Fig.1 showed the graphical LASSO network representing the regularized partial correlations among the 35 items, with 223 of 595 edges being non-zero. Most edges were positive correlations which were colored in blue. The stronger weights between the nodes were SE32 and SE33(r=0.55), SE34 and SE35 (r=0.46), WC10 and WC11 (r=0.40). Several negative correlations were colored in red, such as RF8 and WC10 (r=-0.09), WC10 and EHE19 (r=-0.06), WC11and BrF27 (r=-0.05). We suggested that the negative edge weights were relatively small and did not indicate a corresponding association between these items.
The EGA detected a seven-dimensional structure named EGA (all) structure, see Fig.2. However, the dimensional attribution of items was different. EHE16 from Encourage healthy eating subscale clustered into Dimension2. EHE17, EHE18, EHE19, EHE20, BrF25, BrF26, BrF27clustered into Dimension1. EHE21, BrF22, BrF23, BrF24, BrF28 clustered into Dimension 6. The items of Behavior-restricted feeding dimension and Encourage healthy eating dimension were re-clustered. The remaining items aggregated into the same dimension as the original CPCFBS, see Table 1.
Network loading for items on each of their dimensions were in the moderate and large range, with only EHE16, EHE20, RF1 obtained a value of less than 0.15 (small) in their primary dimensions, see Table 2. In addition, EHE16 displayed substantially equivalent cross-loadings in Dimension1,2,7, which were small network loadings to these dimensions.
As shown in Table 3, the frequency of seven dimensions in EGA (all) structure was 0.766. Other network structures were also identified, especially the structure with six dimensions (0.112) and eight dimensions (0.114). The relatively high frequency of the six dimensions and eight dimensions illustrated that EGA (all) structure was unstable. The Table 4 showed that Dimension 1 and 2 from EGA (all) structure presented low structural consistency, with value of 0.69, 0.35, respectively. Therefore, we examined the stability of items within each dimension using the item replication, see Fig3. EHE16 showed relatively low item stability, with the value of 0.35. Combining with Table 2 for verification, EHE16 had low network loading in all dimensions, while item stability was also poor. This suggested that EHE16 cannot be assigned to any of the dimensions. The unstable item directly contributed to the unstable of structural consistency. To increase the consistency of the network structure, we removed EHE16 and re-analyzed the data using the same method. After removing the unstable item, we detected a final seven-dimensional structure (EGA (del) structure) composed of 34 items, see Fig4.The structural consistency of the EGA (del) structure was significantly improved. The frequency of the seven dimensions improved drastically from 0.766 to 0.855, see Table 3. All items replicated in their particular dimensions have a frequency of at least 0.77, see Fig5.
In the EGA (del) network structure, the first dimension Encourage healthy eating contained seven items (EHE17, EHE18, EHE19, EHE20, BrF25, BrF26, BrF27). The second dimension Responsibility for feeding contained eight items (RF1, RF2, RF3, RF4, RF5, RF6, RF7, RF8). The third dimension Forced feeding contained three items (FF29, FF30, FF31). The fourth dimension Content-restricted feeding contained four items (CrF12, CrF13, CrF14, CrF15). The fifth dimension Supervise eating contained four items (SE32, SE33, SE34, SE35). The sixth dimension Behavior-restricted feeding contained five items (EHE21, BrF22, BrF23, BrF24, BrF28). The seventh dimension Weight concerns contained three items (WC9, WC10, WC11).
The model fit measures of latent variable model (the original CPCFBS structure), and the seven dimensions detected by EGA (all) and EGA (del) are displayed in Table 5. The fit indices indicated that the absolute fit and relative fit of EGA (del) structure (χ2=1777.173, p＜0.01, RMSEA=0.057,CFI=0.883, AIC=65500.993, BIC=65914.290) were better than the original CPCFBS structure and the EGA (all) structure, meanwhile the RMSEA of EGA (del) network model reached good benchmark according to the criteria mentioned above.
The reliability of all structures is displayed in Table 6. The McDonald’s Ω of the original structure, EGA (all) structure and EGA (del) structure indicated that all structures had acceptable reliability (0.74 - 0.90), except for the dimension of forced feeding (0.65). The results showed that the EGA structure had nearly same values of the McDonald’s Ω with the original structure. To better determine the robustness of the results, we calculated Cronbach's alpha coefficients for the three structures. The reliability of the three structures revealed that the Cronbach’s alpha coefficient was in alignment with the McDonald’s Ω levels.