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Table 4 Detailed model fit with age groups 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

70.339

6

<.001

.997

 

.071 [.056–.086]

 

 Weak

53.053

12

<.001

.998

+.001

.040 [.029–.051]

−.031

 Strong

229.439

42

<.001

.991

−.007

.046 [.040–.051]

+.006

Austria

 Configural

69.963

6

<.001

.995

 

.088 [.070–.107]

 

 Weak

63.326

12

<.001

.996

+.001

.056 [.043–.070]

−.032

 Strong

333.863

42

<.001

.978

−.018

.071 [.064–.078]

+.015

 Partial strong

165.872

38

<.001

.990

−.006

.049 [.042–.057]

−.007

Canada

 Configural

138.55

6

<.001

.996

 

.055 [.047–.063]

 

 Weak

143.366

12

<.001

.996

.000

.039 [.033–.044]

−.016

 Strong

463.435

42

<.001

.987

−.009

.037 [.034–.040]

−.002

Czech Republic

 Configural

10.956

6

<.001

.999

 

.023 [.000–.045]

 

 Weak

29.365

12

<.001

.996

−.003

.031 [.017–.045]

+.008

 Strong

155.095

42

<.001

.974

.022

.042 [.035–.049]

+.011

 Partial strong

108.095

38

<.001

.984

.012

.035 [.027–.042]

+.004

Denmark

 Configural

35.701

6

<.001

.998

 

.049 [.034–.065]

 

 Weak

50.137

12

<.001

.998

.000

.039 [.028–.051]

−.010

 Strong

250.675

42

<.001

.987

.011

.049 [.043–.055]

+.010

 Partial strong

124.509

38

<.001

.995

−.003

.033 [.027–.040]

−.006

Estonia

 Configural

116.955

6

<.001

.996

 

.094 [.800–.110]

 

 Weak

118.751

12

<.001

.996

.000

.065 [.055–.076]

−.029

 Strong

311.634

42

<.001

.990

−.006

.056 [.050–.061]

−.009

France

 Configural

105.361

6

<.001

.994

 

.093 [.078–.108]

 

 Weak

92.977

12

<.001

.995

+.001

.059 [.048–.071]

−.034

 Strong

266.046

42

<.001

.987

−.008

.053 [.047–.059]

−.006

Germany

 Configural

66.486

6

<.001

.995

 

.084 [.066–.102]

 

 Weak

49.271

12

<.001

.997

+.002

.046 [.033–.060]

−.038

 Strong

250.396

42

<.001

.982

.015

.059 [.052–.066]

+.013

 Partial strong

136.768

38

<.001

.992

−.005

.043 [.035–.050]

−.003

Ireland

 Configural

136.305

6

<.001

.994

 

.112 [.096–.129]

 

 Weak

117.613

12

<.001

.995

+.001

.071 [.060–.083]

−.041

 Strong

302.272

42

<.001

.987

−.008

.060 [.054–.066]

−.011

Italy

 Configural

90.465

6

<.001

.995

 

.102 [.084–.121]

 

 Weak

99.735

12

<.001

.995

.000

.073 [.061–.087]

−.029

 Strong

150.705

42

<.001

.993

−.002

.044 [.036–.051]

−.029

Japan

 Configural

134.913

6

<.001

.991

 

.121 [.104–.139]

 

 Weak

102.297

12

<.001

.994

+.003

.072 [.059–.085]

−.049

 Strong

239.764

42

<.001

.986

−.008

.057 [.050–.064]

−.015

Korea

 Configural

59.904

6

<.001

.998

 

.069 [.054–.086]

 

 Weak

58.323

12

<.001

.999

.001

.046 [.034–.058]

−.023

 Strong

374.008

42

<.001

.989

−.010

.065 [.059–.071]

+.019

 Partial strong

242.069

36

<.001

.993

−.006

.055 [.049–.062]

+.009

The Netherlands

 Configural

60.941

6

<.001

.997

 

.081 [.063–.100]

 

 Weak

74.174

12

<.001

.996

−.001

.061 [.048–.075]

−.020

 Strong

224.406

42

<.001

.989

−.007

.056 [.049–.063]

−.005

Poland

 Configural

29.587

6

<.001

.999

 

.049 [.032–.067]

 

 Weak

59.505

12

<.001

.998

−.001

.049 [.037–.062]

.000

 Strong

208.863

42

<.001

.991

−.007

.049 [.043–.056]

.000

Slovak Republic

 Configural

102.937

6

<.001

.998

 

.103 [.086–.121]

 

 Weak

106.906

12

<.001

.998

.000

.072 [.060–.085]

−.031

 Strong

213.481

42

<.001

.996

−.002

.052 [.045–.059]

−.020

Spain

 Configural

160.601

6

<.001

.986

 

.125 [.108–.142]

 

 Weak

142.012

12

<.001

.988

+.002

.081 [.069–.093]

−.044

 Strong

272.084

42

<.001

.979

−.009

.057 [.051–.064]

−.024

Sweden

 Configural

19.070

6

<.001

.999

 

.042 [.022–.065]

 

 Weak

23.160

12

<.001

.999

.000

.028 [.009–.045]

−.014

 Strong

309.409

42

<.001

.971

.028

.073 [.065–.080]

+.045

 Partial strong

110.016

38

<.001

.992

−.007

.040 [.031–.048]

+.012

United Kingdom

 Configural

106.198

6

<.001

.995

 

.081 [.068–.095]

 

 Weak

86.582

12

<.001

.997

+.002

.050 [.040–.060]

−.031

 Strong

363.668

42

<.001

.985

.012

.055 [.050–.060]

+.005

 Partial strong

169.435

38

<.001

.995

−.002

.037 [.031–.043]

−.013

United States

 Configural

87.444

6

<.001

.994

 

.100 [.082–.119]

 

 Weak

73.386

12

<.001

.996

+.002

.061 [.048–.075]

−.039

 Strong

168.389

42

<.001

.991

−.005

.047 [.040–.055]

−.014

  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 italic; partial MI has only been tested if assumptions of full MI did not hold