## 4 Analysis Results
### Measurement Model
#### 4.1.4. Discriminant Validity  
To distinguish effectiveness, the square root of the average variance (AVE) of a given structure was compared with the correlation between that structure and other structures [60]. If the square root of the constructed AVE is greater than the off-diagonal elements in the corresponding rows and columns, it indicates that the index is more closely  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Construct** & **Model** & \(\chi^{2}\) & **DF** & \(\Delta\chi^{2}\) & \(\Delta\)**DF** & \(p\)**-Value** & **Target Coefficient** \\ \hline \multirow{2}{*}{CQ} & First order & 353.771 & 113 & \multirow{2}{*}{8.231} & \multirow{2}{*}{2} & \multirow{2}{*}{0.016} & \multirow{2}{*}{0.977} \\  & Second-order & 362.002 & 115 & & & & \\ \hline \multirow{2}{*}{ESE} & First order & 161.225 & 48 & \multirow{2}{*}{16.902} & \multirow{2}{*}{2} & \multirow{2}{*}{0.000} & \multirow{2}{*}{0.905} \\  & Second-order & 178.127 & 50 & & & & \\ \hline \hline \end{tabular} Note: \(\chi^{2}\): Chi-square DF: degree of freedom; CQ: cultural intelligence; ESE: English self-efficacy.  
\end{table}
Table 4: Confirmatory factor analysis of second-order model.  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Construct**} & \multirow{2}{*}{**Item**} & \multicolumn{4}{c}{**Significance of Estimated Parameters**} & \multicolumn{2}{c}{**Item Reliability**} & \multicolumn{2}{c}{**Construct Reliability**} & \multicolumn{2}{c}{**Convergence Validity**} \\ \cline{3-8}  & & **Unstd.** & **S.E.** & **Unstd./S.E.** & \(p\)**-Value** & **Std.** & **SMC** & **CR** & **AVE** \\ \hline ESEL & ESEL1 & 1.000 & & & 0.900 & 0.810 & 0.908 & 0.768 \\  & ESEL2 & 0.926 & 0.041 & 22.475 & 0.000 & 0.845 & 0.714 & & \\  & ESEL3 & 1.021 & 0.042 & 24.600 & 0.000 & 0.883 & 0.780 & & \\ \hline EESES & EES4 & 1.000 & & & 0.819 & 0.671 & 0.860 & 0.672 \\  & EESES5 & 0.972 & 0.052 & 18.551 & 0.000 & 0.840 & 0.706 & & \\  & EES56 & 1.101 & 0.066 & 16.644 & 0.000 & 0.799 & 0.638 & & \\ ESER & ESERT & 1.000 & & & 0.807 & 0.651 & 0.859 & 0.671 \\  & ESER8 & 1.130 & 0.061 & 18.624 & 0.000 & 0.874 & 0.764 & & \\  & ESER9 & 0.935 & 0.058 & 15.999 & 0.000 & 0.773 & 0.598 & & \\ ESEW & ESEW10 & 1.000 & & & 0.783 & 0.613 & 0.836 & 0.631 \\  & ESEW11 & 0.907 & 0.052 & 17.286 & 0.000 & 0.845 & 0.714 & & \\  & ESEW12 & 0.912 & 0.061 & 14.963 & 0.000 & 0.752 & 0.566 & & \\ CQ & MCQ & 1.000 & & & 0.649 & 0.421 & 0.851 & 0.593 \\  & CCQ & 1.205 & 0.151 & 8.002 & 0.000 & 0.808 & 0.653 & & \\  & OCQ & 1.352 & 0.164 & 8.248 & 0.000 & 0.852 & 0.726 & & \\  & BCQ & 1.213 & 0.151 & 8.012 & 0.000 & 0.766 & 0.587 & & \\ ESE & ESEL & 1.000 & & & 0.742 & 0.551 & 0.905 & 0.706 \\  & EESES & 0.909 & 0.073 & 12.491 & 0.000 & 0.852 & 0.726 & & \\  & ESER & 0.891 & 0.074 & 12.072 & 0.000 & 0.845 & 0.714 & & \\  & ESEW & 1.165 & 0.094 & 12.336 & 0.000 & 0.917 & 0.841 & & \\ \hline \hline \end{tabular} Note: Unstd.: unstandardized factor loadings; Std.: standardized factor loadings; SMC: square multiple correlations; CR: composite reliability; AVE: average variance extracted; MCQ: meta-cognitive cultural intelligence; CCQ: cognitive cultural intelligence; OCQ: motivational cultural intelligence; BCQ: behavioral-cultural intelligence; ESE: English self-efficacy listening; ESE: English self-efficacy speaking ESER: English self-efficacy reading; ESEW: English self-efficacy writing; CQ: cultural intelligence; ESE: English self-efficacy.  
\end{table}
Table 3: _Cont._related to the structure. In Table 5, the numbers in bold on the diagonal indicate the square root of AVE. Since all the numbers in the diagonal direction are larger than the non-diagonal numbers, the validity of the discrimination seems to be satisfactory for all constructions.