Factor analysis
Because Mardia’s multivariate normality test showed that both multivariate skewness and kurtosis were significant (Mardia skewness=41.39, p<0.001; and kurtosis=326.60, p< 0.001), suggesting that the data failed to maintain normal distribution, the MLR estimator was employed for factor analysis. A sensitivity analysis was also conducted with the WLSMV estimator to compare with MLR, and no significant difference in results emerged.
Table 2 shows the fit indices for the twelve alternative models using the MLR. Of the twelve models, the three-factor bifactor CFA model was unacceptable because of the lack of positive definiteness of the covariance matrix.
As can be seen in
Table 2, the CFI, TLI, SRMR, and RMSEA values for the two-factor models comprising emotional and eudaimonic well-being indicated sufficient fit (CFI=0.955-0.968; TLI=0.939-0.946; SRMR=0.024-0.039; RMSEA=0.061-0.064). Also, the CFI, TLI, SRMR, and RMSEA values for the two-factor models comprising social and hedonic well-being indicated acceptable fit (CFI=0.957-0.973; TLI=0.939-0.961; SRMR=0.024-0.033; RMSEA=0.051-0.064) except for the two-factor model comprising social and hedonic well-being with CFA (CFI=0.881; TLI=0.858; SRMR=0.053; RMSEA=0.098). In addition, the fit indices for the three-factor models, except for the three-factor bifactor CFA model, indicated good fit (CFI=0.968-0.983; TLI=0.944-0.963; SRMR=0.017-0.035; RMSEA=0.050-0.061).
The improvement in model fit was examined using AIC and SSABIC. The two-factor bifactor CFA model (model 2) had an improved fit over the two-factor CFA solution (model 1) (ΔAIC=-39.290, ΔSSABIC=-35.469). Regarding the twofactor ESEM solutions of the MHC-SF, the two-factor bifactor ESEM model (model 4) had a better fit than the two-factor ESEM model (model 3) (ΔAIC=-38.534, ΔSSABIC=-35.258). Also, the fit of the two-factor ESEM solution (model 3) was better than the two-factor CFA model (model 1) (ΔAIC=-4.430, ΔSSABIC=-1.155), though the difference was modest. Concerning the two-factor bifactor solutions of the MHC-SF, the fit of the two-factor bifactor ESEM (model 4) was superior to the two-factor bifactor CFA model (model 2) (ΔAIC=-3.674, ΔSSABIC=-0.944), though the difference was negligible.
Regarding the two-factor ESEM solutions of the MHC-SF, the two-factor bifactor ESEM solution (model 8) was better than the two-factor ESEM solution (model 7) (ΔAIC=-38.534, ΔSSABIC=-35.258). Concerning the two-factor bifactor solutions of the MHC-SF, the two-factor bifactor ESEM (model 8) had better fit than the two-factor bifactor CFA model (model 6) (ΔAIC=-5.966, ΔSSABIC=-8.696).
In addition, the three-factor bifactor ESEM model (model 12) had a better fit than the three-factor ESEM model (model 11) (ΔAIC=-22.525, ΔSSABIC=-19.522). Also, the fit of the three-factor ESEM solution (model 11) was better than the three-factor CFA model (model 9) (ΔAIC=-9.500, ΔSSABIC=-3.494), though the difference was small.
Regarding the CFA solutions of the MHC-SF, the three-factor CFA model (model 9) had a better fit than the two-factor CFA models (model 1 and 5) (ΔAIC=-33.464 and -193.507, ΔSSABIC=-32.919 and -192.961). Also, concerning the ESEM solutions of the MHC-SF, the three-factor ESEM model (model 11) showed a better fit than the two-factor ESEM models (model 3 and 7) (ΔAIC=-38.534, ΔSSABIC=-35.258). In addition, as to the bifactor ESEM solutions of the MHC-SF, the three-factor bifactor ESEM model (model 12) had a better fit than the two-factor bifactor ESEM models (model 4 and 8) (ΔAIC=-22.525, ΔSSABIC=-19.522).
These findings indicated that the bifactor models gave a more precise picture of the structure than the first-order models and three-factor models offered a more accurate representation of the data than the two-factor models. Of the eleven alternative models, the fit of the three-factor bifactor ESEM model was better than the other models.
Table 3 presents the standardized factor loadings of the three-factor bifactor ESEM model of the MHC-SF. Examining parameter estimates in the three-factor bifactor ESEM model, the best fitting model of the alternative models, revealed a well-defined general factor with all loadings above 0.50 (λ=0.638-0.825, M=0.725). The emotional well-being (λ=0.442-0.656, M=0.568) factor accounted for a significant amount of variance when controlling for the general factor, whereas mean target loadings were lower than 0.50 and the lowest loadings on a factor were lower than 0.30 in social wellbeing (λ=0.042-0.613, M=0.302), and psychological well-being (λ=-0.072-0.388, M=0.260) factors, indicating reduced specificity after controlling for the general factor. In social well-being factor, three social well-being items (items 6, 7, and 8) had a salient loading on this factor (λ≥0.30) while two social well-being items (items 4 and 5) did not load on the intended factor (λ<0.30). Three psychological well-being items (items 12, 13, and 14) had a salient loading on the psychological well-being factor (λ≥0.30) while three psychological wellbeing items (items 9, 10, and 11) failed to load on the intended factor (λ<0.30).