Parental involvement and social skills of school-aged children with intellectual disabilities: the role of parenting stress and social support

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However, the mechanisms underlying this relationship remain unclear. Objectives This study aimed to examine the relationship between parental involvement and social skills in children with ID, assess the mediating role of parenting stress, and explore the moderating effect of social support on the relationship between parenting stress and children’s social skills. Methods Using convenience sampling, 692 parents of children with ID (aged 6–18) from special education schools in Zhongshan and Heze, China (May-July 2024) were recruited. Participants completed the Social Responsiveness Scale-Short Form, Parental Involvement Questionnaire, Parenting Stress Index-Short Form-15, and Multidimensional Scale of Perceived Social Support. SPSS was used for descriptive statistics and SmartPLS was to examine the mediation and moderation effects. Results Parental involvement had a significant positive direct effect on children’s social skills (β = -0.099, p < 0.01, due to the reverse scoring of the SRS-SF). Parenting stress partially mediated this relationship (indirect effect: β = -0.074, p < 0.01), with higher parental involvement significantly associated with lower parenting stress (β = -0.137, p < 0.01). Parenting stress partially mediated this relationship (indirect effect: β = -0.074, p < 0.01), with higher involvement being associated with lower stress (β = -0.137, p < 0.01) and lower stress predicting better social skills (β = 0.543, p < 0.001). Social support significantly moderated the negative relationship between parenting stress and children’s social skills (β = 0.056, p < 0.05), with higher levels of social support mitigating the negative effects of parenting stress. Conclusions : This study revealed a complex interplay between parental involvement, parenting stress, and social support in shaping social skills development in children with ID. These findings support an integrated intervention approach that enhances parental involvement, reduces parenting stress, and strengthens social support systems. However, the cross-sectional nature of this study precludes causal interpretations, warranting longitudinal investigation to establish temporal relationships. Children with intellectual disabilities Social skill Parental involvement Parenting stress Social support Figures Figure 1 Figure 2 Figure 3 Introduction Children with intellectual disabilities (ID) navigate unique developmental pathways, with social adaptation being an important area of growth for them. Their distinctive cognitive processing styles and emotional regulation approaches may lead to different social interaction patterns within school, family, and community contexts [ 1 ]. Existing research has extensively examined intrinsic factors affecting children’s social skills, including cognitive impairment [ 2 ], age-related differences [ 3 ], and gender differences [ 4 ]. However, a growing body of evidence suggests that the family environment is a key external factor in promoting the social development of children with ID [ 5 – 6 ]. According to Bronfenbrenner’s ecological systems theory, children’s development is influenced by the interactions between individuals and their environment. Among these, the family, as the most direct microsystem, shapes children’s behavioral patterns and directly and indirectly influences their social functioning development through interactions with other systems such as schools and communities [ 7 ]. Parental involvement, as a direct means of supporting childre n’s development, has significant research value. Previous studies have confirmed that parental involvement can significantly enhance self-efficacy and social skills among typically developing children [ 6 ]. However, due to the need for long-term and intensive caregiving [ 8 ], parents of children with ID often experience higher levels of parenting stress [ 9 ], emotional exhaustion, and role conflicts [ 10 ]. Such high-stress conditions may lead to negative parenting behaviors, thereby weakening the positive effects of parental involvement [ 11 ]. Consequently, it is necessary to clarify the specific mechanisms by which parental involvement influences the development of social skills in children with ID. Social support, an important external resource that moderates parenting stress, can potential ly improve the quality of parental involvement in children’s education. Research indicates that parents who receive adequate social support can cope with parenting stress more effectively and demonstrate more positive parental involvement behaviors [ 12 ]. Based on this, the current study attempts to integrate the stress process model [ 13 ] and social support buffering model [ 14 ] to propose a new moderated mediation model that hypothesizes that parenting stress mediates the process by which parental involvement affects children’s social skills, whereas social support moderates the relationship between parenting stress and children’s social skills, thereby forming an integrated pathway of family system influence. Furthermore, cultural context profoundly affects parental involvement patterns and their effectiveness. Compared with Western cultures, which emphasize children’s independence and self-expression, Chinese culture emphasizes collectivism and relationship orientation [ 15 ]. Deeply influenced by Confucian culture, Chinese parents typically hold high educational expectations