The relationship between social adaptation and parenting styles in left-behind and non-left-behind children: a network analysis

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Fu, Qinqiu Gao, Xiuli Guo, Binrong R. Dai This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6169635/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Numerous theoretical and empirical studies have demonstrated that parenting styles significantly influence the social adaptation of left-behind children. Previous research typically categorized parenting styles into distinct types before investigating the relationship between these types and the overall social adaptation levels of left-behind children. However, this approach did not allow for an exploration of the specific dimensions of parenting styles and social adaptation that may be directly related to one another. This study use network analysis to conceptualize parenting styles and social adaptation as a network of interrelated dimensions. The objective is to identify key dimensions and to examine the correlations among these dimensions. A total of 2,452 children were included in this study (n left-behind =713, n non-left-behind =1739;Mage = 12.13, SD = 2.95). The results indicated that interpersonal adaptation and learning adaptation are core dimensions within the social adaptation(SA) networks of both left-behind and non-left-behind children. interpersonal adaptation , learning adaptation , father refused , and mother refused constitute the core dimensions of the parenting styles and social adaptation (PS-SA) network for left-behind children, while interpersonal adaptation , learning adaptation , mother refused ', and mother's emotional warmth form the core dimensions of the PS-SA network for non-left-behind children. The network comparisons indicate that the connection strengths between father refused and interpersonal adaptation , father refused and learning adaptation , as well as father's emotional warmth and learning adaptation are more robust in the PS-SA network of left-behind children; the connection strengths between mother's emotional warmth and positive emotional adaptation , as well as interpersonal adaptation and learning adaptation , are stronger in the PS-SA network of non-left-behind children. This study contributed to the conceptualization and visualization of the relationship between parenting styles and social adaptation. The findings can assist parents and schools in implementing more targeted adaptation education for left-behind children. Social Adaptation Parenting Styles Network Analysis Rural Left-Behind Children Warning timeliness analysis Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Introduction Left-behind children are young individuals under the age of 17 whose parents are employed in distant locations, resulting in their being looked after by a single parent or without direct guardianship. As of 2020, the number of such children in China reached 41.77 million 1 . The absence of parental care can leave these young individuals feeling neglect and discrimination 2 , which may diminish their sense of safety and give rise to a spectrum of adverse emotional responses, including depression, anxiety, and isolation 3 – 4 . Furthermore, they may develop patterns of social withdrawal and even aggressive behavior 5 – 6 , impeding their integration and adaptation to society. Consequently, the social adaptation of left-behind children has garnered considerable attention. Social adaptation encompasses an individual's ongoing efforts to align their physical and psychological well-being with the shifting demands of their social environment 7 . It's a multifaceted concept that evolves with an individual's developmental stage. Emotional responses and behavioral expressions that reflect individual social adaptation are thought to be influenced by both personal developmental phases and the broader social environment. For left-behind children, the challenges of social adaptation may vary in relevance and significance based on the child's developmental stage and the specific social context in which they find themselves 8 . Research on the social adaptation of left-behind children has been approached from two primary orientations. The first direction involves categorizing these children into groups with varying levels of social adaptation based on specific dimensions, followed by a comparison of the differences among these groups. For instance, LI et al. utilized latent class analysis (LCA) to categorize left-behind children into three groups: well-adapted, difficult to adapt, and impulsive, according to their emotional and behavioral challenges 9 .This study revealed significant gender and grade variations in emotional and behavioral issues among rural left-behind children across these categories. The second research direction involves comparing the overall social adaptation scores of rural left-behind children with those of non-left-behind children to evaluate their levels of social adaptability. Meanwhile, a meta-analysis of 13 studies found that left-behind children exhibited lower levels of social adaptability. The first research direction focused on a single dimension of social adaptation, neglecting the interaction between different dimensions 10 .The first research direction focuses solely on the social adaptation of left-behind children from a single perspective, neglecting to explore the interrelationships among various dimensions of social adaptation. The second research direction, rooted in the traditional latent variable model, assumes that all dimensions of social adaptation are influenced by common factors and that each dimension contributes equally to social adaptation. However, these orientations fail to pinpoint the key adaptive dimensions crucial for the development of left-behind children. In response to these shortcomings, researchers have proposed estimating the complex relationships among various social adaptation issues, including depression, through the lens of complex systems 11 . They utilized graphical model visualization to conceptualize social adaptation as a complex network system, interconnected across multiple dimensions, with nodes and connecting lines representing the network. This approach is referred to as network analysis. Network analysis was conducted by treating each dimension of social adaptation as a network node. The connections between these nodes represent the relationships among the dimensions, while the thickness of the connections indicates the strength of the correlations. Additionally, the node centrality index reflects the significance of each node within the network. This approach underscores the interconnections among various dimensions of social adaptation and highlights key dimensions through statistical modeling 12 . It effectively addresses the limitations of traditional latent variable models, which often struggle to capture the complex patterns of connections between dimensions, thus providing a foundation for analyzing the most critical aspects of children's development 13 . Consequently, the primary objective of this study is to explore the structure and core dimensions of the social adaptation network among rural children, as well as to compare the differences in network structure between left-behind children and their non-left-behind counterparts. Ecological systems theory posits that the family plays a crucial role in the microsystem 14 . Within the family unit, parenting style emerges as a key protective factor with significant implications for the social adaptation of left-behind children 15 . Studies have shown that positive parenting practices, such as emotional warmth, are associated with lower levels of anxiety, depression, loneliness, and problem behaviors, while enhancing happiness in left-behind children 16 – 17 . Conversely, negative parenting styles characterized by rejection, over-protection have been linked to adverse social adaptation outcomes in these children 18 . Furthermore, researches indicate that parenting styles not only have a direct impact on the social adaptation of left-behind children, but also exert indirect effects through variables like self-control and parent-child conflict 19 – 20 . Numerous studies have indicated that parenting styles significantly impact the social adaptation of rural left-behind children. However, existing studies have two main limitations. Firstly, most studies have focused on mothers' parenting styles, neglecting the influence of fathers' parenting behaviors. Hoeve et al. conducted a meta-analysis of 161 studies and discovered that less than 20% of them specifically examined fathers' parenting behaviors 21 . Family systems theory suggests that both parents' parenting styles interact and influence each other rather than acting independently 22 . Therefore, it is essential to simultaneously consider the effects of both father's and mother's parenting styles on the social adjustment of rural left-behind children within in a unified model.Secondly, prior findings have mainly used regression analysis to explore the influence of parenting styles on social adaptation, neglecting the specific mechanisms through which parenting styles directly influence social adaptation. Utilizing network analysis, researchers can enhance their comprehension of how parenting styles influence social adaptation and create tailored intervention strategies for improvement. Therefore, the second aim of this study is to employ network analysis techniques to investigate the intricate connection between parenting styles and social adaptation. Additionally, the research seeks to analyze the structural variances in the relationship network between parental parenting styles and social adaptation among left-behind children and non-left-behind children, offering empirical data to elevate the social adaptation levels of rural left-behind children. Methods Participants A total of 2,919 children participated in the study. After excluding participants due to incomplete data or identical selecting responses (i.e., selecting the same number), the final sample comprised 2,452 participants, yielding a valid response rate of 84.00%. The sample was approximately evenly distributed by gender, consisting of 1,095 boys (48.9%) and 1,143 girls (51.1%). Participants were aged between 9 and 16 years and were categorized into two groups: left-behind children (n = 713; age range: 9–16; Mage = 12.36, SD = 2.93) and non-left-behind children (n = 1,739; age range: 9–16; Mage = 12.03, SD = 3.08). The gender distribution was similar in both groups, with 48.7% females among left-behind children and 51.5% among non-left-behind children. Procedure For the recruitment of both left-behind and non-left-behind children, we selected nine primary and secondary schools situated in the rural regions of Yancheng, Lianyungang, and Taizhou in Jiangsu Province, China. Data collection took place in December 2022, during which participants completed the questionnaire in approximately 20 to 30 minutes. In accordance with the guidelines established by the ethics committee, participants provided informed consent. We obtained research consent from school leaders and head teachers, while ensuring parental informed consent for participants aged 15 years or younger. This study received approval from the ethics committee of Yancheng Teachers University. All procedures adhered to the ethical standards set forth by the responsible committee on human experimentation and complied with the Helsinki Declaration. Measurements Social Adaptation The social adaptation of rural children was assessed with the Rural Children Social Adaptation Questionnaire (RCSAQ) 7 , a widely utilized tool to evaluate the social adjustment of children in rural China. The scale includes five dimensions: interpersonal adaptation, learning adaptation, positive emotional adaptation, cognitive adaptation, and life adaptation, comprising a total of 26 items on a 5-point Likert scale ranging from 1 (not like me at all) to 5 (completely like me). Each dimension represents a positive aspect, and higher scores indicate a higher level of social adaptation for the rural children. The overall Cronbach's α coefficient for the scale was 0.89, and the Cronbach's α coefficient of each dimension was between 0.83 and 0.90. Parenting Styles Parenting styles was assessed with Chinese version of the short-form Egna Minnen av Barndoms Uppfostran (s-EMBU) 23 . The s-EMBU consisted of two subscales: one for fathers and one for mothers. Each subscale is further divided into three dimensions: emotional warmth, rejection, and over-protection. Emotional warmth is considered a positive dimension, while rejection and over-protection are viewed as negative dimensions. In total, the overall scale comprises a total of 42 items, with each subscale contains 21 items that are identical in content. Each item was rated on a 4-point Likert scale, ranging from 1 = strongly disagree to 4 = strongly agree. A higher score indicates a higher tendency for the child's father or mother to exhibit this particular parenting style. The overall Cronbach's α coefficient for the scale was 0.91, and the Cronbach's α coefficient for two subscales were 0.90 and 0.93. Statistical Analyses Questionnaires were distributed and collected on-site, resulting in some missing values in the item-level data. To address this, we employed the average to impute the missing values. Prior to conducting any analyses, we assessed the data for normality of distribution by examining skewness and kurtosis. The skewness values ranged from -0.56 to 0.84, while the kurtosis values ranged from -0.65 to 0.70, both of which fall within acceptable ranges (skewness < 3 and kurtosis < 10) 24 . In this study, SPSS version 25.0 was used for descriptive statistical analysis, internal consistency reliability test and correlation analysis, and R4.3.1 in RStudio 1.2.5033 was was used used to estimate PS-SA network structure and network comparison. The network analysis approach follows the standard guidelines published by Epskamp 25 . Network Estimation The network structure of continuous variables was estimated using the EBICglasso function from the qgraph package 26 . We estimated a Gaussian graphical model (GGM) using the