, and SRMR met the acceptable thresholds."
Case 5. Fit falls short of the thresholds — the conditions for still submitting
CFI 0.86, RMSEA 0.092. Honestly, these are not good numbers. Can you still submit the paper in this situation?
The short answer is that there are cases where you can. There are conditions, though.
First, when the scale is theoretically important and measures a construct that did not previously exist. In an early scale-development study measuring a new concept, reviewers do not expect perfect fit either. There is room to persuade on the strength of the theoretical contribution and item quality.
Second, when you can clearly explain the reason for the shortfall. If a methodological explanation is available — "because the sample was small," "because the construct being measured is multidimensional in nature" — you can describe it as a limitation and still submit.
Third, when the other validity evidence is sufficient. If other grounds such as content validity, convergent validity, and criterion validity are solid, they can offset a shortfall in CFA fit.
Conversely, if the shortfall stems from a problem with the items themselves, revising the items comes before submission. If you are in a situation where CFI 0.86 only barely clears the threshold after applying ten or more modification indices, that model has been forced to fit the data.
What modidoc supports at the rigorous-validation stage
modidoc's rigorous-validation stage automatically computes CFI, RMSEA, and SRMR after running CFA and presents the results against the acceptable thresholds. It also lets you check the top modification-index items and whether a theoretical rationale has been entered for them. This process is implemented internally as the C5 rigorous-validation engine.
Frequently asked questions
Should I apply the CFI 0.90 or 0.95 threshold?
It depends on the sample size and the journal's standards. If the sample is small — under 200 — treat 0.90 as the lower bound; if the sample is large and you are targeting an SSCI-tier journal, 0.95 is the realistic goal. Hu & Bentler (1999) proposed 0.95, but rather than applying it as an absolute criterion, the principle is to judge comprehensively together with RMSEA and SRMR.
If I apply modification indices, do I have to disclose it in the paper?
Yes. If you added error covariances or modified paths, you must state in the methods section how many modification indices you applied and why. If you do not disclose it, a reviewer may grow suspicious looking only at the fit numbers. Transparent reporting raises the credibility of the model.
Why should I report the RMSEA 90% confidence interval?
A single RMSEA value is an estimate, so it carries uncertainty. If the upper bound of the 90% confidence interval strays well beyond 0.10, there is a risk that the model fit is being reported as better than it is. Conversely, if the upper bound is 0.08 or below, that is evidence the model fits stably. Most CFA software produces it automatically, so reporting it alongside the value is standard.
The next article covers convergent and discriminant validity, the stages after CFA. It looks concretely at how to judge when AVE falls short of 0.5 and whether to use the HTMT or the Fornell-Larcker criterion.
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