for their children and support their development through structured guidance and control [ 6 , 16 ]. These cultural characteristics may lead Chinese families to adopt more protective involvement strategies than autonomy-promoting ones when raising children with ID. The current study addresses the significant limitations of the existing literature. Previous research has tended to examine factors such as parental involvement and parenting stress in isolation, overlooking the complex dynamic interactions among these variables. However, many findings based on Western cultural contexts fail to effectively explain the impact of the unique protective parenting style characteristic of China's collectivist culture on the social development of children with intellectual disabilities (ID). This study aimed to construct an integrated model and, through a questionnaire-based approach, systematically investigate how parental involvement, parenting stress, and social support The theoretical contributions of this study are as follows: ① deepening the applicability of ecological systems theory and family systems theory in the field of special education; ② constructing a dynamic integrated model to reveal the mechanisms within the family system of children with ID; and ③ exploring culturally specific influencing factors to enrich cross-cultural research in special education. On a practical level, this study provides empirical evidence for designing scientifically informed and precise family support programs, thereby promoting the social functioning and long-term development of children with ID. Literature review and hypotheses Parental involvement and social skills Social skills refer to a series of learned behavioral abilities that individuals display in social interactions, enabling them to interact effectively with others and adapt to various social environments [ 17 ]. Operationally, these abilities typically manifest as measurable behavioral expressions such as cooperation, self-assertion, self-control, and responsibility [ 1 ]. For children with ID, Social skills have special significance for children with ID, primarily encompassing three core dimensions: social orientation (e.g., initiating greetings and maintaining eye contact), emotional regulation (e.g., identifying and expressing emotions and managing conflicts), and environmental adaptation (e.g., following rules, sharing, and cooperating) [ 5 , 6 , 18 ]. Children with ID face unique challenges in their development of these skills. Cognitive processing limitations make it difficult to understand social cues, and they have relatively limited opportunities to experience diverse social situations [ 4 ]. However, these social skills are crucial for successful integration into educational environments and broader society. Dean and Chang [ 19 ] confirmed that social skill levels directly predicted the quality of social inclusion and psychological adaptation of children with autism in mainstream educational environments, emphasizing the critical role of these abilities in their educational success. Parental involvement refers to the time, energy, and resources parents invest in their children’s education and development [ 8 ], manifested in activities within the home environment (e.g., shared reading and emotional support) and extending to the school and community levels (e.g., home-school communication and volunteer service) [ 20 ]. Epstein systematizes parental involvement into six types: parenting, communication, volunteering, learning at home, decision-making participation, and community collaboration [ 17 ]. This provides a theoretical foundation for understanding the multidimensional nature of parental involvement in education. Parental involvement presents unique patterns and greater significance in children with ID. Compared to typically developing children, children with ID require more intensive and continuous support, demanding parental involvement across multiple dimensions [ 21 ]. Zhang et al. [ 5 ] found that parents of Chinese children with ID not only need to directly assist with learning tasks, but also more actively provide emotional support, facilitate teacher-student communication and peer interaction, and construct a holistic developmental environment. This multilevel involvement, which targets the special needs of children with ID, is crucial for social skill development [ 18 ]. The impact of parental involvement on the social skill development of children with ID can be understood using two complementary theoretical frameworks. Bronfenbrenner’s ecological systems theory provides a multilevel analytical perspective that explains how child development is embedded within interacting environmental systems [ 7 ]. Within this framework, parents create structured social learning contexts through direct interactions at the micro -system level. At the mesosystem level, they ensure consistency in educational goals and support strategies by connecting family and school environments, which is particularly crucial for children with ID who have limited cognitive processing abilities. Complementary to this, Epstein’s theory of overlapping spheres of influence emphasizes how the three main influential domains—family, school, and community—overlap and work together [ 22 ]. When these three systems collaborate closely, they form the most advantageous “overlapping influence zone” for child development. This collaboration is especially important for children with ID, who experience difficulties in recognizing social cues and generalizing skills. Parents create learning continuity