Structural Equation Tool Calculator

• Chi-square/df: χ²_m / df_m
• RMSEA (approx): sqrt( max( (χ²_m - df_m) / (df_m(N-1)), 0 ) )
• CFI: 1 - max(χ²_m-df_m,0) / max(χ²_b-df_b, χ²_m-df_m)
• TLI (NNFI): ((χ²_b/df_b) - (χ²_m/df_m)) / ((χ²_b/df_b) - 1)
• NFI: (χ²_b - χ²_m) / χ²_b
• IFI: (χ²_b - χ²_m) / (χ²_b - df_b)
• SRMR (approx from residual summary): sqrt( SSE / count )
  SSE is the sum of squared residual correlations; count is the number of unique residual elements.
• AIC / BIC (approx): AIC = χ²_m + 2k, BIC = χ²_m + k ln(N)

1. Run your SEM and collect χ²_m, df_m, and N.
2. Optionally capture baseline (independence) χ²_b and df_b.
3. Enter k to obtain AIC/BIC/ECVI; enter p to auto-fill residual count.
4. If you can summarize residual correlations, enter SSE and count for SRMR.
5. Click Calculate; review indices and interpretation notes.
6. Use the CSV/PDF buttons to export results for reporting.

Fit indices computed from core outputs

This calculator converts your model chi-square (χ²m), degrees of freedom (dfm), and sample size (N) into commonly reported fit indices. The χ²/df ratio is a quick parsimony check, while RMSEA summarizes approximate misfit per degree of freedom using N. Because χ² grows with sample size, these derived indices help you compare models more consistently across studies. It supports quick documentation for reporting teams.

Baseline comparison for incremental fit

When you supply the independence (baseline) model statistics (χ²b and dfb), the tool estimates CFI, TLI, NFI, and IFI. These indices quantify improvement over a “no-covariance” structure. For example, CFI compares the noncentrality of the target model against the baseline, producing values near 1.00 when the target greatly reduces misfit. TLI can exceed 1.0; use it comparatively.

Residual summaries for SRMR screening

If you can export residual correlations, you may summarize them as SSE (sum of squared residual correlations) and a residual count. The tool then approximates SRMR as √(SSE/count). This is a practical screening step: lower SRMR indicates smaller average residual discrepancies, complementing RMSEA which focuses on global misfit. If residual count is unknown, you can enter observed variables (p) and the calculator can use p(p+1)/2 as a typical unique-moment count.

Information criteria and complexity signals

By entering the number of free parameters (k), the calculator provides approximate AIC, BIC, and ECVI. These criteria reward fit while penalizing complexity, supporting model selection when comparing non-nested alternatives. The added k/df ratio is a compact complexity flag: high values indicate many parameters per degree of freedom. Smaller AIC and ECVI generally indicate better expected predictive performance, while BIC applies a stronger penalty of k·ln(N) and favors simpler models as N increases.

Reporting workflow and decision support

Use the results block to review RMSEA, CFI, and SRMR together, then read the interpretation notes generated from typical thresholds (e.g., RMSEA ≤ 0.06, CFI ≥ 0.90, SRMR ≤ 0.08). Export CSV for appendices and PDF for quick sharing. Always report estimator, any scaling corrections, and confidence intervals from your SEM software to accompany these quick-check estimates. When comparing models, prioritize theory, modification rationale, and cross-validation over chasing marginal threshold gains.

1) What inputs are required to calculate results?

Enter χ²m, dfm, and N. These power χ²/df and RMSEA. Optional baseline, k, and residual summaries add more indices.

2) Where do baseline values come from?

Use the independence (null) model reported by your SEM software, often labeled baseline or independence. Provide χ²b and dfb together for CFI, TLI, NFI, and IFI.

3) How do I approximate SRMR using this tool?

Export residual correlations, compute SSE as the sum of squared residual correlations, and set count to the number of unique residual elements. If you know p, count can be p(p+1)/2.

4) Are AIC and BIC exact in this calculator?

They are quick approximations using χ²m plus penalties (2k or k·ln(N)). For exact values, rely on your SEM package, especially when using robust estimators or scaled χ².

5) What fit thresholds should I rely on?

Treat thresholds as guidelines, not pass/fail rules. Compare indices across plausible models, consider theory and diagnostics, and report confidence intervals for RMSEA when available.

6) Why might my software and this tool show different indices?

Robust estimators, scaling corrections, missing-data handling, and small-sample adjustments can change reported indices. This tool uses standard approximations from the entered statistics for consistency checks and quick reporting drafts.