Estimating and validating the structure of feeding behavior networks

Purpose Network analysis has been widely used in psychometrics over the past decade, yet it is unknown that whether this methodology could be applied in the field of child health assessment such as caregivers’ feeding behavior and child eating behavior. Our study leveraged network psychometrics method to estimating and examining the network structure of Chinese Preschoolers’ Caregivers’ Feeding Behavior Scale (CPCFBS), and compared the applicability of network methods in the feeding behavior scale. Methods The CPCFBS was previously applied in a sample of 768 preschoolers’ caregivers, used to estimate the structure of feeding behavior networks. Network structure was estimated with Gaussian Graphical Model. Dimensionality was detected using Exploratory Graph Analysis (EGA). The network structural consistency was tested using EGA bootstrap. The network structure was compared with the original structure using model fit indices and reliability. Results A seven-dimensional EGA network was explored after rearranging four items and deleting one item with unstable structural consistency. The absolute fit and relative fit of EGA structure were better than the original structure. The EGA structure had nearly same values of the reliability with the original structure. Conclusion Our study presented a novel perspective for feeding behavior analytical strategies, and demonstrated that network analysis was applicable and superior in exploring the structure of feeding behavior scales. Level of evidence Level V, cross-sectional descriptive study. Supplementary Information The online version contains supplementary material available at 10.1007/s40519-022-01489-1.


Introduction
Childhood obesity has become a serious public health problem in China nowadays [1]. Studies have shown that many metabolic diseases, cardiovascular diseases, and cancers were closely related to obesity in childhood [2]. The age of 3-6 years is the preschool age in China and is also a critical period for obesity prevention [3]. Evidence suggested that caregivers' feeding behaviors shape children's eating habits and play an important role in childhood obesity [4,5]. Caregivers control when, what, and how their children eat and drink, as well as provide the eating environment to set the emotional tone for eating occasions [5]. It is therefore critically important to identify inappropriate caregivers' feeding behaviors in children's early stage.
Feeding behavior is a complex system associated with a variety of factors. To accurately assess feeding behavior, several scales were developed and validated based on different race, culture, and eating habits [5][6][7]. Recently, Hao Zhang and Xinrui Li have contributed equally to this manuscript, and they are co-first authors.

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Chinese Preschoolers' Caregivers' Feeding Behavior Scale (CPCFBS) has been developed and evaluated using standard development process [8]. The researchers selected items and extracted dimensions accordingly based on the characteristics of Chinese dietary culture, such as feeding environment of single-child families and caregivers' excessive concern about children's weight [8]. As a validated scale, the CPCFBS has been promoted for use in some regions of China.
Scale development is mostly concerned with measurement construction and performance evaluation. Traditional measurement theory [e.g., Classical Test Theory (CTT), Generalizability Theory, and Item Response Theory] consider latent variable models as a standard conceptualization of measurement [9] in which observational variables were seen to be incurred by a common underlying cause [10]. Nevertheless, network analysis elaborates on the occurrence of observational variables as led by their mutual associations and interactions and thus to form an interconnected network [11]. Mutual influence among variables is usually measured by regularized partial correlations [12]. Network analysis has been widely used to explore structures of psychological, biological, and other systems [13] and researchers have demonstrated that network analysis can be used as a new approach to identify the structure of complex systems with interacted elements [11,14,15]. Network analysis informs a novel perspective to understand scales [16]; however, it has not been developed in the use of children's health monitoring.
In this study, we leveraged network psychometrics method to conduct an exploratory study of the CPCFBS by estimating the network structure, using a large-scaled dataset of Chinese caregivers. Based on the network analysis approach and previous research, we expected to provide a novel perspective on the application of network methods, aiming at demonstrating how the network model can be applied to the establishment of dataset and the validation of network structures (e.g., dimensionality, structural consistency) in the feeding behavior scale research areas.