across environments by maintaining close communication with teachers and reinforcing the social skills taught at school in their daily lives [ 23 ]. Together, these theoretical frameworks indicate that in promoting the social skill development of children with ID, parents serve as both direct constructors of the social environment and key facilitators of school-based social education. They effectively addressed these children’s inherent challenges in acquiring and generalizing their social skills by establishing a consistent and coherent support system. Cross-cultural research has provided rich evidence to support the positive impact of parental involvement on the social skills of various groups of children. Multiple studies have consistently found that parental involvement play s a key role in typically developing children. Dekker and Kamerling’s large-sample study in the Netherlands showed that parents not only enhance children’s social abilities through modeling, motivation, and guidance but also partially alleviate social challenges arising from school ethnic diversity [ 17 ]. Similarly, LaRosa et al. found that family educational involvement and home-school communication quality significantly predicted children’s social-emotional development [ 20 ]. Notably, Magaly et al.’s research in Peru revealed the unique contribution of fathers’ involvement, particularly in boys’ social development, emphasizing the necessity for diverse caregiver participation [ 24 ]. This positive influence was verified in groups of children with special needs and was consistent across disability types. Bennett and Hay’s research on children with physical disabilities [ 25 ] and Calderon’s study on children with hearing impairments found that high levels of parental educational involvement were significantly correlated with better social skill development [ 26 ]. Most relevantly, Zhang et al. ’s findings in a sample of Chinese children with ID further confirmed this relationship; in an environment of home-school collaboration, high-quality parental involvement can significantly promote the social ability development of children with ID [ 5 ]. The above research spans different cultural backgrounds (European, Latin American, and Asian) and encompasses typically developing children and various groups with special needs. These results suggest that parental involvement may be a universal protective factor for children’s social development and that this protective effect is particularly important for children with limited cognitive abilities. Based on this empirical evidence, this study proposes the following hypothesis: H1: Parental involvement has a significant positive predictive effect on the social skills of school-aged children with ID. Parental involvement and parenting stress Parenting stress is a complex state shaped by multiple factors, including child characteristics, parental psychological resources, and environmental support [ 9 ]. Although traditional research has explored how parenting stress influences parental involvement, recent theoretical and empirical studies have revealed that parental involvement can actively reduce parenting stress through two key pathways. On one hand, high levels of involvement create more frequent positive interaction opportunities, optimizing parents’ emotional experiences of their parental role. Crnic and Ross [ 27 ] showed that positive father s’ involvement was significantly associated with lower levels of parenting stress, indicating that direct participation in parenting practices enhances parents’ perceived competence, and that this improvement in self-efficacy is closely linked to stress reduction. However, parents can improve their children’s behavioral performance through quality involvement [ 28 ]. A longitudinal study by Goodrum et al. demonstrated that when mothers actively participated in their children’s education and daily activities, their reported levels of parenting stress decreased significantly over time [ 29 ]. This may be because the reduction in children’s behavioral problems serves as positive feedback, further dissolving parents’ stress experiences [ 30 ] and forming a virtuous cycle of stress reduction. This bidirectional reciprocal process not only reflects the dynamic nature of member interactions in the family system but also provides a theoretical foundation for understanding how parental involvement buffer s stress in families with children with ID. These findings align with the stress-buffering model [ 31 ], indicating that positive involvement as an adaptive coping strategy can alleviate stress in the family system. Quality involvement is particularly important for parents of children with ID, as it provides problem-solving tools and emotional resources to help parents address special parenting challenges more effectively. Based on the above analysis, this study proposes the following hypothesis: H2: Parental involvement significantly and negatively affects parenting stress. Parenting stress and social skills Multiple studies have supported the negative impact of parenting stress on children’s social skills. Crum and Moreland confirmed that high levels of parenting stress significantly reduced social competence and emotional regulation abilities in children aged 2–6 by increasing abuse potential [ 32 ]. This suggests that high parenting stress may lead parents to adopt inappropriate parenting behaviors, thereby hindering their children’s development of social skill s. More compelling evidence has been provided by longitudinal studies. Using cross-lagged analysis, Neece