graphical lasso (i.e., glasso) in combination with the extended Bayesian information criterion (EBIC) 27 . In this study, we estimated the SA network and PS-SA network for three groups: left-behind children, non-left-behind children, and the overall sample of children. In the network models, each variable was designated as a 'node' and the connections between variables were denoted as 'edges'. The thickness of the edges in the network diagram indicates the strength of the connections between nodes, with thicker edges denoted stronger relationships and thinner edges denoted weaker relationships. In the current models, we have set the gamma hyper parameter to a default value of 0.5. Furthermore, to enhance visualization across the three networks, we utilized the averageLayout function from the qgraph package. Centrality estimation The centrality Plot function in the graph package was employed to calculate three commonly used indices of centrality: strength, closeness, betweenness. The strength centrality was assessed by summing all edges for each node, indicating a higher value for nodes with multiple symptoms occurring simultaneously 28 . Closeness centrality was assessed by calculating the reciprocal of the sum of shortest path lengths between all nodes, reflecting the average distance between nodes and all other nodes in the network. A higher closeness centrality suggests that a symptom's impact spreads quickly to other symptoms 29 . Betweenness centrality was assessed by measuring the shortest path lengths between any two nodes, indicating nodes that act as bridges connecting different symptoms and potential target symptoms for interventions 30 . In addition to the three traditional indices of centrality, this study also employs expected influence centrality, which is defined as the sum of the edge weights connected to a node. A higher expected influence centrality indicates greater influence of the node within the network structure. Unlike traditional methods of measuring centrality, the calculation of the expected influence index retains the signs of edge weights that are less than zero, rather than taking their absolute values. This approach allows for the consideration of both positive and negative relationships within the network, thereby facilitating a more accurate assessment of node influence 31 . Network accuracy and stability The bootnet package was utilized to estimate accuracy and stability in the network model. Initially, the accuracy of edge weights was assessed by bootstrapping 95% confidence intervals (i.e., CIs) of the edge weights. Narrow bootstrapped CIs enoted low sampling variability in edge-weights, indicating that an accurate network was estimated. Subsequently, node centrality stability was evaluated using a case-dropping subset bootstrap method to determine how well the order of centralities was maintained across different subsets of data. The correlation stability coefficient (CS-coefficient) was employed to quantify this stability, measuring the maximum drop in proportions required to retain highly correlated nodes (r > 0.7). The CS-coefficient above 0.25 was considered acceptable, while a value exceeding 0.5 was deemed excellent 24 . Lastly, bootstrapped difference tests were conducted on centrality indices of the nodes to ascertain if they exhibited significant differences from each other. Network comparison The Network Comparison Test package was used to compare the networks of rural left-behind children and non-rural left-behind children. Three tests were conducted to evaluate these differences: a test for network structure invariance, a test for global strength invariance, and a test for edge strength invariance 32 . The network structure invariance test assessed variations in the strength of the maximum edge within the network; the global strength invariance test assessed differences in the total edge strength; and the edge strength invariance test examined variances in specific edges within the network. Results Descriptive statistics and correlation analyses Table 1 presents the descriptive statistics for the study variables. As shown in Figure 1, father refused (FR) (P<0.05), mother refused (MR) (P<0.05) were significantly negatively associated with interpersonal adaptation(IA), learning adaptation (LA), positive emotional adaptation (PEA) and cognitive adaptation (CA). mother's emotional warmth (MEW) (P<0.001) and father's emotional warmth (FEW) (P0.05) and paternal overprotection (PO) (P>0.05) did not show significant relationships with IA, LA, CA, and AL. Additionally, the correlation between MR, FR, and AL (P>0.05) was also found to be non-significant. Table 1. Descriptive statistics for main variables . Variable left-behind (n=713) non-left-behind (n=1739) all of children (n = 2452) Min Max M ± SD Min Max M ± SD Min Max M ± SD 1 MR 6 23 1.74 ± 0.66 6 23 1.67 ± 0.60 6 23 1.70 ± 0.62 2 MEW 7 28 2.90 ± 0.72 7 28 3.01 ± 0.68 7 28 2.97 ± 0.69 3 MO 7 28 2.36 ± 0.57 7 28 2.34 ± 0.56 7 28 2.34 ± 0.56 4 FR 6 24 1.68 ± 0.63 6 24 1.65 ± 0.62 6 24 1.67 ± 0.63 5 FEW 7 28 2.85 ± 0.72 7 28 2.92 ± 0.72 7 28 2.88 ± 0.72 6 PO 7 28 2.30 ± 0.54 7 28 2.31 ± 0.50 7 28 2.31 ± 0.51 7 IA 13 50 3.98 ± 0.69 10 50 4.10 ± 0.68 10 50 4.02 ± 0.69 8 LA 6 30 3.92 ± 0.82 10 30 4.02 ± 0.78 6 30 3.94 ± 0.80 9 PEA 4 20 3.83 ± 0.89 4 20 3.98 ± 0.83 4 20 3.89 ± 0.86 10 CA 3 15 4.20 ± 0.76 3 15 4.29 ± 0.72 3 15 4.23 ± 0.74 11 AL 4 15 3.68 ± 0.96 4 15 3.75 ± 0.92 4 15 3.66 ± 0.93 Social adaptation networks Network estimation To comprehend the network structure of social adaptation (SA), we estimated three regularized networks based on left-behind children (Figure 2A), non-left-behind children (Figure 2B), and overall children(Figure 2C), encompassing all 5 dimensions. This resulted in a total of 10 edges (5*(5-1) / 2). In the social adaptation network of the overall sample of children and the non-left-behind children sample, there are 10 edges with non-zero weights (mean weight 0.05 and 0.06).The social adaptation network for left-behind children includes 9 edges with non-zero weights (mean weight 0.04). Figure 2 demonstrates the significant strength of internal connections within each dimension. Centrality estimation Fig 3 illustrates the centrality of each dimension in the three SA networks. The highest strength centrality was observed in IA and LA, showing significant differences from the strength centrality of other dimensions. This suggests that these two dimensions had the most profound impact on the individual.The dimensions of IA and LA demonstrated the highest closeness centrality, suggesting their significant potential to quickly impact other dimensions. IA had the highest betweenness centrality among non-left-behind children and children in general, whereas both IA and LA had the highest betweenness centrality among left-behind children. The dimensions of IA and LA demonstrated the highest closeness centrality, suggesting they have a more significant impact on the other items in the network. The dimensions of IA and LA demonstrated the highest expected influence centrality, suggesting they have a more significant impact on the other items in the network. Ultimately, IA and LA emerged as the core dimensions in the three SA networks. Network accuracy and stability The results of edge-weight bootstrapping (Table 2) indicate that the three network estimations were moderately accurate. The CS coefficients for strength, closeness, and betweenness, and expected influence in all three networks are above 0.50, suggesting that the overall network stability was excellent. Table 2. CS-coefficient of different groups in SA network structures. Betweenness Closeness Strength Expected Influence All of children 0.128 0.750 0.750 0.750 left-behind children 0.517 0.749 0.749 0.749 Non-left-behind children 0.129 0.750 0.750 0.750 Network comparison Network comparisons between left-behind children and non-left-behind children were conducted through three tests. First , the network structure invariance test, revealed no significant differences in the overall network structure between the two groups (p=0.08>0.05), indicating similar structures. Second, the global strength invariance test, also showed no significant differences in the strength of SA networks (p=0.15>0.05). Third, the edge invariance test highlighted that certain edges differed significantly between left-behind children and non-left-behind children (left-behind children=1.73, non-left-behind children=1.24; p=0.01<0.05). Significant differences were observed at 3 edges between left-behind children and non-left-behind children. More specifically, the edge connecting between CA and AL , CA and LA, as well as AL and PEA were significantly stronger in non-left-behind children compared to their left-behind counterparts (p < 0.05). Combined networks Network estimation To comprehend the network structure of parenting styles and social adaptation(PS-SA), we estimated three regularized networks based on left-behind children(Figure 4A), non-left-behind children(Figure 4B) and overall children(Figure 4C), encompassing all 11 dimensions. This resulted in a total of 55edges (11*(11-1)/2). In the PS-SA network of the overall sample of children and the non-left-behind children sample, there are 29 edges with non-zero weights(mean weight 0.05 and 0.05). The social adaptation network for left-behind children includes 32 edges with non-zero weights(mean weight 0.06). Figure 4 demonstrates the significant strength of internal connections within each dimension. Centrality estimation Figure 5 illustrates the centrality of each dimension in the three PS-SA networks. Prior to constructing the network structure, each dimension was standardized due to the varying scoring methods used in the questionnaires for parenting style and social adaptation. In terms of strength centrality, IA, LA, PEA, and MEW demonstrated the highest strength centrality among non-left-behind children as well as the overall child population. In contrast, IA, LA, FEW, and MEW exhibited the highest strength centrality among left-behind children. In terms of closeness centrality, MEW, LA, IA, and MR demonstrated the highest closeness centrality among non-left-behind children as well as the overall child population. In contrast, IA, LA, FEW, and MEW exhibited the highest closeness centrality among left-behind children. In terms of betweenness centrality, IA, MR, LA, and FEW demonstrated the highest betweenness centrality among non-left-behind children; MR, MEW, IA, and FEW had the highest betweenness centrality among overall child population;and IA, FEW, LA and MR exhibited he highest betweenness centrality among left-behind children. In terms of expected influence centrality, LA, IA, PEA, and PO were identified as the most influential variables across the three networks. Network accuracy and stability The results of edge-weight bootstrapping (Table 3) indicate that the three network estimations were moderately accurate. The CS coefficients for strength, closeness, and betweenness, and expected influence in all three networks are above 0.50, suggesting that the overall network stability was excellent. Table 3. CS-coefficient of different groups in PS-SA network structures Betweenness Closeness Strength Expected Influence All of children 0.517 0.750 0.750 0.750 left-behind children 0.128 0.595 0.749 0.749 Non-left-behind children 0.516 0.750 0.750 0.750 Network comparison Network comparisons between left-behind children and non-left-behind children were conducted through three tests. First , the network structure invariance test, revealed no significant differences in the overall network structure between the two groups (p=0.13>0.05), indicating similar structures. Second, The global strength invariance test showed a significant difference in PS-SA network strength (p=0.03<0.05), with left-behind children exhibiting higher strength invariance. Third, the edge invariance test highlighted that certain edges differed significantly between left-behind children and non-left-behind children (left-behind children=4.13, non-left-behind children=6.34; p=0.01<0.05). Significant differences were observed at 12 edges between left-behind children and non-left-behind children. Specifically, the connections between FR and IA, FR and LA, as well as FEW and LA were significantly stronger in left-behind children compared to their non-left-behind counterparts (p < 0.05). On the other hand, the connections between MEW and PEA, IA and LA, were significantly stronger in non-left-behind children compared to their left-behind counterparts (p < 0.05). Discussion This study is the first to utilize network analysis in examining the core dimensions of social adaptation among left-behind children and non-left-behind children, as well as the relationship between parenting styles and social adaptation. Firstly, This study identified the central dimensions of SA networks across different groups. Secondly, this study identified the central dimensions of PS-SA networks across different groups. Lastly, this study conducted three tests to compare the differences in SA networks and PS-SA networks between left-behind children and non-left-behind children. By employing a network approach, the study provides new insights into which dimensions have the most significant impact on children's social adaptation and how parenting style and social adjustment dimensions are interconnected within the network. These findings can inform the development of precise and effective interventions. Social adaptation networks This research found that left-behind children had significantly lower social adaptation scores compared to non-left-behind children, aligning with previous studies 33-34 . Network analysis results reveal that 'IA' and 'LA' were the core dimensions in three SA network structures, highlighting the importance of interpersonal adaptation and learning adaptation for both groups of children. These dimensions played a critical role in social adaptation and can have implications for various other areas. Children who struggle with interpersonal or academic adjustment may experience challenges in emotional well-being, life adjustments, and may exhibit maladaptive behaviors 35 . Specifically, those with poor interpersonal adjustment may