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Large-scale Assessments in Education

An IERI – International Educational Research Institute Journal

Table 3 Detailed model fit with gender as grouping variable

From: Same but different? Measurement invariance of the PIAAC motivation-to-learn scale across key socio-demographic groups

Model

χ2

df

p

CFI

ΔCFI

RMSEA [CI]

ΔRMSEA

Australia

 Configural

81.374

4

<.001

.996

 

.077 [.063–.092]

 

 Weak

84.874

7

<.001

.996

.000

.059 [.048–.070]

−.018

 Strong

124.831

22

<.001

.995

−.001

.038 [.032–.045]

−.021

Austria

 Configural

84.728

4

<.001

.994

 

.099 [.081–.118]

 

 Weak

63.823

7

<.001

.996

+.002

.063 [.049–.077]

−.036

 Strong

97.422

22

<.001

.994

−.002

.041 [.033–.049]

−.022

Canada

 Configural

153.708

4

<.001

.995

 

.058 [.051–.066]

 

 Weak

128.028

7

<.001

.996

+.001

.040 [.034–.046]

−.018

 Strong

139.3

22

<.001

.996

.000

.022 [.019–.026]

−.018

Czech Republic

 Configural

13.218

4

<.001

.998

 

.032 [.014–.051]

 

 Weak

39.506

7

<.001

.993

−.005

.045 [.032–.059]

+.013

 Strong

149.141

22

<.001

.972

−.021

.050 [.043–.058]

+.005

 Partial strong

89.442

20

<.001

.985

−.008

.039 [.031–.047]

−.006

Denmark

 Configural

33.317

4

<.001

.998

 

.049 [.034–.064]

 

 Weak

39.003

7

<.001

.998

.000

.038 [.027–.051]

−.011

 Strong

68.101

22

<.001

.997

−.001

.026 [.019–.033]

−.012

Estonia

 Configural

121.68

4

<.001

.996

 

.097 [.083–.112]

 

 Weak

130.72

7

<.001

.996

.000

.075 [.064–.087]

−.022

 Strong

276.459

22

<.001

.991

−.005

.061 [.055–.067]

−.014

 Partial strong

173.830

20

<.001

.995

−.001

.051 [.044–.058]

−.024

Finland

 Configural

102.075

4

<.001

.988

 

.104 [.087–.122]

 

 Weak

77.632

7

<.001

.991

+.003

.067 [.054–.080]

−.037

 Strong

92.742

22

<.001

.991

.000

.038 [.030 to .046]

−.029

France

 Configural

98.941

4

<.001

.994

 

.090 [.076–.106]

 

 Weak

74.73

7

<.001

.996

+.002

.058 [.046–.070]

−.032

 Strong

87.035

22

<.001

.996

.000

.032 [.025–.039]

−.026

Germany

 Configural

99.725

4

<.001

.992

 

.105 [.088–.124]

 

 Weak

99.61

7

<.001

.992

.000

.078 [.065–.092]

−.027

 Strong

100.641

22

<.001

.993

+.001

.041 [.033–.049]

−.037

Ireland

 Configural

152.789

4

<.001

.992

 

.120 [.104–.136]

 

 Weak

120.73

7

<.001

.994

+.002

.079 [.067–.092]

−.041

 Strong

158.997

22

<.001

.993

−.001

.049 [.042–.056]

−.030

Italy

 Configural

99.324

4

<.001

.994

 

.108 [.090–.127]

 

 Weak

72.843

7

<.001

.996

+.002

.068 [.054–.083]

−.040

 Strong

94.207

22

<.001

.996

.000

.040 [.032–.049]

−.028

Japan

 Configural

153.559

4

<.001

.989

 

.130 [.113–.148]

 

 Weak

145.401

7

<.001

.990

+.001

.095 [.082–.108]

−.035

 Strong

207.013

22

<.001

.987

−.003

.062 [.054–.070]

−.033

 Partial strong

161.373

18

<.001

.990

.000

.060 [.052–.069]

−.035

Korea

 Configural

65.833

4

<.001

.998

 

.074 [.059–.091]

 

 Weak

55.934

7

<.001

.998

.000

.050 [.038–.063]

−.024

 Strong

137.537

22

<.001

.996

−.002

.043 [.037–.050]

−.007

The Netherlands

 Configural

60.788

4

<.001

.996

 

.082 [.065–.101]

 

 Weak

48.642

7

<.001

.997

+.001

.053 [.040–.068]

−.029

 Strong

71.33

22

<.001

.997

.000

.033 [.024–.041]

−.020

Norway

 Configural

34.036

4

<.001

.996

 

.061 [.043–.081]

 

 Weak

53.634

7

<.001

.995

−.001

.058 [.044–.073]

−.003

 Strong

56.746

22

<.001

.996

+.001

.028 [.019–.037]

−.030

Poland

 Configural

22.623

4

<.001

.999

 

.044 [.027–.062]

 

 Weak

30.195

7

<.001

.999

.000

.037 [.024–.051]

−.007

 Strong

68.606

22

<.001

.998

−.001

.029 [.022–.037]

−.008

Slovak Republic

 Configural

114.657

4

<.001

.998

 

.110 [.093–.128]

 

 Weak

96.867

7

<.001

.998

.000

.075 [.062–.089]

−.035

 Strong

100.765

22

<.001

.998

.000

.040 [.032–.048]

−.035

Spain

 Configural

152.478

4

<.001

.987

 

.122 [.106–.139]

 

 Weak

137.571

7

<.001

.988

+.001

.087 [.074–.099]

−.035

 Strong

155.157

22

<.001

.988

.000

.049 [.042–.057]

−.038

Sweden

 Configural

39.923

4

<.001

.996

 

.070 [.052–.091]

 

 Weak

28.547

7

<.001

.998

+.002

.041 [.026–.058]

−.029

 Strong

61.956

22

<.001

.996

−.002

.032 [.023–.041]

−.009

United Kingdom

 Configural

117.83

4

<.001

.995

 

.087 [.074–.100]

 

 Weak

102.074

7

<.001

.996

+.001

.060 [.050–.070]

−.027

 Strong

116.039

22

<.001

.996

.000

.034 [.028–.040]

−.026

United States

 Configural

85.259

4

<.001

.994

 

.100 [.082–.119]

 

 Weak

68.033

7

<.001

.996

+.002

.065 [.052–.080]

−.035

 Strong

97.729

22

<.001

.994

−.002

.041 [.033–.050]

−.024

  1. df, degrees of freedom; CFI, comparative fit index; RMSEA, root mean square error of approximation; CI, confidence interval; following Cheung and Rensvold (2002) and Chen (2007), model fit of the more restrictive model should be considered to be significantly worse if the CFI drops by more than .01 and the RMSEA increases by more than .015; changes in CFI and RMSEA that exceed these cutoff values are printed in italics; partial MI has only been tested if assumptions of full MI did not hold
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