Data
Data were from the CPCFBS research [8] which specifically aimed at urban and rural caregivers whose children were in kindergartens located in the city of Jinan and Xi'an, China. The inclusion criteria for the participants and data collection procedures were presented in detail in the literature [8]. A sample of 768 preschoolers' caregivers was recruited at baseline. The caregiver was defined as "the primary caregiver cared for the child's daily living (e.g., diet, sleeping, and activity) at home after school and over the weekend" [8]. All participants completed the CPCFBS in its entirety. Demographic characteristics of the participants are shown in Table S1. Among all participants, 52% were from urban and 48% were from rural area, 76.2% were the children's parents and 23.8% were the children's grandparents and others. 53.4% of the children were male and 46.6% were female. The age of children ranged from 3 to 6 years (M = 4.9 years old, SD = 1.0), of which 31.5% were 3 to 4 years old, 33.5% were 4 to 5 years old, and 35.0% were 5 to 6 years old. The median caregiver education level was senior high school. The median family monthly income was $750-$1500.

Measures
The CPCFBS developed by Jing Yuan [8] was used in our investigation. The measure was comprised of 35 items and seven dimensions: Responsibility for feeding, Weight concerns, Content-restricted feeding, Behavior-restricted feeding, Encourage healthy eating, Forced feeding, and Supervise eating. The items were measured on a 5-point Likert scale, ranging from 1 "never" to 5 "always". According to the manual, reverse items were negatively scored, and higher scores of each dimension indicated a greater tendency of caregivers to feed their children in this manner.
The CPCFBS was developed according to a strict standard scale development process. CTT statistical method was used to select items. The main techniques used in CTT to assess the data were Principal Component Analysis and factor analysis, which was constructed based on latent variable models and focused on extracting common covariates among variables to generate factors [17].

Network estimation and visualization
A network comprised variables (e.g., CPCFBS items) that were presented by nodes, and edges between nodes represented the associations between variables [23]. For our multivariate normal data, we chose the qgraph and bootnet package to estimate the CPCFBS network with Gaussian Graphical Model (GGM), in which edges represented partial correlations between nodes [24]. It was critically important that the associations in GGM construction helped us distinguish the risky feeding behavior of preschoolers' caregivers [23]. As the number of nodes increased, more edges would be estimated. However, since many edges are spurious correlations, the larger number of nodes may lead to model over-fitting and unstable network [23,25]. The Graphical Least Absolute Shrinkage and Selection Operator (GLASSO) was used to penalize and shrink edge weights, and set edges with small partial correlations to zero to result in a sparse network that reflects only the most accurate edges [26]. We estimated the best-fitting network model using the Extended Bayesian Information Criterion (EBIC) [27,28], the tuning parameter of EBIC determines the sparseness of the network. The higher value of (ranges from 0 to 1), the more parsimonious the models would be estimated [12]. The function "EBICglasso" in bootnet package was used with the default value of = 0.5. To visualize the network system, the Fruchterman-Reingold algorithm was used to determine nodes layout [29], which distributed strong connected nodes closer to the center of the network or otherwise decentralized [23].

Dimension detection
In the network, nodes form clusters (communities, dimensions) according to the strength of the relevance. Recent studies have proved that network was statistically equivalent to traditional latent variable model, yet their mechanisms were different [30]. To accurately estimate the number of dimensions of CPCFBS networks, we employed EGA, which outperformed the traditional factor analysis methods (e.g., exploratory factor analysis, parallel analysis) [31]. EGA applied the default community detection algorithm walktrap [32] to investigate the number of communities and automatically classify items to their corresponding community. The algorithm using "random walks" iteratively traversed over neighboring edges, with larger edge weights being more probable paths of travel, a community was then detected by its proportion of densely connected edges to sparsely connected edges [33]. The output of the network detected by EGA was a plot that the nodes of the same cluster were colored separately to give an intuitive visual interpretation [34].
After dimensionality was detected using the EGAnet package, we calculated network loadings which is roughly equivalent to factor loadings [35]. Network loadings indicate the contribution of each item to more than one dimension (i.e., cross-loading) and the items that are poorly related to any dimensions [35]. Compared to factor loadings, network loadings are evaluated after the number of factors has been extracted from the network's structure. Nodes are assigned to particular domains via a community detection algorithm rather than the traditional factor analytical standard of their largest loading in the loading matrix [35]. Christensen and Golino [35] recommended effect size guidelines: small (0.15), moderate (0.25), and large (0.35) network loadings.