exhibit feelings of loneliness, social withdrawal, and aggression 36-37 , while those with academic struggles may face internalizing issues like self-doubt, anxiety, and depression 38 . These difficulties can hinder their ability to effectively adapt to their current social environment. Furthermore, this study found that the connection between IA and AL showed the strongest correlation in all three SA networks, followed by the connection between IA and PEM. These results indicate a significant bidirectional relationship between interpersonal adaptation, learning adaptation, and positive emotional adaptation, which supports the idea of predictive relationships in the developmental cascade theory 39 . Liu et al. also discovered a bidirectional predictive relationship between interpersonal adaptation and emotional adaptation in college students, which is consistent with the findings of this study 40 . Finally, we also examined the network variations in SA network between rural left-behind children and non-rural left-behind children. The findings revealed no significant differences in network structure invariance and global strength invariance between the two groups, but a notable distinction in edge invariance. Specifically, the connections between nodes in the SA network of rural left-behind children were weak, indicating a lack of robust interactions across various dimensions of social adaptation within this group. In line with the developmental cascade theory of social adaptation, positive development in one dimension should positively influence other dimensions of adaptation 41 . However, the study found weaker connection strengths between nodes in the SA network of left-behind children, suggesting that higher scores on certain positive adaptation dimensions do not consistently translate into higher scores on other dimensions. This highlights that the limited interconnection among different social adaptation dimensions in left-behind children impedes the establishment of a positive development cycle. Combined networks A correlation analysis was conducted to investigate the relationship between children's social adaptation and parents' parenting styles. The findings demonstrated a significant positive correlation between social adaptation and positive parenting styles, as well as a significant negative correlation with negative parenting styles, which is consistent with prior research 42-43 . Network analysis revealed that the core dimensions in the PS-SA network for left-behind children were 'IA', 'LA', 'FR', and 'MR', while for non-left-behind children, the core dimensions were 'IA', 'LA', 'MR', and 'MEW'. This indicates that left-behind children experienced higher levels of rejection from their fathers, whereas non-left-behind children perceived more emotional warmth from their mothers. Left-behind children often experience higher levels of rejection from their fathers due to two primary factors. Firstly, fathers in these families often work long hours away from home, leading to limited interactions with their children. Secondly, rural left-behind children may be more sensitive to rejection 44 , further exacerbating their sense of being rejected by their fathers. In contrast, non-left-behind children typically receive more emotional support and warmth from their mothers. This difference could be attributed to the fact that in left-behind families, mothers may also work outside the home or bear the sole responsibility for family care, resulting in less time for emotional bonding and attention to their children's daily needs 45 . As a result, the emotional warmth provided by mothers does not play a significant role in the social adaptation of left-behind children. Differences were observed in the networks of left-behind children compared to their non-counterparts. Specifically, we found that rural left-behind children show significantly stronger associations between FR and IA, FR and LA, as well as FEW and LA. Conversely, non-left-behind children exhibit significantly stronger associations between MEW and PEA, as well as between IA and LA. These findings indicate that left-behind children might struggle with learning and interpersonal adjustment issues when experienced higher levels of paternal rejection. Previous studies have also shown that paternal rejection can lead to a lack of social skills in children, resulting in difficulties in interpersonal and academic adjustment 46 . Conversely, the presence of emotional warmth from fathers has been linked to better academic adaptability in children, possibly due to variations in fathers' involvement in their children's lives and education 47 . Left-behind children often have limited communication with their fathers and are more likely to experience conflicts over academic matters, which can impede their academic adjustment. Moreover, mothers of non-left-behind children appear to exert a more significant influence on their children's emotional well-being. This may be attributed to the fact that these mothers have more time and energy to dedicate to addressing their children's emotional needs, thereby helping them to effectively manage negative emotions and moods. Implications Utilizing network analysis technology, we uncovered the social adaptation network structure characteristics of left-behind children and non-left-behind children. We also examined the influence of parental parenting styles on social adaptation, providing new insights into the analysis of social adaptation issues faced by left-behind children and their underlying causes. This research findings can assist parents and schools in implementing more tailored adaptive education for left-behind children. The study emphasizes the importance of interpersonal adaptation and learning adaptation for both left-behind children and non-left-behind children, highlighting the significance of nurturing children's interpersonal skills and learning strategies through family and school education. Moreover, the study reveals that left-behind children often experience a sense of rejection from their fathers, and positive development in one aspect of adaptation does not necessarily lead to improvement in other areas. Hence, fathers are encouraged to invest more time and effort in the education of left-behind children. By fostering communication between fathers and children, imparting correct worldviews and interpersonal skills, the social adaptation of left-behind children can be enhanced. Limitations and future directions Despite the novelty of our study and the valuable findings presented, these limitations should be acknowledged. The primary limitation of this study is that the development of network models relies on cross-sectional studies and group-level data, which may not adequately elucidate the causal associations between nodes. Therefore, longitudinal intra-individual analyses, such as dynamic networks 48 , are necessary to complement our findings. The second limitation of this study is the reliance on self-report measures, which may be subject to self-report biases 49 . Future research could consider incorporating clinician-administered interviews to assess problematic or addictive behaviors. The third limitation of this study is its exclusive focus on the relationship between parenting styles and social adaptation. However, children's social adaptation is a multifaceted concept that is developmentally specific. It is influenced not only by family factors but also by various elements within the school and broader social environments 50 . Future research should consider simultaneously investigating the impact mechanisms of multiple factors on children's social adaptation. Conclusions To the best of our knowledge, this is the first study to utilize network analysis technology in comparing the social adaptation network structural characteristics of left-behind children and non-left-behind children, as well as to examine the influence of parental parenting styles on social adaptation. This study enhances the understanding of the interrelationship between parental rearing styles and the social adjustment. First, within the SA network, we found that the core symptoms of left-behind children and their non-left-behind counterparts are identical, with both groups exhibiting IA and LA. This suggests that these two dimensions serve as the most effective indicators of children's social adaptation. A comparison of the networks of both groups revealed similar network structures and global strengths, yet notable differences in specific dimension associations. Second, within the PS-SA network, we found that the core symptoms of left-behind children differ from those of non-left-behind children. Specifically, IA, LA, FR, and MR comprise the core dimensions of the left-behind children network, whereas IA, LA, MR, and MEW constitute the core dimensions of the non-left-behind children network. Although the networks of both groups displayed similar structures, they varied in global strength and specific dimension associations. The observed differences in core symptoms and symptom relationships within the PS-SA framework offer new insights for developing strategies aimed at enhancing the social adaptation of left-behind children. Declarations Ethics approval and consent to participate This study was approved by the Ethics Committee of Yancheng Teachers University. All procedures were conducted in compliance with relevant ethical guidelines and regulations. In line with the requirements of the ethics committee, informed consent was obtained from all participants. For participants under the age of 15, written informed consent was secured from their parents or legal guardians, while research consent was also obtained from school administrators and head teachers prior to the study. Consent for publication Not applicable. Availability of data and materials The datasets and materials used during the current study available from the corresponding author on reasonable request. Competing interests The authors declare that they have no known competing financial interests. Funding Social Science Foundation of Jiangsu Province in 2024 (No. 24JYC002) . Authors' contributions S. F. designed the study protocol, conducted data collection and substantially revised the manuscript. Q. G. wrote the first draft of the paper. X. G. conducted the data analysis. B. D. designed the study protocol, assisted in revising the paper. All authors have read and agreed to the published version of the manuscript. Acknowledgements The authors thank the Project of the 15th Jiangsu Province primary and secondary school teaching research Project (No. 2023JY15-GX-L03). References National Bureau of Statistics《What the 2020 Census Can Tell Us About Children in China Facts and Figures 》(https://www.stats.gov.cn/zs/tjwh/tjkw/tjzl/202304/t20230419_1938814.html). (Chinese) Cao, H. B., Wang, J. X., Zhang, K. Relationship Between Perceived Discrimination and Mental Health of Left-behind Children:A Meta-analysis of Chinese Students. Psychological Exploration . 2022; 42(06): 546-555. (Chinese) Fellmeth, G., Rose-Clarke, K., Zhao, C., Busert, L. K., Zheng, Y., Massazza, A., ... Devakumar, D. Health impacts of parental migration on left-behind children and adolescents: a systematic review and meta-analysis. The Lancet . 2018; 392: 2567-2582. Wang, Y., Liu, W., Wang, W., Lin, S., Lin, D., Wang, H. 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Children and Youth Services Review. 2018; 95:308-315. Moilanen, K. L., Shaw, D. S., Maxwell, K. L. Developmental cascades: Externalizing, internalizing, and academic competence from middle childhood to early adolescence. Development and psychopathology. 2010; 22: 635-653. Jin, S., Liu, J., Miao, M. Family incivility impedes interpersonal adaptation and increases loneliness in adolescents: self-compassion as a mediator. Mindfulness . 2023; 14(08): 2014-2025. Chen, D., Drabick, D. A., Burgers, D. E. A developmental perspective on peer rejection, deviant peer affiliation, and conduct problems among youth. Child Psychiatry & Human Development. 2015; 46: 823-838. Deighton, J., Humphrey, N., Belsky, J., Boehnke, J., Vostanis, P., Patalay, P. Longitudinal pathways between mental health difficulties and academic performance during middle childhood and early adolescence. British Journal of Developmental Psychology. 2018;36(01): 110-126 . Masten, A. S., Roisman, G. I., Long, J. D., Burt, K. B., Obradović, J., Riley, J. R., ... Tellegen, A. Developmental cascades: linking academic achievement and externalizing and internalizing symptoms over 20 years. Developmental psychology. 2005; 41(05): 733. Liu, H., Li, Y. The Reciprocal Effects of Emotional Adjustment, Social Adjustment and Academic Adjustment among Freshmen: A Longitudinal Study. Psychological Development and Education. 2024; (05): 270-278. (Chinese) Masten, A. S., Cicchetti, D. Developmental cascades. Development and psychopathology . 2010; 22(03): 491-495 . Lavasani M G , Borhanzadeh S , Afzali L ,et al. The relationship between perceived parenting styles, social support with psychological well- being. Procedia - Social and Behavioral Sciences .2011; 15: 1852-1856. Guo, X., Hao, C., Wang, W., Li, Y. Parental Burnout, Negative Parenting Style, and Adolescents’ Development. Behavioral Sciences . 2024; 14(03): 161 . Sun, H., Zhang, T. The Effectiveness of Forgiveness Intervention to Decrease of Rejection Sensitivity:A Study Based on Left-Behind Children. Studies of Psychology and Behavior . 2021; 19(01): 111-117. Lv, J., Liu, L. On the Evolution and Effect of the Family Structure and Functions of Left-at-home Rural Children. Chinese Journal of Special Education . 2011; 10 (01): 59-62. Rohner, R. P. , Britner, P. A. Worldwide mental health correlates of parental acceptance-rejection: review of cross-cultural and intracultural evidence. Cross-Cultural Research: The Journal of Comparative Social Science . 2002; 36(01):16-47. Ki, P. School adjustment and academic performance: influences of the interaction frequency with mothers versus fathers and the mediating role of parenting behaviours. Early Child Development and Care . 2020; 190(07): 1123-1135. Bos, F. M., Snippe, E., De Vos, S. et al. Can we jump from cross-sectional to dynamic interpretations of networks implications for the network perspective in psychiatry. Psychotherapy and psychosomatics . 