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Table 6 Detailed model fit with migration background (i.e., native language same as test language) 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 85.551 4 <.001 .996   .079 [.065–.094]  
 Weak 65.431 7 <.001 .997 +.001 .051 [.040–.062] −.028
 Strong 146.139 22 <.001 .994 −.003 .042 [.035–.048] −.019
Austria
 Configural 72.68 4 <.001 .995   .091 [.073–.110]  
 Weak 59.994 7 <.001 .996 +.001 .061 [.047–.075] −.030
 Strong 118.108 22 <.001 .993 −.003 .046 [.038–.054] −.015
Canada
 Configural 164.491 4 <.001 .995   .060 [.053–.068]  
 Weak 136.178 7 <.001 .996 +.001 .041 [.035–.047] −.019
 Strong 264.565 22 <.001 .992 −.004 .032 [.028–.035] −.009
Denmark
 Configural 37.121 4 <.001 .998   .052 [.037–.067]  
 Weak 35.175 7 <.001 .998 .000 .036 [.025–.048] −.016
 Strong 259.287 22 <.001 .984 .014 .059 [.053–.065] +.023
 Partial strong 119.111 19 <.001 .993 −.005 .041 [.034–.048] +.005
France
 Configural 106.976 4 <.001 .994   .094 [.079–.110]  
 Weak 75.066 7 <.001 .996 +.002 .058 [.047–.070] −.036
 Strong 96.052 22 <.001 .995 −.001 .034 [.027–.041] −.024
Germany
 Configural 82.137 4 <.001 .993   .095 [.078–.114]  
 Weak 92.633 7 <.001 .993 .000 .075 [.062–.089] −.020
 Strong 121.364 22 <.001 .991 −.002 .046 [.038–.054] −.029
Ireland
 Configural 132.024 4 <.001 .993   .111 [.095–.127]  
 Weak 91.795 7 <.001 .996 +.003 .068 [.056–.081] −.043
 Strong 246.612 22 <.001 .988 −.008 .063 [.056–.070] −.005
Italy
 Configural 70.996 4 <.001 .996   .091 [.073–.110]  
 Weak 68.216 7 <.001 .996 .000 .066 [.052–.080] −.025
 Strong 85.641 22 <.001 .996 .000 .038 [.030–.046] −.028
The Netherlands
 Configural 57.754 4 <.001 .997   .080 [.063–.099]  
 Weak 46.094 7 <.001 .998 +.001 .052 [.038–.066] −.028
 Strong 110.544 22 <.001 .995 −.003 .044 [.036–.052] −.008
Norway
 Configural 37.756 4 <.001 .996   .065 [.047–.085]  
 Weak 31.434 7 <.001 .997 +.001 .042 [.028–.057] −.023
 Strong 254.662 22 <.001 .972 .025 .073 [.065–.081] +.031
 Partial strong 159.394 20 <.001 .983 .014 .059 [.051–.068] +.017
Slovak Republic
 Configural 110.189 4 <.001 .998   .108 [.091–.126]  
 Weak 86.835 7 <.001 .998 .000 .071 [.058–.084] −.037
 Strong 116.951 22 <.001 .998 .000 .044 [.036–.051] −.027
Spain
 Configural 144.822 4 <.001 .987   .119 [.103–.136]  
 Weak 142.655 7 <.001 .987 .000 .088 [.076–.101] −.031
 Strong 120.345 22 <.001 .991 +.004 .042 [.035–.050] −.046
Sweden
 Configural 37.098 4 <.001 .996   .068 [.049–.088]  
 Weak 27.512 7 <.001 .998 +.002 .040 [.025–.057] −.028
 Strong 160.727 22 <.001 .985 .013 .059 [.051–.068] +.019
 Partial strong 156.084 20 <.001 .985 .013 .061 [.053–.070] +.021
United Kingdom
 Configural 119.614 4 <.001 .995   .087 [.074–.101]  
 Weak 100.439 7 <.001 .996 +.001 .059 [.049–.070] −.028
 Strong 212.626 22 <.001 .991 −.004 .048 [.042–.054] −.011
United States
 Configural 100.785 4 <.001 .993   .109 [.091–.128]  
 Weak 74.171 7 <.001 .995 +.002 .069 [.055–.083] −.040
 Strong 109.647 22 <.001 .994 −.001 .044 [.036–.053] −.025
  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