and Baker found that parenting stress at age six significantly predicted social skill deficits at age eight, while the reverse predictive path (from early social skills to later parenting stress) was not statistically significant [ 33 ]. This finding strongly supports the unidirectional causal relationship between parenting stress and social skills, establishing early parenting stress as a key predictor of children’s social development. Intervention studies have further validated this association. Neece’s study of parents of children with developmental delays demonstrated that mindfulness intervention programs that reduced parental stress significantly improved children’s social behavior. When parents’ stress levels decrease, they can provide more consistent and positive parenting environments, thus promoting the development of their children’s social skills [ 34 ]. For children with ID, this relationship may be even more critical, as they need more structured guidance in social learning; when parents reduce positive interactions due to stress, these children lose valuable social learning opportunities [ 33 ]. Based on this empirical evidence, this study proposes the following hypothesis: H3: Parenting stress significantly negatively impacts the social skills of school-aged children with ID. The Mediating Role of Parenting Stress The stress process model [ 13 ] and family systems theory [ 35 ] jointly establish a theoretical framework for understanding the relationships between parental involvement, parenting stress, and children’s social skills. The “resource-stress-outcome” chain proposed by the stress process model complements the dynamic cyclical characteristics of family interaction systems emphasized in family systems theory. These theoretical perspectives suggest that parental involvement, as a positive resource, can alleviate parenting stress, while reduced stress can promote children’s social development by optimizing the quality of parent-child interactions. Although existing research has not directly examined the complete mediation model, strong support exists for each link: parental involvement has been proven to strengthen family functioning and effectively reduce parenting stress, with mothers’ deep involvement in childcare significantly reducing role stress and improving parent-child relationships [ 29 ]. Parenting stress affects children’s social skill development by influencing their emotional regulation, parenting behavior choices, and interaction sensitivity [ 32 ]. The current study shows a notable gap in the population of children with ID. Most studies examine these relationships separately. In particular, while Neece and Baker’s longitudinal study confirmed the predictive effect of parenting stress on social skills [ 36 ], it did not include parental involvement. This mediating mechanism is especially crucial for children with ID as they rely more heavily on structured parental support to compensate for their social deficits. When parental stress is low, parents can provide targeted social guidance and practice opportunities, which are vital for the social development of children with cognitive limitations. The Chinese cultural context offers a unique perspective for understanding this mediation mechanism. In the Chinese context, parents of children with ID face dual pressure due to concerns about their children’s development and gaps in social expectations. In a culture that emphasizes “face” and family continuity, children are viewed as symbols of social status, which gives parenting stress a significant social characteristic. Chinese parents must frequently respond to judgments from their social networks, and this social pressure may further strengthen the impact of parenting stress on parent-child interactions [ 36 ]. Based on theoretical integration, existing evidence, cultural specificity, and the unidirectional relationships established in H2 and H3, this study proposes the following hypothesis: H4: Parenting stress plays a significant mediating role between parental involvement and social skills in school-aged children with ID. The Moderating Role of Social Support Parenting stress is typically directly associated with negative developmental outcomes in children, such as deficiencies in social skills and increased behavioral problems. However, this relationship is influenced by complex protective factors, including parent-child relationships and family learning environments [ 37 – 38 ]. Among many protective factors, social support is a critical external resource that can buffer the adverse effects of parenting stress. Although previous research has explored the profound impact of parental stress on child development [ 39 ] and the positive effects of social support on parental emotional adjustment and behavioral optimization [ 40 ], research on how social support moderates the relationship between parenting stress and social skills in children with ID is limited. This research gap restricts understanding and implementation of precise intervention strategies. Social support refers to various forms of assistance that individuals receive from their social networks, including emotional, informational, and instrumental support [ 41 ]. According to the stress-buffering model, social support serves as a protective resource that can buffer the effects of significant stress, thereby mitigating the negative impact of stress on psychological health and behavior [ 12 ]. Particularly for parents raising children with ID who generally face higher levels of parenting stress and complex