2017; 86(03):175-177. Caputo, A. Social desirability bias in self-reported well-being measures: Evidence from an online survey. Universitas Psychologica . 2017; 16(02): 245-255. Fan, X. H., Fang, X. Y., et al. The effect of cumulative risk related to family adversity on socialadjustment among left-behind children in China: The mediating role of stress and the moderating role of psychosocial resources. Acta Psychologica Sinica . 2023; 55(08): 1270-1284.(Chinese) Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-6169635","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":442770748,"identity":"8f83fa02-8992-468d-9f64-7bdad4d1b997","order_by":0,"name":"Shuying Y. Fu","email":"","orcid":"","institution":"Tianjin Normal University","correspondingAuthor":false,"prefix":"","firstName":"Shuying","middleName":"Y.","lastName":"Fu","suffix":""},{"id":442770750,"identity":"b3cfa761-364d-4bc9-9fa8-d79a316c1568","order_by":1,"name":"Qinqiu Gao","email":"","orcid":"","institution":"Tianjin Normal University","correspondingAuthor":false,"prefix":"","firstName":"Qinqiu","middleName":"","lastName":"Gao","suffix":""},{"id":442770752,"identity":"ee9b7009-95a8-4238-8d60-6048dcd688fe","order_by":2,"name":"Xiuli Guo","email":"","orcid":"","institution":"Tianjin Normal University","correspondingAuthor":false,"prefix":"","firstName":"Xiuli","middleName":"","lastName":"Guo","suffix":""},{"id":442770754,"identity":"35aefc74-a8c3-4d36-9c29-c23b6bfbebc9","order_by":3,"name":"Binrong R. Dai","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAt0lEQVRIiWNgGAWjYBAC9gYg8QHKkSBKC88BBgbGGVDVxGth5iFNi0T6M2nbNrs6gwPMB2/zMNjlEaElx0w6ty1ZwuAAW7I1D0NyMUEt9hI5bEAtB4BaeMykeRgOJDYQ5TBLsBb+b8RqSTCTZoTYwkakFp43xpY955IlZx5mM7acY5BMhBb29Ic3fpTZ8fMdb354402FHWEtQMAiwcgGpJhBbAMi1IPUfmD4Q5zKUTAKRsEoGKEAALNLM7lGFyw7AAAAAElFTkSuQmCC","orcid":"","institution":"Jiangsu Provincial University Key Lab of Child Cognitive Development and Mental Health, Yancheng Teachers University","correspondingAuthor":true,"prefix":"","firstName":"Binrong","middleName":"R.","lastName":"Dai","suffix":""}],"badges":[],"createdAt":"2025-03-06 10:38:12","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-6169635/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6169635/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":80807469,"identity":"f23418d5-93f1-4cf0-ab95-36d2659c63b8","added_by":"auto","created_at":"2025-04-17 09:39:23","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":61023,"visible":true,"origin":"","legend":"\u003cp\u003eHeat map correlations.\u003c/p\u003e\n\u003cp\u003eNotes:(1)*p\u0026lt;0.05,**p\u0026lt;0.01,***p\u0026lt;0.001. (2)The lower triangular matrix displays the correlation coefficients, with each value indicating the Spearman's c correlation coefficient. Only those coefficients that are statistically significant (p \u0026lt; 0.01) are included in the lower triangular matrix. (3)The upper triangular matrix illustrates the significance levels, while the empty boxes indicate coefficients do not survive this correction.\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-6169635/v1/f91ab4f02be5ccd828762c17.png"},{"id":80807470,"identity":"b644ee95-6d4f-4a00-8c44-5fe7762da55f","added_by":"auto","created_at":"2025-04-17 09:39:23","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":133846,"visible":true,"origin":"","legend":"\u003cp\u003eNetwork structure of social adaptation.\u003c/p\u003e\n\u003cp\u003eNotes: (1) A, B, and C respectively represent the social adaptation network structure of children as a whole, left-behind children, and non-left-behind children. (2) Green lines mean positive connections, and the edge thickness indicates correlation strength. (3) To facilitate visual comparisons of the network structures across different groups, this study employs the average layout function, ensuring that the positions of identical nodes remain consistent.\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-6169635/v1/9ae6a1005eaab44007874bbb.png"},{"id":80808365,"identity":"1363d3d4-b0e9-4f01-9d4c-6a2f9a187907","added_by":"auto","created_at":"2025-04-17 09:47:24","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":132070,"visible":true,"origin":"","legend":"\u003cp\u003eCentrality plots for networks.\u003c/p\u003e\n\u003cp\u003eNote: The X-axis represents the centrality indices as standardized z-scores, indicating that a higher estimate corresponds to greater centrality of the item, while the Y-axis displays the 5 variables.\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-6169635/v1/ea6dd20ff4298ba8f14a7146.png"},{"id":80807473,"identity":"764d5456-a100-4620-9bda-8afe5ee784f4","added_by":"auto","created_at":"2025-04-17 09:39:24","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":313017,"visible":true,"origin":"","legend":"\u003cp\u003eNetwork structure of parenting styles-social adaptation.\u003c/p\u003e\n\u003cp\u003eNotes: (1)A, B, and C respectively represent the social adaptation network structure of children as a whole, left-behind children, and non-left-behind children. (2)Green lines mean positive connections, red lines mean negative connections, and the edge thickness indicates correlation strength. (3)To facilitate visual comparisons of the network structures across different groups, this study employs the average layout function, ensuring that the positions of identical nodes remain consistent.\u003c/p\u003e","description":"","filename":"4.png","url":"https://assets-eu.researchsquare.com/files/rs-6169635/v1/62674e0bdbf5ace52d2c9913.png"},{"id":80807480,"identity":"43b35e5e-1383-4d0d-8099-74fd269715dd","added_by":"auto","created_at":"2025-04-17 09:39:24","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":233427,"visible":true,"origin":"","legend":"\u003cp\u003eCentrality plots for networks .\u003c/p\u003e\n\u003cp\u003eNote: The X-axis represents the centrality indices as standardized z-scores, indicating that a higher estimate corresponds to greater centrality of the item, while the Y-axis displays the 11 variables.\u003c/p\u003e","description":"","filename":"5.png","url":"https://assets-eu.researchsquare.com/files/rs-6169635/v1/51f37a17ecb1c05dc77070ad.png"},{"id":85914481,"identity":"0362213e-8fc7-4cff-a7ff-4135e2fec934","added_by":"auto","created_at":"2025-07-03 06:32:08","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1639040,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6169635/v1/6ac97616-9851-438d-80e9-7f3a8ba22abc.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"The relationship between social adaptation and parenting styles in left-behind and non-left-behind children: a network analysis","fulltext":[{"header":"Introduction","content":"\u003cp\u003e Left-behind children are young individuals under the age of 17 whose parents are employed in distant locations, resulting in their being looked after by a single parent or without direct guardianship. As of 2020, the number of such children in China reached 41.77 million\u003csup\u003e\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u003c/sup\u003e. The absence of parental care can leave these young individuals feeling neglect and discrimination\u003csup\u003e\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e\u003c/sup\u003e, which may diminish their sense of safety and give rise to a spectrum of adverse emotional responses, including depression, anxiety, and isolation\u003csup\u003e\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e\u003c/sup\u003e. Furthermore, they may develop patterns of social withdrawal and even aggressive behavior\u003csup\u003e\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e\u003c/sup\u003e, impeding their integration and adaptation to society. Consequently, the social adaptation of left-behind children has garnered considerable attention. Social adaptation encompasses an individual's ongoing efforts to align their physical and psychological well-being with the shifting demands of their social environment\u003csup\u003e\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e\u003c/sup\u003e. It's a multifaceted concept that evolves with an individual's developmental stage. Emotional responses and behavioral expressions that reflect individual social adaptation are thought to be influenced by both personal developmental phases and the broader social environment. For left-behind children, the challenges of social adaptation may vary in relevance and significance based on the child's developmental stage and the specific social context in which they find themselves\u003csup\u003e\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eResearch on the social adaptation of left-behind children has been approached from two primary orientations. The first direction involves categorizing these children into groups with varying levels of social adaptation based on specific dimensions, followed by a comparison of the differences among these groups. For instance, LI et al. utilized latent class analysis (LCA) to categorize left-behind children into three groups: well-adapted, difficult to adapt, and impulsive, according to their emotional and behavioral challenges\u003csup\u003e\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e\u003c/sup\u003e.This study revealed significant gender and grade variations in emotional and behavioral issues among rural left-behind children across these categories. The second research direction involves comparing the overall social adaptation scores of rural left-behind children with those of non-left-behind children to evaluate their levels of social adaptability. Meanwhile, a meta-analysis of 13 studies found that left-behind children exhibited lower levels of social adaptability. The first research direction focused on a single dimension of social adaptation, neglecting the interaction between different dimensions\u003csup\u003e\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e\u003c/sup\u003e.The first research direction focuses solely on the social adaptation of left-behind children from a single perspective, neglecting to explore the interrelationships among various dimensions of social adaptation. The second research direction, rooted in the traditional latent variable model, assumes that all dimensions of social adaptation are influenced by common factors and that each dimension contributes equally to social adaptation. However, these orientations fail to pinpoint the key adaptive dimensions crucial for the development of left-behind children.\u003c/p\u003e \u003cp\u003eIn response to these shortcomings, researchers have proposed estimating the complex relationships among various social adaptation issues, including depression, through the lens of complex systems\u003csup\u003e\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e\u003c/sup\u003e. They utilized graphical model visualization to conceptualize social adaptation as a complex network system, interconnected across multiple dimensions, with nodes and connecting lines representing the network. This approach is referred to as network analysis.\u003c/p\u003e \u003cp\u003eNetwork analysis was conducted by treating each dimension of social adaptation as a network node. The connections between these nodes represent the relationships among the dimensions, while the thickness of the connections indicates the strength of the correlations. Additionally, the node centrality index reflects the significance of each node within the network. This approach underscores the interconnections among various dimensions of social adaptation and highlights key dimensions through statistical modeling\u003csup\u003e\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e\u003c/sup\u003e. It effectively addresses the limitations of traditional latent variable models, which often struggle to capture the complex patterns of connections between dimensions, thus providing a foundation for analyzing the most critical aspects of children's development\u003csup\u003e\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e\u003c/sup\u003e. Consequently, the primary objective of this study is to explore the structure and core dimensions of the social adaptation network among rural children, as well as to compare the differences in network structure between left-behind children and their non-left-behind counterparts.\u003c/p\u003e \u003cp\u003eEcological systems theory posits that the family plays a crucial role in the microsystem \u003csup\u003e\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e\u003c/sup\u003e. Within the family unit, parenting style emerges as a key protective factor with significant implications for the social adaptation of left-behind children \u003csup\u003e\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e\u003c/sup\u003e. Studies have shown that positive parenting practices, such as emotional warmth, are associated with lower levels of anxiety, depression, loneliness, and problem behaviors, while enhancing happiness in left-behind children\u003csup\u003e\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e\u003c/sup\u003e. Conversely, negative parenting styles characterized by rejection, over-protection have been linked to adverse social adaptation outcomes in these children\u003csup\u003e\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e\u003c/sup\u003e. Furthermore, researches indicate that parenting styles not only have a direct impact on the social adaptation of left-behind children, but also exert indirect effects through variables like self-control and parent-child conflict\u003csup\u003e\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eNumerous studies have indicated that parenting styles significantly impact the social adaptation of rural left-behind children. However, existing studies have two main limitations. Firstly, most studies have focused on mothers' parenting styles, neglecting the influence of fathers' parenting behaviors. Hoeve et al. conducted a meta-analysis of 161 studies and discovered that less than 20% of them specifically examined fathers' parenting behaviors\u003csup\u003e\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e\u003c/sup\u003e. Family systems theory suggests that both parents' parenting styles interact and influence each other rather than acting independently\u003csup\u003e\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e\u003c/sup\u003e. Therefore, it is essential to simultaneously consider the effects of both father's and mother's parenting styles on the social adjustment of rural left-behind children within in a unified model.Secondly, prior findings have mainly used regression analysis to explore the influence of parenting styles on social adaptation, neglecting the specific mechanisms through which parenting styles directly influence social adaptation. Utilizing network analysis, researchers can enhance their comprehension of how parenting styles influence social adaptation and create tailored intervention strategies for improvement. Therefore, the second aim of this study is to employ network analysis techniques to investigate the intricate connection between parenting styles and social adaptation. Additionally, the research seeks to analyze the structural variances in the relationship network between parental parenting styles and social adaptation among left-behind children and non-left-behind children, offering empirical data to elevate the social adaptation levels of rural left-behind children.