method note
Which fit index to report, and when
Which fit indices should I report in structural equation modelling?
Report at least one absolute index (χ²/df or SRMR), one comparative index (CFI or TLI) and one error-of-approximation index (RMSEA) together. Common thresholds: CFI and TLI ≥.95 good, ≥.90 acceptable; RMSEA and SRMR ≤.05 good, ≤.08 acceptable; χ²/df ≤3 good, ≤5 acceptable. These are conventions — sample size, model complexity and estimator all shift them.
Why one index is not enough
Each index is sensitive to a different aspect of the model. χ² is over-sensitive to sample size: in large samples even small deviations turn significant. CFI and TLI compare the model against the independence model. RMSEA rewards parsimony by accounting for degrees of freedom. SRMR reports the magnitude of residual correlations directly. Because they measure different things, they do not substitute for one another.
Which index a paper omits carries more information than the ones it prints. Quietly dropping the index that failed its cut-off is common and indefensible.
When the cut-offs mislead
RMSEA runs high systematically in small samples; rejecting a model on RMSEA alone below n = 200 is a mistake. CFI is pulled down in models with many items and many factors. With ordinal (Likert) data and maximum likelihood estimation the indices are biased; an appropriate estimator such as WLSMV should be used.
When fit is poor
Chasing modification indices and correlating error terms does not improve the model; it fits it to the sample. Every freed parameter needs a theoretical justification, and it must be reported. Unjustified respecification will not replicate.
The work behind this note
- How and When to Use Which Fit Indices? A Practical and Critical Review of the Methodology2020 · 132 citations
- Structural Equation Modeling (SEM) for Social and Behavioral Sciences Studies: Steps Sequence and Explanation2024 · 44 citations
- Factor Analysis and Validity in Social Sciences: Application of Exploratory and Confirmatory Factor Analyses2017 · 2,435 citations
Other method notes
- Exploratory or confirmatory? Which factor analysis, and whenShould I use exploratory or confirmatory factor analysis?
- Validity and reliability: what to report, and howHow are validity and reliability reported, and how do they differ?
- Common method variance: preventing, testing, correctingWhat is common method variance and how is it controlled?
Written for researchers and graduate students. Conventions described here are conventions, not rules — check them against your own design before you report.