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Table 4 Invariance tests of the basic CFA model between the Chinese group and American group

From: Are need for affect and cognition culture dependent? Implications for global public health campaigns: a cross-sectional study

Model Description λ2 df p CFI TLI NFI RMSEA AIC ECVI Test ΔCFI ΔRMSEA
M0 Baseline model, no constraints on model parameters 263.124 26 <.001 0.977 0.941 0.966 0.030 607.124 0.283
M1 All factor loadings constrained to be equal 408.270 35 <.001 0.959 0.922 0.947 0.047 704.270 0.329 M1-M0 −0.018 0.017
M2 “Approach” factor loadings constrained to be equal 281.146 31 <.001 0.971 0.949 0.963 0.032 654.146 0.296 M2-M0 −0.006 0.002
M3 “Avoidance” factor loadings constrained to be equal 367.272 31 <.001 0.962 0.943 0.948 0.042 720.272 0.655 M3-M0 −0.015 0.012
M4 All factor loadings constrained to be equal except item NFA_10 292.361 34 <.001 0.969 0.945 0.951 0.039 679.025 0.309 M4-M0 −0.008 0.009
M5 All factor loadings and the vectors of item intercepts constrained to be equal 335.565 73 <.001 0.953 0.929 0.942 0.049 762.515 0.683 M5-M1 −0.006 0.002
M6 All factor loadings and the variances of constructs constrained to be equal 320.461 41 <.001 0.951 0.931 0.944 0.045 738.461 0.398 M6-M1 −0.008 −0.002
M7 All factor loadings and the factor covariance constrained to be equal 518.586 45 <.001 0.946 0.908 0.939 0.061 822.586 0.703 M7-M1 −0.013 0.014
  1. Criteria for accepting the null hypothesis of invariance (Chen et al [43])
  2. ≥ − .010
  3. ≤.015
  4. ΔCFI Change in CFI, ΔRMSEA Change in RMSEA
  5. M0: Testing configural invariance between groups, i.e., H0 = Both groups associate the same subsets of items with the same constructs;
  6. M1-M0: Testing construct-level metric invariance between groups, i.e., H0 = The strength of the relationships between items and their underlying constructs are the same between groups;
  7. M2-M0: Testing the metric invariance of “Approach” between groups, i.e., H0 = The strength of the relationships between 5 approach items and the construct “Approach” are the same between groups;
  8. M3-M0: Testing the metric invariance of “Avoidance” between groups, i.e., H0 = The strength of the relationships between 5 avoidance items and the construct “Avoidance” are the same between groups;
  9. M4-M0: Testing the metric invariance of item NFA_10 between groups, i.e., H0 = The strength of the relationship between NFA_10 and the construct “Avoidance” is the same between groups;
  10. M5-M1: Testing the scalar equivalence of items between groups, i.e., H0 = The values of each item corresponding to the zero value of the underlying constructs are the same between groups;
  11. M6-M1: Testing equivalence of construct variances between groups, i.e., H0 = The variances of “Approach” and “Avoidance” are the same between groups;
  12. M7-M1: Testing the equivalence of construct covariance between groups, i.e., H0 = The covariance between “Approach” and “Avoidance” is the same between groups;