\u003c/p\u003e"},{"header":"Methods","content":"\u003cp\u003e\u003cstrong\u003eParticipants\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eA total of 2,919 children participated in the study. After excluding participants due to incomplete data or identical selecting responses (i.e., selecting the same number), the final sample comprised 2,452 participants, yielding a valid response rate of 84.00%. The sample was approximately evenly distributed by gender, consisting of 1,095 boys (48.9%) and 1,143 girls (51.1%). Participants were aged between 9 and 16 years and were categorized into two groups: left-behind children (n = 713; age range: 9\u0026ndash;16; Mage = 12.36, SD = 2.93) and non-left-behind children (n = 1,739; age range: 9\u0026ndash;16; Mage = 12.03, SD = 3.08). The gender distribution was similar in both groups, with 48.7% females among left-behind children and 51.5% among non-left-behind children.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eProcedure\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eFor the recruitment of both left-behind and non-left-behind children, we selected nine primary and secondary schools situated in the rural regions of Yancheng, Lianyungang, and Taizhou in Jiangsu Province, China. Data collection took place in December 2022, during which participants completed the questionnaire in approximately 20 to 30 minutes. In accordance with the guidelines established by the ethics committee, participants provided informed consent. We obtained research consent from school leaders and head teachers, while ensuring parental informed consent for participants aged 15 years or younger. This study received approval from the ethics committee of Yancheng Teachers University. All procedures adhered to the ethical standards set forth by the responsible committee on human experimentation and complied with the Helsinki Declaration.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eMeasurements\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eSocial Adaptation\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe social adaptation of rural children was assessed with the Rural Children Social Adaptation Questionnaire (RCSAQ)\u003csup\u003e7\u003c/sup\u003e, a widely utilized tool to evaluate the social adjustment of children in rural China. The scale includes five dimensions: interpersonal adaptation, learning adaptation, positive emotional adaptation, cognitive adaptation, and life adaptation, comprising a total of 26 items on a 5-point Likert scale ranging from 1 (not like me at all) to 5 (completely like me). Each dimension represents a positive aspect, and higher scores indicate a higher level of social adaptation for the rural children. The overall Cronbach\u0026apos;s \u0026alpha; coefficient for the scale was 0.89, and the Cronbach\u0026apos;s \u0026alpha; coefficient of each dimension was between 0.83 and 0.90.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eParenting Styles\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eParenting styles was assessed with Chinese version of the short-form Egna Minnen av Barndoms Uppfostran (s-EMBU)\u003csup\u003e23\u003c/sup\u003e. The s-EMBU consisted of two subscales: one for fathers and one for mothers. Each subscale is further divided into three dimensions: emotional warmth, rejection, and over-protection. Emotional warmth is considered a positive dimension, while rejection and over-protection are viewed as negative dimensions. In total, the overall scale comprises a total of 42 items, with each subscale contains 21 items that are identical in content. Each item was rated on a 4-point Likert scale, ranging from 1 = strongly disagree to 4 = strongly agree. A higher score indicates a higher tendency for the child\u0026apos;s father or mother to exhibit this particular parenting style. The overall Cronbach\u0026apos;s \u0026alpha; coefficient for the scale was 0.91, and the Cronbach\u0026apos;s \u0026alpha; coefficient for two subscales were 0.90 and 0.93.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eStatistical Analyses\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eQuestionnaires were distributed and collected on-site, resulting in some missing values in the item-level data. To address this, we employed the average to impute the missing values. Prior to conducting any analyses, we assessed the data for normality of distribution by examining skewness and kurtosis. The skewness values ranged from -0.56 to 0.84, while the kurtosis values ranged from -0.65 to 0.70, both of which fall within acceptable ranges (skewness \u0026lt; 3 and kurtosis \u0026lt; 10)\u003csup\u003e24\u003c/sup\u003e. In this study, SPSS version 25.0 was used for descriptive statistical analysis, internal consistency reliability test and correlation analysis, and R4.3.1 in RStudio 1.2.5033 was was used used to estimate PS-SA network structure and network comparison. The network analysis approach follows the standard guidelines published by Epskamp\u003csup\u003e25\u003c/sup\u003e.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eNetwork Estimation\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe network structure of continuous variables was estimated using the \u003cem\u003eEBICglasso\u003c/em\u003e function from the\u003cem\u003e\u0026nbsp;qgraph\u003c/em\u003e package\u003csup\u003e26\u003c/sup\u003e. We estimated a Gaussian graphical model (GGM) using the graphical lasso (i.e., glasso) in combination with the extended Bayesian information criterion (EBIC)\u003csup\u003e27\u003c/sup\u003e. In this study, we estimated the SA network and PS-SA network for three groups: left-behind children, non-left-behind children, and the overall sample of children. In the network models, each variable was designated as a \u0026apos;node\u0026apos; and the connections between variables were denoted as \u0026apos;edges\u0026apos;. The thickness of the edges in the network diagram indicates the strength of the connections between nodes, with thicker edges denoted stronger relationships and thinner edges denoted weaker relationships. In the current models, we have set the gamma hyper parameter to a default value of 0.5. Furthermore, to enhance visualization across the three networks, we utilized the averageLayout function from the \u003cem\u003eqgraph\u003c/em\u003e package.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCentrality estimation\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe centrality Plot function in the graph package was employed to calculate three commonly used indices of centrality: strength, closeness, betweenness. The strength centrality was assessed by summing all edges for each node, indicating a higher value for nodes with multiple symptoms occurring simultaneously\u003csup\u003e28\u003c/sup\u003e. Closeness centrality was assessed by calculating the reciprocal of the sum of shortest path lengths between all nodes, reflecting the average distance between nodes and all other nodes in the network. A higher closeness centrality suggests that a symptom\u0026apos;s impact spreads quickly to other symptoms\u003csup\u003e29\u003c/sup\u003e. Betweenness centrality was assessed by measuring the shortest path lengths between any two nodes, indicating nodes that act as bridges connecting different symptoms and potential target symptoms for interventions\u003csup\u003e30\u003c/sup\u003e. In addition to the three traditional indices of centrality, this study also employs expected influence centrality, which is defined as the sum of the edge weights connected to a node. A higher expected influence centrality indicates greater influence of the node within the network structure. Unlike traditional methods of measuring centrality, the calculation of the expected influence index retains the signs of edge weights that are less than zero, rather than taking their absolute values. This approach allows for the consideration of both positive and negative relationships within the network, thereby facilitating a more accurate assessment of node influence\u003csup\u003e31\u003c/sup\u003e.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eNetwork accuracy and stability\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe \u003cem\u003ebootnet\u003c/em\u003e package was utilized to estimate accuracy and stability in the network model. Initially, the accuracy of edge weights was assessed by bootstrapping 95% confidence intervals (i.e., CIs) of the edge weights. Narrow bootstrapped CIs enoted low sampling variability in edge-weights, indicating that an accurate network was estimated. Subsequently, node centrality stability was evaluated using a case-dropping subset bootstrap method to determine how well the order of centralities was maintained across different subsets of data. The correlation stability coefficient (CS-coefficient) was employed to quantify this stability, measuring the maximum drop in proportions required to retain highly correlated nodes (r \u0026gt; 0.7). The CS-coefficient above 0.25 was considered acceptable, while a value exceeding 0.5 was deemed excellent\u003csup\u003e24\u003c/sup\u003e. Lastly, bootstrapped difference tests were conducted on centrality indices of the nodes to ascertain if they exhibited significant differences from each other. \u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eNetwork comparison\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe \u003cem\u003eNetwork Comparison Test\u003c/em\u003e package was used to compare the networks of rural left-behind children and non-rural left-behind children. Three tests were conducted to evaluate these differences: a test for network structure invariance, a test for global strength invariance, and a test for edge strength invariance\u003csup\u003e32\u003c/sup\u003e. The network structure invariance test assessed variations in the strength of the maximum edge within the network; the global strength invariance test assessed differences in the total edge strength; and the edge strength invariance test examined variances in specific edges within the network.\u003c/p\u003e"},{"header":"Results","content":"\u003cp\u003e\u003cstrong\u003eDescriptive statistics and correlation analyses\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eTable 1 presents the descriptive statistics for the study variables. As shown in Figure 1, father refused (FR) (P\u0026lt;0.05), mother refused (MR) (P\u0026lt;0.05) were significantly negatively associated with interpersonal adaptation(IA), learning adaptation (LA), positive emotional adaptation (PEA) and cognitive adaptation (CA). mother\u0026apos;s emotional warmth (MEW) (P\u0026lt;0.001) and father\u0026apos;s emotional warmth (FEW) (P\u0026lt;0.001) were significantly positively associated with IA, LA, CA, PEA, adaptation to life (AL). Maternal overprotection (MO) (P\u0026gt;0.05) and paternal overprotection (PO) (P\u0026gt;0.05) did not show significant relationships with IA, LA, CA, and AL. Additionally, the correlation between MR, FR, and AL (P\u0026gt;0.05) was also found to be non-significant.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eTable 1.\u0026nbsp;\u003c/strong\u003eDescriptive statistics for main variables .