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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