Table 1 Fit indices and model comparisons

AIC

BIC

SSABIC

RMSEA

CFI

TLI

χ ²

Δχ ² ( df )

One-factor models EQ items (Allison et al., 2011[36])

1

1f control group (n = 232)

13,673.951

13,942.797

13,695.578

0.090

0.673

0.644

865.2^a

2

1f parent group (n = 439)

25,650.600

25,969.013

25,721.480

0.083

0.833

0.818

1,193.9^a

3

1f autism group (n = 363)

22,451.458

22,755.222

22,507.762

0.087

0.748

0.726

1,123.5^a

Three-factor models EQ items (Lawrence et al., 2004[34])

4

3f control group (n = 232)

14,020.059

14,319.925

14,044.181

0.078

0.781

0.761

833.2^a

5

3f parent group (n = 439)

26,186.672

26,541.825

26,265.731

0.071

0.883

0.873

1,114.3^a

6

3f autism group (n = 363)

23,768.627

24,107.440

23,831.427

0.080

0.802

0.785

1,163.0^a

Three-factor models EQ items (Muncer et al., 2006[35])

7

3f control group (n = 232)

7,731.634

7,897.077

7,744.943

0.048

0.942

0.930

132.7^a

8

3f parent group (n = 439)

14,798.686

14,994.632

14,842.304

0.060

0.950

0.939

222.0^a

9

3f autism group (n = 363)

13,040.850

13,227.781

13,075.499

0.055

0.932

0.918

184.3^a

Three-factor multigroup models EQ items (Muncer et al., 2006[35])

10

3f multigroup all estimates vary (n = 1,034)

35,574.089

36,166.916

35,785.782

0.056

0.938

0.931

589.9^a

11

3f multigroup equal factor loadings (n = 1,034)

35,628.149

36,072.769

35,786.918

0.060

0.921

0.921

703.9^a

114.1 (30) P <0.001

Three-factor model of cognitive empathy (EQ subscale, Eyes and KDEF), emotional empathy (EQ subscale) and social skills (EQ subscale and AQ_soc)

12

3f control group (n = 232)

8,331.507

8,527.971

8,347.312

0.044

0.945

0.936

1,202.4^a

13

3f parent group (n = 439)

16,721.291

16,954.108

16,773.218

0.055

0.947

0.938

3,463.6^a

14

3f autism group (n = 363)

19,949.121

20,171.102

19,990.266

0.067

0.894

0.877

2,162.7^a

Four-factor model of cognitive empathy (EQ subscale), emotional empathy (EQ subscale) social skills (EQ subscale and AQ_soc) and performance-based empathy (Eyes and KDEF)

15

4f control group (n = 232)

8,323.897

8,530.701

8,340.533

0.040

0.955

0.946

176.4^a

16

4f parent group (n = 439)

16,712.141

16,957.074

16,766.664

0.055

0.949

0.939

298.8^a

17

4f autism group (n = 363)

15,687.606

15,921.270

15,730.916

0.053

0.934

0.922

262.5^a

Four-factor multigroup models of cognitive empathy (EQ subscale), emotional empathy (EQ subscale) social skills (EQ subscale and AQ_soc) and performance-based empathy (Eyes and KDEF)

18

4f multigroup all estimates vary (n = 1,034)

40,743.301

41,494.361

41,011.591

0.052

0.938

0.932

808.0^a

19

4f multigroup equal factor loadings (n = 1,034)

40,894.787

41,467.965

41,099.535

0.061

0.909

0.907

1,031.5^a

223.5 (36) P <0.001

Four factor multigroup models specifying sex effects (6 groups)

20

4f multigroup all estimates vary (n = 1,034)

40,757.204

42,190.149

41,269.074

0.058

0.923

0.916

1,332.5^a

21

4f multigroup equal factor loadings and equal variance estimates (n = 1,034)

40,873.332

41,861.570

41,226.345

0.066

0.891

0.893

1,628.6^a

296.1 (90) P <0.001

22

4f multigroup equal factor loadings and free variance (n = 1,034)

40,745.441

41,832.503

41,133.757

0.059

0.914

0.914

1,460.7^a

128.2 (70) P <0.001