\u003c/p\u003e\n\u003ctable border=\"1\" cellspacing=\"0\" cellpadding=\"0\"\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd rowspan=\"2\" style=\"width: 81px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eVariable\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd colspan=\"3\" valign=\"top\" style=\"width: 181px;\"\u003e\n \u003cp\u003eleft-behind (n=713)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 17px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd colspan=\"3\" valign=\"top\" style=\"width: 183px;\"\u003e\n \u003cp\u003enon-left-behind (n=1739)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 16px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd colspan=\"3\" valign=\"top\" style=\"width: 179px;\"\u003e\n \u003cp\u003eall of children (n = 2452)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 49px;\"\u003e\n \u003cp\u003eMin\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 49px;\"\u003e\n \u003cp\u003eMax\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 84px;\"\u003e\n \u003cp\u003eM \u0026plusmn; SD\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 17px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 52px;\"\u003e\n \u003cp\u003eMin\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 52px;\"\u003e\n \u003cp\u003eMax\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 79px;\"\u003e\n \u003cp\u003eM \u0026plusmn; SD\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 16px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 49px;\"\u003e\n \u003cp\u003eMin\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 49px;\"\u003e\n \u003cp\u003eMax\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 81px;\"\u003e\n \u003cp\u003eM \u0026plusmn; SD\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 81px;\"\u003e\n \u003cp\u003e1 MR\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 49px;\"\u003e\n \u003cp\u003e6\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 49px;\"\u003e\n \u003cp\u003e23\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 84px;\"\u003e\n \u003cp\u003e1.74 \u0026plusmn; 0.66\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 17px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 52px;\"\u003e\n \u003cp\u003e6\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 52px;\"\u003e\n \u003cp\u003e23\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 79px;\"\u003e\n \u003cp\u003e1.67 \u0026plusmn; 0.60\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 16px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 49px;\"\u003e\n \u003cp\u003e6\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 49px;\"\u003e\n \u003cp\u003e23\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 81px;\"\u003e\n \u003cp\u003e1.70 \u0026plusmn; 0.62\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 81px;\"\u003e\n \u003cp\u003e2 MEW\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 49px;\"\u003e\n \u003cp\u003e7\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 49px;\"\u003e\n \u003cp\u003e28\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 84px;\"\u003e\n \u003cp\u003e2.90 \u0026plusmn; 0.72\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 17px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 52px;\"\u003e\n \u003cp\u003e7\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 52px;\"\u003e\n \u003cp\u003e28\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 79px;\"\u003e\n \u003cp\u003e3.01 \u0026plusmn; 0.68\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 16px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 49px;\"\u003e\n \u003cp\u003e7\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 49px;\"\u003e\n \u003cp\u003e28\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 81px;\"\u003e\n \u003cp\u003e2.97 \u0026plusmn; 0.69\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 81px;\"\u003e\n \u003cp\u003e3 MO\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 49px;\"\u003e\n \u003cp\u003e7\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 49px;\"\u003e\n \u003cp\u003e28\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 84px;\"\u003e\n \u003cp\u003e2.36 \u0026plusmn; 0.57\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 17px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 52px;\"\u003e\n \u003cp\u003e7\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 52px;\"\u003e\n \u003cp\u003e28\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 79px;\"\u003e\n \u003cp\u003e2.34 \u0026plusmn; 0.56\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 16px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 49px;\"\u003e\n \u003cp\u003e7\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 49px;\"\u003e\n \u003cp\u003e28\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 81px;\"\u003e\n \u003cp\u003e2.34 \u0026plusmn; 0.56\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 81px;\"\u003e\n \u003cp\u003e4 FR\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 49px;\"\u003e\n \u003cp\u003e6\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 49px;\"\u003e\n \u003cp\u003e24\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 84px;\"\u003e\n \u003cp\u003e1.68 \u0026plusmn; 0.63\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 17px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 52px;\"\u003e\n \u003cp\u003e6\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 52px;\"\u003e\n \u003cp\u003e24\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 79px;\"\u003e\n \u003cp\u003e1.65 \u0026plusmn; 0.62\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 16px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 49px;\"\u003e\n \u003cp\u003e6\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 49px;\"\u003e\n \u003cp\u003e24\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 81px;\"\u003e\n \u003cp\u003e1.67 \u0026plusmn; 0.63\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 81px;\"\u003e\n \u003cp\u003e5 FEW\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 49px;\"\u003e\n \u003cp\u003e7\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 49px;\"\u003e\n \u003cp\u003e28\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 84px;\"\u003e\n \u003cp\u003e2.85 \u0026plusmn; 0.72\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 17px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 52px;\"\u003e\n \u003cp\u003e7\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 52px;\"\u003e\n \u003cp\u003e28\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 79px;\"\u003e\n \u003cp\u003e2.92 \u0026plusmn; 0.72\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 16px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 49px;\"\u003e\n \u003cp\u003e7\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 49px;\"\u003e\n \u003cp\u003e28\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 81px;\"\u003e\n \u003cp\u003e2.88 \u0026plusmn; 0.72\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 81px;\"\u003e\n \u003cp\u003e6 PO\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 49px;\"\u003e\n \u003cp\u003e7\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 49px;\"\u003e\n \u003cp\u003e28\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 84px;\"\u003e\n \u003cp\u003e2.30 \u0026plusmn; 0.54\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 17px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 52px;\"\u003e\n \u003cp\u003e7\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 52px;\"\u003e\n \u003cp\u003e28\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 79px;\"\u003e\n \u003cp\u003e2.31 \u0026plusmn; 0.50\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 16px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 49px;\"\u003e\n \u003cp\u003e7\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 49px;\"\u003e\n \u003cp\u003e28\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 81px;\"\u003e\n \u003cp\u003e2.31 \u0026plusmn; 0.51\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 81px;\"\u003e\n \u003cp\u003e7 IA\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 49px;\"\u003e\n \u003cp\u003e13\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 49px;\"\u003e\n \u003cp\u003e50\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 84px;\"\u003e\n \u003cp\u003e3.98 \u0026plusmn; 0.69\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 17px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 52px;\"\u003e\n \u003cp\u003e10\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 52px;\"\u003e\n \u003cp\u003e50\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 79px;\"\u003e\n \u003cp\u003e4.10 \u0026plusmn; 0.68\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 16px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 49px;\"\u003e\n \u003cp\u003e10\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 49px;\"\u003e\n \u003cp\u003e50\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 81px;\"\u003e\n \u003cp\u003e4.02 \u0026plusmn; 0.69\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 81px;\"\u003e\n \u003cp\u003e8 LA\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 49px;\"\u003e\n \u003cp\u003e6\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 49px;\"\u003e\n \u003cp\u003e30\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 84px;\"\u003e\n \u003cp\u003e3.92 \u0026plusmn; 0.82\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 17px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 52px;\"\u003e\n \u003cp\u003e10\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 52px;\"\u003e\n \u003cp\u003e30\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 79px;\"\u003e\n \u003cp\u003e4.02 \u0026plusmn; 0.78\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 16px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 49px;\"\u003e\n \u003cp\u003e6\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 49px;\"\u003e\n \u003cp\u003e30\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 81px;\"\u003e\n \u003cp\u003e3.94 \u0026plusmn; 0.80\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 81px;\"\u003e\n \u003cp\u003e9 PEA\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 49px;\"\u003e\n \u003cp\u003e4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 49px;\"\u003e\n \u003cp\u003e20\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 84px;\"\u003e\n \u003cp\u003e3.83 \u0026plusmn; 0.89\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 17px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 52px;\"\u003e\n \u003cp\u003e4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 52px;\"\u003e\n \u003cp\u003e20\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 79px;\"\u003e\n \u003cp\u003e3.98 \u0026plusmn; 0.83\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 16px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 49px;\"\u003e\n \u003cp\u003e4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 49px;\"\u003e\n \u003cp\u003e20\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 81px;\"\u003e\n \u003cp\u003e3.89 \u0026plusmn; 0.86\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 81px;\"\u003e\n \u003cp\u003e10 CA\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 49px;\"\u003e\n \u003cp\u003e3\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 49px;\"\u003e\n \u003cp\u003e15\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 84px;\"\u003e\n \u003cp\u003e4.20 \u0026plusmn; 0.76\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 17px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 52px;\"\u003e\n \u003cp\u003e3\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 52px;\"\u003e\n \u003cp\u003e15\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 79px;\"\u003e\n \u003cp\u003e4.29 \u0026plusmn; 0.72\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 16px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 49px;\"\u003e\n \u003cp\u003e3\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 49px;\"\u003e\n \u003cp\u003e15\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 81px;\"\u003e\n \u003cp\u003e4.23 \u0026plusmn; 0.74\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 81px;\"\u003e\n \u003cp\u003e11 AL\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 49px;\"\u003e\n \u003cp\u003e4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 49px;\"\u003e\n \u003cp\u003e15\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 84px;\"\u003e\n \u003cp\u003e3.68 \u0026plusmn; 0.96\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 17px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 52px;\"\u003e\n \u003cp\u003e4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 52px;\"\u003e\n \u003cp\u003e15\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 79px;\"\u003e\n \u003cp\u003e3.75 \u0026plusmn; 0.92\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 16px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 49px;\"\u003e\n \u003cp\u003e4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 49px;\"\u003e\n \u003cp\u003e15\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 81px;\"\u003e\n \u003cp\u003e3.66 \u0026plusmn; 0.93\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n\u003c/table\u003e\n\u003cp\u003e\u003cstrong\u003eSocial adaptation networks\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eNetwork estimation\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eTo comprehend the network structure of social adaptation (SA), we estimated three regularized networks based on left-behind children (Figure 2A), non-left-behind children (Figure 2B), and overall children(Figure 2C), encompassing all 5 dimensions. This resulted in a total of 10 edges (5*(5-1) / 2). In the social adaptation network of the overall sample of children and the non-left-behind children sample, there are 10 edges with non-zero weights (mean weight 0.05 and 0.06).The social adaptation network for left-behind children includes 9 edges with non-zero weights (mean weight 0.04). Figure 2 demonstrates the significant strength of internal connections within each dimension.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCentrality estimation\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eFig 3 illustrates the centrality of each dimension in the three SA networks. The highest strength centrality was observed in IA and LA, showing significant differences from the strength centrality of other dimensions. This suggests that these two dimensions had the most profound impact on the individual.The dimensions of IA and LA demonstrated the highest closeness centrality, suggesting their significant potential to quickly impact other dimensions. IA had the highest betweenness centrality among non-left-behind children and children in general, whereas both IA and LA had the highest betweenness centrality among \u0026nbsp;left-behind children. The dimensions of IA and LA demonstrated the highest closeness centrality, suggesting they have a more significant impact on the other items in the network. The dimensions of IA and LA demonstrated the highest expected influence centrality, suggesting they have a more significant impact on the other items in the network. Ultimately, IA and LA emerged as the core dimensions in the three SA networks.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eNetwork accuracy and stability\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe results of edge-weight bootstrapping (Table 2) indicate that the three network estimations were moderately accurate. The CS coefficients for strength, closeness, and betweenness, and expected influence in all three networks are above 0.50, suggesting that the overall network stability was excellent.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eTable 2.\u0026nbsp;\u003c/strong\u003eCS-coefficient of different groups in SA network structures.