AMOS Model Fit Summary
Applied Linguistics Research
Quick Reading Tips
- Focus on the Default model row (your CFA) when collecting indices.
- Saturated model = perfect fit (reference). Independence model = zero correlation (poor fit reference).
- Report a balanced set: one absolute, one/two incremental, one parsimony, and one information criterion.
Fit Index Thresholds Summary
Detailed Breakdown
1. CMIN
NPAR: Free parameters estimated.
CMIN (χ²): Model chi-square. Lower is better. Tests exact fit.
CMIN/DF: "Normed chi-square". Because χ² is sensitive to N, use this.
Rule of thumb: < 3.0 (Good), < 2.0 (Excellent).
2. RMR / GFI
RMR: Root Mean Square Residual. Smaller is better.
GFI: Goodness-of-Fit Index (0-1). Absolute fit.
AGFI: Adjusted GFI (penalizes complexity).
Goal: SRMR ≤ .08. GFI/AGFI ≥ .90.
3. Baseline Comparisons
Compares default model to independence model (worst case).
CFI (Comparative Fit Index) & TLI (Tucker-Lewis) are most common.
Goal: Values ≥ .90 acceptable; ≥ .95 strong.
4. Parsimony
Rewards simpler models. Useful for comparing candidates.
PNFI & PCFI: Parsimonious NFI/CFI.
Goal: > .50 is often cited as acceptable. Interpret comparatively.
5. NCP & FMIN
NCP: Noncentrality parameter. Building block for RMSEA.
FMIN: Minimum discrepancy per sample.
Note: Rarely reported alone. Used for diagnostics.
6. RMSEA
RMSEA: Population misfit per df. Lower is better.
PCLOSE: Test of close fit (H₀: RMSEA ≤ .05). We want PCLOSE > .05.
Goal: < .06 (Good), .06–.08 (Acceptable). Always report the CI.
7. Information Criteria
Trade-off between fit and complexity.
AIC & BIC: Lower is better when comparing rival models.
Usage: Justify chosen model among rivals (lowest AIC wins).
8. ECVI
Expected Cross-Validation Index.
Estimates how well model fits a similar sample.
Lower implies better expected replication.
9. HOELTER
Critical N.
Smallest sample size where χ² becomes significant.
Goal: > 200 (Good), > 75 (Minimal).
Reporting Guide & Example
Match journal style with this structure for reporting.
| AMOS Block | Statistic to Take | Why it matters | Typical Guideline |
|---|---|---|---|
| CMIN | CMIN/DF (Normed χ²) | Sensitivity to sample size makes basic χ² unreliable. | < 3.0 Good |
| RMR, GFI | GFI | Absolute fit without adjusting for df. | > .90 Acceptable |
| Baseline | CFI / TLI | Compares model against worst-case scenario. | > .90 Acceptable |
| RMSEA | RMSEA & PCLOSE | Population misfit; accounts for error of approximation. | < .06 (PCLOSE > .05) |
Copy-ready Example Sentence
“The three-factor CFA showed adequate fit: χ²(132) = 227.61, p < .001, CMIN/DF = 1.724; RMSEA = .052, 90% CI [.040, .063], PCLOSE = .385. Incremental indices were high (CFI = .969, TLI = .964, IFI = .969, NFI = .930), and absolute fit was acceptable (GFI = .916). Parsimony indices were PNFI = .802 and PCFI = .836. Information criteria further supported adequacy (AIC = 305.61; BIC = 446.10).”