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Table 4 Fit indices for multiple-group CFAs of the four-item scale for different levels of measurement invariance

From: Who likes to learn new things: measuring adult motivation to learn with PIAAC data from 21 countries

Model χ2 df χ2/df npar RMSEA (CI) CFI ∆χ2 ∆df ∆χ2/df
Model 1 2256.255 42 53.72 420 0.086 (0.083 0.089) 0.994
Model 2 3045.744 102 29.86 360 0.064 (0.062 0.066) 0.992 1301.509 60 21.69
Model 3a 17977.828 402 44.72 60 0.078 (0.077 0.079) 0.955 14893.465 300 49.64
Model 3b 7702.566 242 31.82 220 0.066 (0.065 0.067) 0.981 4778.658 140 34.13
  1. Model 1 configural invariance without constraints, Model 2 full weak model with factor loading invariance, Model 3a full weak/full strong; Model 3b full weak/partial strong without constraints for all four items on two thresholds (2 and 3); χ 2 χ2 test statistics, df degrees of freedom, npar number of free parameters, CFI comparative fit index, RMSEA root mean square error of approximation. Significant χ2 and ∆χ2 (p < 0.05) are printed in italics