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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