Structural consistency
Structural consistency is defined as the extent to which causally coupled nodes cluster a coherent community within a network [36]. We evaluated structural consistency by the parametric bootstrap EGA (bootEGA) [33] (2500 bootstrap samples), which estimated a network and generated new replications with the same number of nodes as the original network, and then repeated the step until the desired number of bootstrap samples and the replicated datasets were achieved [37]. We explained structural consistency in two ways: (1) frequencies that the dimensions identified, and (2) frequencies that nodes clustered into their particular dimensions as well as other dimensions in the replicated datasets. The latter approach was called item stability [37]. Lower item stability indicated lower structural consistency [38]. A value of 0.75 was set as an acceptable standard for the dimension replication and item stability, advised by Christensen and Golino (2019).

Model fit
Previous studies suggested that the network model and latent variable model can be implemented to explain the variance-covariance structure of observational curious variables [39]. The two approaches are alternative to each other. To examine the model fit, we compared the original structure, EGA (all) structure, and EGA (del) structure via the absolute fit and the relative fit [40]. The absolute fit indicates whether the item responses can be properly interpreted by the dimensional structure. The relative fit indicates which dimensional structure is more suitable as opposed to others. We evaluated the absolute fit using the values of the root-mean-square error of approximation (RMSEA) and the comparative fit index (CFI). The values of RMSEA ≤ 0.05 and CFI ≥ 0.97 indicate a good absolute fit, RMSEA ≤ 0.07 indicate an acceptable absolute fit, and CFI between 0.95 and 0.97 is considered acceptable. The lower value of the Akaike Information Criterion (AIC) and the Bayesian Information Criterion (BIC) indicate the better relative fit [39]. The lavaan package was used for this analysis.

Reliability
To date, Cronbach's alpha coefficient is the most popular approach of reliability. However, researchers suggested a more sensible index of internal consistency: McDonald's Ω [41]. The McDonald's Ω outperformed Cronbach's alpha coefficient in situations such as (A) fewer and more realistic assumptions, and (B) fewer problems associated with inflation and attenuation of internal consistency estimation [22]. We used the R package MBESS to investigated the reliability of full subscale of the original CPCFBS structure and EGA structure with the McDonald's Ω and Cronbach's alpha coefficient. For all 95% Cis, coefficients were computed across 1000 bootstrap samples. Same as Cronbach's alpha coefficient, the score of McDonald's Ω above 0.7 was considered satisfactory for internal consistency [42]. Figure 1 shows 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), and 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), and WC11 and BrF27 (r = -0.05). We suggested that the negative edge weights were relatively small and did not indicate a corresponding association between these items.
Network loading for items on each of their dimensions was 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 Dimension 1, 2, 7, which were small network loadings to these dimensions.

Structural consistency
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. Table 4   Table 2 Dimensions identified by exploratory graph analysis and network loadings for each item Note. The numbers in bold represent the network loadings of the main attribution dimension of items. The meaning of the abbreviations of the items refers to Table 1 Item shows that Dimension 1 and 2 from EGA (all) structure presented low structural consistency, with value of 0.69 and 0.35, respectively. Therefore, we examined the stability of items within each dimension using the item replication; see Fig. 3. 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 Fig. 4. 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 Fig. 5.

Model fit
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

Reliability
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.

