Table 2B.
Model fit results from models with four types of measurement invariance across eight different percentages of contaminated data (Conditions 5–8).
| Model fit | M10–20 | M20–30 | M30–30 | M40–40 |
|---|---|---|---|---|
| Average | CI | |||
| χ2 (df = 4) | 4.60 (1.23, 9.27) | 5.26 (1.36,10.25) | 6.08 (1.49, 12.23) | 6.98 (1.42,14.70) |
| p-value | 0.46 (0, 0.87) | 0.41 (0.04, 0.85) | 0.37 (0.02, 0.83) | 0.34 (0.01, 0.84) |
| % (p < 0.05) | 9.10% | 12.40% | 18% | 24% |
| χ2/df | 1.15 (0.31, 2.32) | 1.32 (0.34, 2.56) | 1.52 (0.37, 3.06) | 1.74 (0.35, 3.67) |
| % (χ2/df < 5) | 99.60% | 98.80% | 98.20% | 96.40% |
| CFI | 1 (1, 1) | 1 (1, 1) | 1 (1, 1) | 1 (1, 1) |
| TLI | 1 (1, 1) | 1 (1, 1) | 1 (1, 1) | 1 (1, 1) |
| RMSEA | 0.01 (0, 0.02) | 0.01 (0, 0.02) | 0.01 (0, 0.03) | 0.01 (0, 0.03) |
| WRMR | 0.32 (0.18, 0.49) | 0.34 (0.18, 0.51) | 0.36 (0.19, 0.56) | 0.38 (0.18, 0.60) |
| Average | WI | |||
| χ2 (df = 7) | 7.39 (3.06, 13.16) | 9.59 (4.03, 16.48) | 12 (5.16, 20.82) | 14.73 (6.53, 24.28) |
| p-value | 0.48 (0.07, 0.88) | 0.35 (0.02, 0.78) | 0.24 (0.00, 0.64) | 0.16 (0.00, 0.48) |
| % (p < 0.05) | 6.70% | 18.80% | 31% | 48% |
| Δχ2 (df = 3) | 2.91 (0.62, 5.73) | 4.29 (0.90, 8.22) | 5.77 (1.43, 10.84) | 7.52 (2.14, 14.10) |
| p-value | 0.50 (0.13, 0.89) | 0.37 (0.04, 0.82) | 0.26 (0.01, 0.70) | 0.18 (0.00, 0.54) |
| % (p < 0.05) | 4.10% | 11.90% | 24% | 40% |
| χ2/df | 1.06 (0.44, 1.88) | 1.37 (0.58, 2.35) | 1.71 (0.74, 2.97) | 2.10 (0.93, 3.47) |
| % (χ2/df < 5) | 99.90% | 99.90% | 99.30% | 97.10% |
| CFI | 1.00 (1.00, 1.00) | 1.00 (1.00, 1.00) | 1.00 (1.00, 1.00) | 1.00 (1.00, 1.00) |
| TLI | 1.00 (1.00, 1.00) | 1.00 (1.00, 1.00) | 1.00 (1.00, 1.00) | 1.00 (1.00, 1.00) |
| RMSEA | 0.01 (0, 0.02) | 0.01 (0, 0.02) | 0.01 (0.01, 0.03) | 0.02 (0.01, 0.03) |
| WRMR | 0.46 (0.30, 0.64) | 0.51 (0.34, 0.69) | 0.57 (0.38, 0.78) | 0.61 (0.42, 0.81) |
| Average | SI | |||
| χ2 (df = 14) | 24.86 (16.33, 34.00) | 35.87 (24.48, 47.56) | 42.66 (29.75, 65.20) | 58.35 (43.18, 74.74) |
| p-value | 0.11 (0.00, 0.29) | 0.02 (0, 0.04) | 0 (0, 0.01) | 0 (0, 0.00) |
| % (p < 0.05) | 54.40% | 92.80% | 99% | 100% |
| Δχ2 (df = 7) | 17.12 (10.05, 24.38) | 26.11 (16.74, 35.55) | 30.49 (20.49, 40.96) | 44.48 (32.09, 57.68) |
| p-value | 0.06 (0.00, 0.19) | 0.01 (0, 0.02) | 0 (0, 0.00) | 0 (0, 0.00) |
| % (p < 0.05) | 68% | 96.30% | 100% | 100% |
| χ2/df | 1.78 (1.17, 2.43) | 2.56 (1.75, 3.40) | 3.05 (2.13, 4.01) | 4.17 (3.08, 5.34) |
| % (χ2/df < 5) | 99.90% | 99.90% | 98.10% | 64.80% |
| CFI | 1.00 (1.00, 1.00) | 1.00 (1.00, 1.00) | 1.00 (1.00, 1.00) | 1.00 (1.00, 1.00) |
| TLI | 1.00 (1.00, 1.00) | 1.00 (1.00, 1.00) | 1.00 (1.00, 1.00) | 1.00 (1.00, 1.00) |
| RMSEA | 0.02 (0.01, 0.02) | 0.02 (0.02, 0.03) | 0.03 (0.02, 0.03) | 0.08 (0.07, 0.09) |
| WRMR | 0.88 (0.71, 1.05) | 1.01 (0.84, 1.18) | 1.10 (0.92, 1.28) | 1.22 (1.05, 1.39) |
| Average | STRI | |||
| χ2 (df = 18) | 56.93 (43.76, 71) | 142.39 (120.59, 166.35) | 274.36 (242.99, 306.85) | 419.28 (380.01, 458.87) |
| p-value | 0 (0, 0) | 0 (0, 0) | 0 (0, 0) | 0 (0, 0) |
| % (p < 0.05) | 99.80% | 100% | 100% | 100% |
| Δχ2 (df = 4) | 30.98 (21.14, 42.22) | 98.93 (80.73, 117.49) | 211.28 (185.80, 237.63) | 312.01 (282.08, 342.41) |
| p-value | 0 (0, 0) | 0 (0, 0) | 0 (0, 0) | 0 (0, 0) |
| % (p < 0.05) | 99.90% | 100% | 100% | 100% |
| χ2/df | 3.16 (2.43, 3.94) | 7.91 (6.70, 9.24) | 15.24 (13.50, 17.05) | 23.29 (21.11, 25.49) |
| % (χ2/df < 5) | 99.70% | 0% | 0% | 0% |
| CFI | 1.00 (1.00, 1.00) | 0.99 (0.99, 1.00) | 0.99 (0.98, 0.99) | 0.99 (.98, 0.99) |
| TLI | 1.00 (1.00, 1.00) | 0.99 (0.99, 1.00) | 0.99 (0.99, 0.99) | 0.99 (0.99, 0.99) |
| RMSEA | 0.03 (0.02, 0.03) | 0.05 (0.04, 0.05) | 0.07 (0.07, 0.08) | 0.09 (0.08, 0.09) |
| WRMR | 1.39 (1.22, 1.56) | 2.13 (1.97, 2.31) | 2.97 (2.80,3.15) | 3.53 (3.36, 3.70) |
Averages are listed with 10th and 90th percentile ranges indicated in parentheses; M0–0, M5–5, M10–10, M20–20, M10–20, M20–30, M30–30, and M40–40 indicates models estimated with certain percent contaminated data for two groups; Indices suggesting unsatisfactory model fit indicated in bold.