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Large-scale Assessments in Education

An IERI – International Educational Research Institute Journal

Table 5 Detailed model fit with level of education 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

60.600

6

<.001

.997

 

.065 [.051–.080]

 

 Weak

55.650

12

<.001

.998

+.001

.041 [.031–.052]

−.024

 Strong

352.464

42

<.001

.985

−.013

.059 [.053–.064]

+.018

partial strong

168.260

36

<.001

.993

−.005

.041 [.035–.048]

.000

Austria

 Configural

90.464

6

<.001

.993

 

.101 [.083–.120]

 

 Weak

78.036

12

<.001

.995

+.002

.063 [.050–.077]

−.038

 Strong

173.244

42

<.001

.990

−.005

.048 [.040–.055]

−.015

Canada

 Configural

136.690

6

<.001

.996

 

.054 [.047–.063]

 

 Weak

141.781

12

<.001

.996

.000

.038 [.033–.044]

−.016

 Strong

433.715

42

<.001

.987

−.009

.036 [.033–.039]

−.002

Czech Republic

 Configural

14.133

6

.030

.998

 

.030 [.009–.050]

 

 Weak

16.602

12

.100

.999

+.001

.016 [.000–.033]

−.014

 Strong

113.970

42

<.001

.982

−.017

.033 [.026–.041]

+.017

 Partial strong

105.489

38

<.001

.983

−.016

.034 [.026–.042]

+.018

Denmark

 Configural

37.178

6

<.001

.998

 

.050 [.035–.066]

 

 Weak

38.582

12

<.001

.998

.000

.033 [.021–.045]

−.017

 Strong

259.534

42

<.001

.984

−.014

.050 [.044–.056]

+.017

 Partial strong

160.743

38

<.001

.991

−.007

.040 [.033–.046]

+.007

Estonia

 Configural

142.473

6

<.001

.994

 

.105 [.090–.120]

 

 Weak

133.942

12

<.001

.995

+.001

.070 [.060–.081]

−.035

 Strong

295.322

42

<.001

.989

−.006

.054 [.048–.060]

−.016

Finland

 Configural

99.526

6

<.001

.988

 

.101 [.084–.119]

 

 Weak

102.328

12

<.001

.989

+.001

.070 [.058–.083]

−.031

 Strong

409.204

42

<.001

.954

−.035

.076 [.069–.083]

+.006

 Partial strong

219.040

34

<.001

.977

−.012

.060 [.052–.068]

−.010

France

 Configural

113.081

6

<.001

.993

 

.069 [.081–.112]

 

 Weak

140.387

12

<.001

.991

−.002

.074 [.064–.086]

+.005

 Strong

278.606

42

<.001

.984

−.007

.054 [.048–.060]

−.020

Germany

 Configural

110.476

6

<.001

.990

 

.110 [.093–.129]

 

 Weak

103.551

12

<.001

.991

+.001

.073 [.060–.086]

−.037

 Strong

217.898

42

<.001

.983

−.008

.054 [.047–.061]

−.019

Ireland

 Configural

129.028

6

<.001

.994

 

.109 [.093–.125]

 

 Weak

115.225

12

<.001

.995

+.001

.070 [.059–.082]

−.039

 Strong

404.758

42

<.001

.981

−.014

.071 [.064–.077]

+.001

 Partial strong

216.412

34

<.001

.991

−.004

.056 [.049–.063]

−.015

Italy

 Configural

77.084

6

<.001

.995

 

.094 [.076–.113]

 

 Weak

87.66

12

<.001

.995

.000

.068 [.055–.082]

−.026

 Strong

156.213

42

<.001

.993

−.002

.045 [.037–.052]

−.023

Japan

 Configural

163.744

6

<.001

.988

 

.134 [.117–.152]

 

 Weak

143.148

12

<.001

.990

+.002

.086 [.074–.099]

−.048

 Strong

284.701

42

<.001

.981

−.009

.063 [.056–.070]

−.023

Korea

 Configural

64.351

6

<.001

.998

 

.072 [.057–.089]

 

 Weak

58.634

12

<.001

.998

.000

.046 [.034–.058]

−.026

 Strong

440.681

42

<.001

.984

−.014

.071 [.065–.078]

+.025

 Partial strong

232.12

31

<.001

.992

−.006

.059 [.052–.066]

+.013

The Netherlands

 Configural

62.104

6

<.001

.996

 

.082 [.064–.101]

 

 Weak

49.041

12

<.001

.997

+.001

.047 [.034–.061]

−.035

 Strong

226.269

42

<.001

.986

−.011

.056 [.049–.063]

+.009

 Partial strong

152.187

34

<.001

.991

−.006

.050 [.042–.058]

+.003

Norway

 Configural

66.560

6

<.001

.993

 

.087 [.069–.107]

 

 Weak

49.041

12

<.001

.997

+.004

.047 [.034–.061]

−.040

 Strong

194.135

42

<.001

.982

−.015

.052 [.045–.060]

+.005

 Partial strong

88.911

34

<.001

.994

−.003

.035 [.026–.044]

−.012

Poland

 Configural

23.953

6

<.001

.999

 

.043 [.026–.061]

 

 Weak

54.087

12

<.001

.997

−.002

.046 [.034–.059]

+.003

 Strong

165.163

42

<.001

.992

−.005

.042 [.036–.049]

−.004

Spain

 Configural

144.966

6

<.001

.986

 

.118 [.102–.135]

 

 Weak

131.807

12

<.001

.988

+.002

.078 [.066–.090]

−.040

 Strong

236.637

42

<.001

.981

−.007

.053 [.046–.060]

−.025

Sweden

 Configural

47.064

6

<.001

.995

 

.075 [.056–.096]

 

 Weak

31.601

12

<.001

.998

+.003

.037 [.021–.053]

−.038

 Strong

114.695

42

<.001

.992

−.006

.038 [.030–.046]

+.001

United Kingdom

 Configural

100.643

6

<.001

.995

 

.079 [.066–.093]

 

 Weak

78.061

12

<.001

.996

+.001

.047 [.037–.057]

−.032

 Strong

323.446

42

<.001

.985

−.011

.052 [.046–.057]

+.005

 Partial strong

140.926

34

<.001

.994

−.002

.035 [.029–.041]

−.012

United States

 Configural

79.823

6

<.001

.994

 

.095 [.077–.114]

 

 Weak

78.191

12

<.001

.995

+.001

.064 [.051–.077]

−.031

 Strong

237.685

42

<.001

.985

−.010

.059 [.051–.066]

−.005

  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
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