Discussion
The purpose of this study was to re-explore the structure of the CPCFBS using network analysis in a large sample of preschoolers' caregivers from China. To the best of our knowledge, this is the first study applying network analysis to the study of feeding behavior. We aimed to investigate whether a network structure would better explain the CPCFBS dimensionality and its item responses. Many researchers have adapted the ideology of some measurements in psychology to evaluate caregivers' feeding behavior scales. With the intersection development of psychometrics, new methods like network analysis have been widely used in psychological scales and have been approved to have remarkable advances. For instance, Hudson Golino et al. [35] investigated the structure of the Children's Concentration and Empathy Scale (CCES) using network analysis. They refined and reassessed the CCES for better interpretation. Ribeiro Santiago et al. [35] employed a multimethod approach (traditional method and network analysis) to evaluate the EQ-5D-5L. The results of their research showed excellent psychometric properties. Therefore, it was worth to try to investigate the feeding behavior scale using network analysis. The different methods brought novel and interesting information on the structure.
In this study, we demonstrated the use of GGM to investigate relationships between items and implemented EGA to detect the dimension. After testing the structural consistency, we finally acquired a seven-dimensional network structure with 34 items. The results suggested that the clustered dimensions were slightly different in the original CPCFBS structure and the EGA (all) structure. The EGA structure appeared to have better statistical power. Our study illustrated that network analysis was a fitting method to explore the feeding behavior of caregivers for preschoolers.
In terms of network estimation, its essential feature was to focus on interrelationships among observational variables (e.g., scale items), which was not presented in the traditional structural exploration [30]. We found items with strong associations by analyzing the partial correlation of the global data. For instance, the highest weight of correlation examined for SE32 I will supervise my child so she or he drinks less (e.g., cola, pulpy juices) and SE33 I will supervise my child so she or he eats less high-fat food (e.g., beef jerky, sausage, fried food) indicated that caregivers supervised their children's drinks and high-calorie food in the meantime. The results suggested that the analysis and guidance on caregivers' certain feeding behaviors should extend to the items with strong correlations, since they may occur simultaneously.
The dimensionality structure detected via EGA was consistent with the original CPCFBS seven-dimensional structure, while certain items were rearranged. EGA (all) structure was unstable, since its frequencies of dimensions identified by bootEGA were dispersed and the structural consistency was relatively low. One of the reasons that some dimensions were not as stable as others was because of the low stability of items. [33]. Interestingly, EHE16 I will serve my child fresh vegetables and fruits each day was not consistently clustered into a unique dimension (i.e., network cross-loadings) and had a serious problem with item stability. It was probably the main factor that led to the instability of the EGA network structure. We decided to remove the unstable item to obtain a reliable network structure [EGA (del) structure]. The rearrangement of Encourage healthy eating items (EHE21) and Behavior-restricted feeding items (BrF25, BrF26, BrF27) was found in this sample. It was reasonable that the assignment of these three items to respective  dimensions could be interpreted from Chinese contextual background. The computation of model fit provided a robust support for the EGA (del) seven-dimensional structure. All the coefficients suggested that the network structure was stable enough to meet the requirements. The reliability of all three structures were consider to be equivalent and adequate. Although the network analysis eliminated a small number of items from CPCFBS, the approach enabled the CPCFBS to be more optimally structured, which was believed to be more important. The structure explored through the method of network analysis also proved that the CPCFBS scale was a well-developed scale and could be recommended for use.

Limitations and future directions
Our results indicate that network analysis is a useful tool to explore the structure of feeding behavior. Yet, there are a few limitations worth to notice when using this method. First, network analysis is the process of capturing the associations among items and it requires the analysis of the stability of items and structures. Thus, the items are the fundamental condition for analytical process. To ensure that the final structure is both stable and reliable, the researchers need to find a balancing state between item selection and classification. Second, GGM is the cross-sectional model, so that it can only analyze the correlation of the items without interpreting the causality of the items. In future research, we could investigate network time-series analysis to study the cause of feeding behavior items. Finally, due to the lack of application of network analysis in the field, more data from different measurements should be used to replicate the results with the new network structure of feeding behaviors. Further research is needed to explore the centrality, an exclusive measurement feature for network analysis, and to address practical challenges in feeding behavior. This may help researchers to identify the priority targets (e.g., highly central items) and corresponding outcomes in different types of feeding behavior.

What is already known on this subject?
The caregivers' feeding behavior are associated with childhood obesity. Previous studies to develop and validate measures of caregiver's feeding behavior provide a powerful base. Nevertheless, the feeding behavior structure estimated with the novel network analysis has not been investigated.

What this study adds?
The current study employed network analysis to investigate the CPCFBS in large sample of Chinese preschoolers' caregivers. A seven-dimensional scale structure was obtained by deleting one unstable item and rearranging four items. The dimensional structure was more stable than that of the original CPCFBS. The evaluation indicators of the network structure were satisfactory. Our research provided evidence that children health behavior scales can be well conceptualized as a network analysis system.