\u003c/p\u003e\n\u003ctable border=\"0\" cellspacing=\"0\" cellpadding=\"0\" width=\"99%\"\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 26px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 18px;\"\u003e\n \u003cp\u003eBetweenness\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 18px;\"\u003e\n \u003cp\u003eCloseness\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 18px;\"\u003e\n \u003cp\u003eStrength\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 18px;\"\u003e\n \u003cp\u003eExpected Influence\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 26px;\"\u003e\n \u003cp\u003eAll of children\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 18px;\"\u003e\n \u003cp\u003e0.128\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 18px;\"\u003e\n \u003cp\u003e0.750\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 18px;\"\u003e\n \u003cp\u003e0.750\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 18px;\"\u003e\n \u003cp\u003e0.750\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 26px;\"\u003e\n \u003cp\u003eleft-behind children\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 18px;\"\u003e\n \u003cp\u003e0.517\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 18px;\"\u003e\n \u003cp\u003e0.749\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 18px;\"\u003e\n \u003cp\u003e0.749\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 18px;\"\u003e\n \u003cp\u003e0.749\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 26px;\"\u003e\n \u003cp\u003eNon-left-behind children\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 18px;\"\u003e\n \u003cp\u003e0.129\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 18px;\"\u003e\n \u003cp\u003e0.750\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 18px;\"\u003e\n \u003cp\u003e0.750\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 18px;\"\u003e\n \u003cp\u003e0.750\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n\u003c/table\u003e\n\u003cp\u003e\u003cstrong\u003eNetwork comparison\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eNetwork comparisons between left-behind children and non-left-behind children were conducted through three tests. First , the network structure invariance test, revealed no significant differences in the overall network structure between the two groups (p=0.08\u0026gt;0.05), indicating similar structures. Second, the global strength invariance test, also showed no significant differences in the strength of SA networks (p=0.15\u0026gt;0.05). Third, the edge invariance test highlighted that certain edges differed significantly between left-behind children and non-left-behind children (left-behind children=1.73, non-left-behind children=1.24; p=0.01\u0026lt;0.05). Significant differences were observed at 3 edges between left-behind children and non-left-behind children. More specifically, the edge connecting between CA and AL , CA and LA, as well as AL and PEA were significantly stronger in non-left-behind children compared to their left-behind counterparts (p \u0026lt; 0.05).\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCombined networks\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eNetwork estimation\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eTo comprehend the network structure of parenting styles and social adaptation(PS-SA), we estimated three regularized networks based on left-behind children(Figure 4A), non-left-behind children(Figure 4B) and overall children(Figure 4C), encompassing all 11 dimensions. This resulted in a total of 55edges (11*(11-1)/2). In the PS-SA network of the overall sample of children and the non-left-behind children sample, there are 29 edges with non-zero weights(mean weight 0.05 and 0.05). The social adaptation network for left-behind children includes 32 edges with non-zero weights(mean weight 0.06). Figure 4 demonstrates the significant strength of internal connections within each dimension. \u0026nbsp;\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCentrality estimation\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eFigure 5 illustrates the centrality of each dimension in the three PS-SA networks. Prior to constructing the network structure, each dimension was standardized due to the varying scoring methods used in the questionnaires for parenting style and social adaptation. In terms of strength centrality, IA, LA, PEA, and MEW demonstrated the highest strength centrality among non-left-behind children as well as the overall child population. In contrast, IA, LA, FEW, and MEW exhibited the highest strength centrality among \u0026nbsp; left-behind children. In terms of closeness centrality, MEW, LA, IA, and MR demonstrated the highest closeness centrality among non-left-behind children as well as the overall child population. In contrast, IA, LA, FEW, and MEW exhibited the highest closeness centrality among left-behind children. In terms of betweenness centrality, IA, MR, LA, and FEW demonstrated the highest betweenness centrality among non-left-behind children; MR, MEW, IA, and FEW had the highest betweenness centrality among overall child population;and IA, FEW, LA and MR exhibited he highest betweenness centrality among left-behind children. In terms of expected influence centrality, LA, IA, PEA, and PO were identified as the most influential variables across the three networks.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eNetwork accuracy and stability\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe results of edge-weight bootstrapping (Table 3) indicate that the three network estimations were moderately accurate. The CS coefficients for strength, closeness, and betweenness, and expected influence in all three networks are above 0.50, suggesting that the overall network stability was excellent.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eTable 3.\u0026nbsp;\u003c/strong\u003eCS-coefficient of different groups in PS-SA network structures\u003c/p\u003e\n\u003cdiv align=\"center\"\u003e\n \u003ctable border=\"0\" cellspacing=\"0\" cellpadding=\"0\" width=\"99%\"\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 26px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 17px;\"\u003e\n \u003cp\u003eBetweenness\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 17px;\"\u003e\n \u003cp\u003eCloseness\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 14px;\"\u003e\n \u003cp\u003eStrength\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 22px;\"\u003e\n \u003cp\u003eExpected Influence\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 173px;\"\u003e\n \u003cp\u003eAll of children\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 17px;\"\u003e\n \u003cp\u003e0.517\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 17px;\"\u003e\n \u003cp\u003e0.750\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 14px;\"\u003e\n \u003cp\u003e0.750\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 22px;\"\u003e\n \u003cp\u003e0.750\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 173px;\"\u003e\n \u003cp\u003eleft-behind children\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 17px;\"\u003e\n \u003cp\u003e0.128\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 17px;\"\u003e\n \u003cp\u003e0.595\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 14px;\"\u003e\n \u003cp\u003e0.749\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 22px;\"\u003e\n \u003cp\u003e0.749\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 173px;\"\u003e\n \u003cp\u003eNon-left-behind children\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 17px;\"\u003e\n \u003cp\u003e0.516\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 17px;\"\u003e\n \u003cp\u003e0.750\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 14px;\"\u003e\n \u003cp\u003e0.750\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 22px;\"\u003e\n \u003cp\u003e0.750\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n\u003c/div\u003e\n\u003cp\u003e\u003cstrong\u003eNetwork comparison\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eNetwork comparisons between left-behind children and non-left-behind children were conducted through three tests. First , the network structure invariance test, revealed no significant differences in the overall network structure between the two groups (p=0.13\u0026gt;0.05), indicating similar structures. Second, The global strength invariance test showed a significant difference in PS-SA network strength (p=0.03\u0026lt;0.05), with left-behind children exhibiting higher strength invariance. Third, the edge invariance test highlighted that certain edges differed significantly between left-behind children and non-left-behind children (left-behind children=4.13, non-left-behind children=6.34; p=0.01\u0026lt;0.05). Significant differences were observed at 12 edges between left-behind children and non-left-behind children. Specifically, the connections between FR and IA, FR and LA, as well as FEW and LA were significantly stronger in left-behind children compared to their non-left-behind counterparts (p \u0026lt; 0.05). On the other hand, the connections between MEW and PEA, IA and LA, were significantly stronger in non-left-behind children compared to their left-behind counterparts (p \u0026lt; 0.05).\u003c/p\u003e"},{"header":"Discussion","content":"\u003cp\u003eThis study is the first to utilize network analysis in examining the core dimensions of social adaptation among left-behind children and non-left-behind children, as well as the relationship between parenting styles and social adaptation. Firstly, This study identified the central dimensions of SA networks across different groups. Secondly, this study identified the central dimensions of PS-SA networks across different groups. Lastly, this study conducted three tests to compare the differences in SA networks and PS-SA networks between left-behind children and non-left-behind children. By employing a network approach, the study provides new insights into which dimensions have the most significant impact on children\u0026apos;s social adaptation and how parenting style and social adjustment dimensions are interconnected within the network. These findings can inform the development of precise and effective interventions.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eSocial adaptation networks\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThis research found that left-behind children had significantly lower social adaptation scores compared to non-left-behind children, aligning with previous studies\u003csup\u003e33-34\u003c/sup\u003e. Network analysis results reveal that \u0026apos;IA\u0026apos; and \u0026apos;LA\u0026apos; were the core dimensions in three SA network structures, highlighting the importance of interpersonal adaptation and learning adaptation for both groups of children. These dimensions played a critical role in social adaptation and can have implications for various other areas. Children who struggle with interpersonal or academic adjustment may experience challenges in emotional well-being, life adjustments, and may exhibit maladaptive behaviors\u003csup\u003e35\u003c/sup\u003e. Specifically, those with poor interpersonal adjustment may exhibit feelings of loneliness, social withdrawal, and aggression\u003csup\u003e36-37\u003c/sup\u003e, while those with academic struggles may face internalizing issues like self-doubt, anxiety, and depression\u003csup\u003e38\u003c/sup\u003e. These difficulties can hinder their ability to effectively adapt to their current social environment.\u003c/p\u003e\n\u003cp\u003eFurthermore, this study found that the connection between IA and AL showed the strongest correlation in all three SA networks, followed by the connection between IA and PEM. These results indicate a significant bidirectional relationship between interpersonal adaptation, learning adaptation, and positive emotional adaptation, which supports the idea of predictive relationships in the developmental cascade theory\u003csup\u003e39\u003c/sup\u003e. Liu et al. also discovered a bidirectional predictive relationship between interpersonal adaptation and emotional adaptation in college students, which is consistent with the findings of this study\u003csup\u003e40\u003c/sup\u003e.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eFinally, we also examined the network variations in SA network between rural left-behind children and non-rural left-behind children. The findings revealed no significant differences in network structure invariance and global strength invariance between the two groups, but a notable distinction in edge invariance. Specifically, the connections between nodes in the SA network of rural left-behind children were weak, indicating a lack of robust interactions across various dimensions of social adaptation within this group. In line with the developmental cascade theory of social adaptation, positive development in one dimension should positively influence other dimensions of adaptation\u003csup\u003e41\u003c/sup\u003e. However, the study found weaker connection strengths between nodes in the SA network of left-behind children, suggesting that higher scores on certain positive adaptation dimensions do not consistently translate into higher scores on other dimensions. This highlights that the limited interconnection among different social adaptation dimensions in left-behind children impedes the establishment of a positive development cycle.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCombined networks\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eA correlation analysis was conducted to investigate the relationship between children\u0026apos;s social adaptation and parents\u0026apos; parenting styles. The findings demonstrated a significant positive correlation between social adaptation and positive parenting styles, as well as a significant negative correlation with negative parenting styles, which is consistent with prior research\u003csup\u003e42-43\u003c/sup\u003e.