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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