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eNetwork analysis revealed that the core dimensions in the PS-SA network for left-behind children were \u0026apos;IA\u0026apos;, \u0026apos;LA\u0026apos;, \u0026apos;FR\u0026apos;, and \u0026apos;MR\u0026apos;, while for non-left-behind children, the core dimensions were \u0026apos;IA\u0026apos;, \u0026apos;LA\u0026apos;, \u0026apos;MR\u0026apos;, and \u0026apos;MEW\u0026apos;. This indicates that left-behind children experienced higher levels of rejection from their fathers, whereas non-left-behind children perceived more emotional warmth from their mothers. Left-behind children often experience higher levels of rejection from their fathers due to two primary factors. Firstly, fathers in these families often work long hours away from home, leading to limited interactions with their children. Secondly, rural left-behind children may be more sensitive to rejection\u003csup\u003e44\u003c/sup\u003e, further exacerbating their sense of being rejected by their fathers. In contrast, non-left-behind children typically receive more emotional support and warmth from their mothers. This difference could be attributed to the fact that in left-behind families, mothers may also work outside the home or bear the sole responsibility for family care, resulting in less time for emotional bonding and attention to their children\u0026apos;s daily needs\u003csup\u003e45\u003c/sup\u003e. As a result, the emotional warmth provided by mothers does not play a significant role in the social adaptation of left-behind children.\u003c/p\u003e\n\u003cp\u003eDifferences were observed in the networks of left-behind children compared to their non-counterparts. Specifically, we found that rural left-behind children show significantly stronger associations between FR and IA, FR and LA, as well as FEW and LA. Conversely, non-left-behind children exhibit significantly stronger associations between MEW and PEA, as well as between IA and LA. These findings indicate that left-behind children might struggle with learning and interpersonal adjustment issues when experienced higher levels of paternal rejection. Previous studies have also shown that paternal rejection can lead to a lack of social skills in children, resulting in difficulties in interpersonal and academic adjustment\u003csup\u003e46\u003c/sup\u003e. Conversely, the presence of emotional warmth from fathers has been linked to better academic adaptability in children, possibly due to variations in fathers\u0026apos; involvement in their children\u0026apos;s lives and education\u003csup\u003e47\u003c/sup\u003e. Left-behind children often have limited communication with their fathers and are more likely to experience conflicts over academic matters, which can impede their academic adjustment. Moreover, mothers of non-left-behind children appear to exert a more significant influence on their children\u0026apos;s emotional well-being. This may be attributed to the fact that these mothers have more time and energy to dedicate to addressing their children\u0026apos;s emotional needs, thereby helping them to effectively manage negative emotions and moods.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eImplications\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eUtilizing network analysis technology, we uncovered the social adaptation network structure characteristics of left-behind children and non-left-behind children. We also examined the influence of parental parenting styles on social adaptation, providing new insights into the analysis of social adaptation issues faced by left-behind children and their underlying causes.\u003c/p\u003e\n\u003cp\u003eThis research findings can assist parents and schools in implementing more tailored adaptive education for left-behind children. The study emphasizes the importance of interpersonal adaptation and learning adaptation for both left-behind children and non-left-behind children, highlighting the significance of nurturing children\u0026apos;s interpersonal skills and learning strategies through family and school education. Moreover, the study reveals that left-behind children often experience a sense of rejection from their fathers, and positive development in one aspect of adaptation does not necessarily lead to improvement in other areas. Hence, fathers are encouraged to invest more time and effort in the education of left-behind children. By fostering communication between fathers and children, imparting correct worldviews and interpersonal skills, the social adaptation of left-behind children can be enhanced.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eLimitations and future directions\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eDespite the novelty of our study and the valuable findings presented, these limitations should be acknowledged. The primary limitation of this study is that the development of network models relies on cross-sectional studies and group-level data, which may not adequately elucidate the causal associations between nodes. Therefore, longitudinal intra-individual analyses, such as dynamic networks\u003csup\u003e48\u003c/sup\u003e, are necessary to complement our findings. The second limitation of this study is the reliance on self-report measures, which may be subject to self-report biases\u003csup\u003e49\u003c/sup\u003e. Future research could consider incorporating clinician-administered interviews to assess problematic or addictive behaviors. The third limitation of this study is its exclusive focus on the relationship between parenting styles and social adaptation. However, children\u0026apos;s social adaptation is a multifaceted concept that is developmentally specific. It is influenced not only by family factors but also by various elements within the school and broader social environments\u003csup\u003e50\u003c/sup\u003e. Future research should consider simultaneously investigating the impact mechanisms of multiple factors on children\u0026apos;s social adaptation.\u003c/p\u003e"},{"header":"Conclusions","content":"\u003cp\u003e \u003cul\u003e \u003cli\u003e \u003cp\u003eTo the best of our knowledge, this is the first study to utilize network analysis technology in comparing the social adaptation network structural characteristics of left-behind children and non-left-behind children, as well as to examine the influence of parental parenting styles on social adaptation. This study enhances the understanding of the interrelationship between parental rearing styles and the social adjustment. First, within the SA network, we found that the core symptoms of left-behind children and their non-left-behind counterparts are identical, with both groups exhibiting IA and LA. This suggests that these two dimensions serve as the most effective indicators of children's social adaptation. A comparison of the networks of both groups revealed similar network structures and global strengths, yet notable differences in specific dimension associations. Second, within the PS-SA network, we found that the core symptoms of left-behind children differ from those of non-left-behind children. Specifically, IA, LA, FR, and MR comprise the core dimensions of the left-behind children network, whereas IA, LA, MR, and MEW constitute the core dimensions of the non-left-behind children network. Although the networks of both groups displayed similar structures, they varied in global strength and specific dimension associations. The observed differences in core symptoms and symptom relationships within the PS-SA framework offer new insights for developing strategies aimed at enhancing the social adaptation of left-behind children.\u003c/p\u003e \u003c/li\u003e \u003c/ul\u003e \u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eEthics approval and consent to participate\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThis study was approved by the Ethics Committee of Yancheng Teachers University. \u0026nbsp;All procedures were conducted in compliance with relevant ethical guidelines and regulations. In line with the requirements of the ethics committee, informed consent was obtained from all participants. For participants under the age of 15, written informed consent was secured from their parents or legal guardians, while research consent was also obtained from school administrators and head teachers prior to the study.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eConsent for publication\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eNot applicable.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAvailability of data and materials\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe datasets and materials used during the current study available from the corresponding author on reasonable request.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCompeting interests\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe authors declare that they have no known competing financial interests.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eFunding\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eSocial Science Foundation of Jiangsu Province in 2024 (No. 24JYC002) .\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAuthors\u0026apos; contributions\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eS. F.\u003c/strong\u003e designed the study protocol, conducted data collection and substantially revised the manuscript.\u003cstrong\u003e\u0026nbsp;\u003c/strong\u003e\u003cstrong\u003eQ. G.\u003c/strong\u003ewrote the first draft of the paper. \u003cstrong\u003eX. G.\u0026nbsp;\u003c/strong\u003econducted the data analysis. \u003cstrong\u003eB. D.\u003c/strong\u003e designed the study protocol, assisted in revising the paper. All authors have read and agreed to the published version of the manuscript.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAcknowledgements\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe authors thank the Project of the 15th Jiangsu Province primary and secondary school teaching research Project (No. 2023JY15-GX-L03).\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n \u003cli\u003eNational Bureau of Statistics《What the 2020 Census Can Tell Us About Children in China Facts and Figures 》(https://www.stats.gov.cn/zs/tjwh/tjkw/tjzl/202304/t20230419_1938814.html). (Chinese)\u003c/li\u003e\n \u003cli\u003eCao, H. B., Wang, J. X., Zhang, K. Relationship Between Perceived Discrimination and Mental Health of Left-behind Children:A Meta-analysis of Chinese Students. \u003cem\u003ePsychological Exploration\u003c/em\u003e. 2022; 42(06): 546-555. \u0026nbsp;(Chinese)\u003c/li\u003e\n \u003cli\u003eFellmeth, G., Rose-Clarke, K., Zhao, C., Busert, L. 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The effect of cumulative risk related to family adversity on socialadjustment among left-behind children in China: The mediating role of stress and the moderating role of psychosocial resources. \u003cem\u003eActa Psychologica Sinica\u003c/em\u003e. 2023; 55(08): 1270-1284.(Chinese)\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Social Adaptation, Parenting Styles, Network Analysis, Rural Left-Behind Children, Warning timeliness analysis","lastPublishedDoi":"10.21203/rs.3.rs-6169635/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6169635/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eNumerous theoretical and empirical studies have demonstrated that parenting styles significantly influence the social adaptation of left-behind children. Previous research typically categorized parenting styles into distinct types before investigating the relationship between these types and the overall social adaptation levels of left-behind children. However, this approach did not allow for an exploration of the specific dimensions of parenting styles and social adaptation that may be directly related to one another. This study use network analysis to conceptualize parenting styles and social adaptation as a network of interrelated dimensions. The objective is to identify key dimensions and to examine the correlations among these dimensions. A total of 2,452 children were included in this study (n\u003csub\u003eleft-behind\u003c/sub\u003e=713, n\u003csub\u003enon-left-behind\u003c/sub\u003e =1739;Mage\u0026thinsp;=\u0026thinsp;12.13, SD\u0026thinsp;=\u0026thinsp;2.95). The results indicated that \u003cem\u003einterpersonal adaptation\u003c/em\u003e and \u003cem\u003elearning adaptation\u003c/em\u003e are core dimensions within the social adaptation(SA) networks of both left-behind and non-left-behind children. \u003cem\u003einterpersonal adaptation\u003c/em\u003e, \u003cem\u003elearning adaptation\u003c/em\u003e, \u003cem\u003efather refused\u003c/em\u003e, and \u003cem\u003emother refused\u003c/em\u003e constitute the core dimensions of the parenting styles and social adaptation (PS-SA) network for left-behind children, while \u003cem\u003einterpersonal adaptation\u003c/em\u003e, \u003cem\u003elearning adaptation\u003c/em\u003e, \u003cem\u003emother refused\u003c/em\u003e', and \u003cem\u003emother's emotional warmth\u003c/em\u003e form the core dimensions of the PS-SA network for non-left-behind children. The network comparisons indicate that the connection strengths between \u003cem\u003efather refused\u003c/em\u003e and \u003cem\u003einterpersonal adaptation\u003c/em\u003e, \u003cem\u003efather refused\u003c/em\u003e and \u003cem\u003elearning adaptation\u003c/em\u003e, as well as \u003cem\u003efather's emotional warmth\u003c/em\u003e and \u003cem\u003elearning adaptation\u003c/em\u003e are more robust in the PS-SA network of left-behind children; the connection strengths between \u003cem\u003emother's emotional warmth\u003c/em\u003e and \u003cem\u003epositive emotional adaptation\u003c/em\u003e, as well as \u003cem\u003einterpersonal adaptation\u003c/em\u003e and \u003cem\u003elearning adaptation\u003c/em\u003e, are stronger in the PS-SA network of non-left-behind children. This study contributed to the conceptualization and visualization of the relationship between parenting styles and social adaptation. The findings can assist parents and schools in implementing more targeted adaptation education for left-behind children.\u003c/p\u003e","manuscriptTitle":"The relationship between social adaptation and parenting styles in left-behind and non-left-behind children: a network analysis","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-04-17 09:39:19","doi":"10.21203/rs.3.rs-6169635/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"96491c51-ca78-4851-8356-238c91f7751a","owner":[],"postedDate":"April 17th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2025-07-03T06:24:01+00:00","versionOfRecord":[],"versionCreatedAt":"2025-04-17 09:39:19","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-6169635","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-6169635","identity":"rs-6169635","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}