challenges, social support plays an important role in promoting positive parenting behaviors, optimizing psychological health, and improving child developmental outcomes [ 42 ]. The social support buffering model supports the theory that social support acts as a moderating variable. This model suggests that economic and psychological stress adversely affect child development by influencing family functioning and parent-child interactions. Social support can also function as a protective external resource to mitigate negative pathways [ 43 ]. Although research that specifically examin es the moderating effects of social support is relatively scarce, few studies have provided empirical evidence for this hypothesis. For example, Lee et al. demonstrated that social support could moderate the relationship between economic stress and parental emotional distress, thereby reducing disruptive parenting behaviors and improving child developmental outcomes [ 44 ]. Notably, Hooper et al. ’s study of families participating in the Early Head Start program found that children demonstrated optimal social-emotional skills in families with low stress and high family functioning (including higher levels of social support) [ 45 ]. This study directly supported the moderating role of social support in the relationship between family stress and children’s socioemotional development. Based on the above theoretical and empirical analyses, this study proposes the following hypotheses: H5: Social support moderates the relationship between parenting stress and social skills in children with ID. Specifically, among parents with high levels of social support, the negative correlation between parenting stress and children’s social skills was significantly weakened. This study fills an important gap by providing a theoretical foundation for developing family intervention strategies. These findings will help us to better design supportive programs to ensure that children with ID receive more support and developmental opportunities within complex parenting contexts. The conceptual framework is illustrated in Fig. 1 . Methods Research design and sampling procedure This study employed a cross-sectional survey design using convenience sampling to select special education schools in Heze City (northern China) and Zhongshan City (southern China) as survey sites. These locations were chosen to represent different geographical regions and levels of economic development in China, thereby enhancing the generalizability of our findings. The selected special education schools serve school-aged children who have been formally diagnosed with ID and hold nationally recognized disability certificates. The inclusion criteria for parents were as follows: (1) cohabitation with a child with ID for more than three months; (2) absence of severe cognitive impairments or mental illness that would prevent understanding of the questionnaire content; and (3) voluntary participation in the research. To prevent stigmatization during the research process, this study implemented multilevel protective measures: sampling exclusively from special education schools to avoid labeling that might occur in integrated environments; establishing collaborative relationships with school principals to leverage existing trust foundations and increase acceptance of participation; using capability-oriented expression frameworks in all research communications, emphasizing that the purpose of the research was to enhance support systems rather than focus on deficits; and ensuring destigmatizing language in research materials and interaction processes. These measures created a research environment that respected participants’ dignity and protected their family privacy while enhancing the effectiveness of data collection. Data collection procedures The G * Power software was used to calculate the minimum required sample size. Considering that the research model involved five predictor variables (parenting stress, parental involvement, social support, interaction between parental involvement and parenting stress, and interaction between parenting stress and social support) with a medium effect size (0.15), desired statistical power of 0.90, and a significance level of 0.05, the minimum requirement was 116 respondents. Data were collected from May to July, 2024. The researchers first obtained approval and support from the principals of the special education schools in Heze and Zhongshan. Subsequently, the teachers introduced the research purpose to the parents and obtained informed consent, emphasizing questionnaire anonymity and the principle of voluntary participation. With parental consent, teachers distributed electronic questionnaires through class WeChat groups, and the researchers communicated with the teachers to track the progress of the questionnaire submissions. A total of 774 questionnaires were collected, with 22 incomplete questionnaires or questionnaires with obvious response patterns eliminated. Following Cohen’s recommendation [ 46 ], responses falling outside three standard deviations from the mean were considered outliers, resulting in the exclusion of 60 outliers. The final sample included 692 valid questionnaires, representing an effective response rate of 89.4%, which far exceeded the minimum requirement and was sufficient to support data analysis. Among the valid responses, children with ID included 341 were boys (49.3%) and 351 were girls (50.7%). The age distribution of children with ID was 190 aged 6–9 years (27.5%), 232 aged 10–12 years (33.5%), 167 aged 13–15 years (24.1%), and 103 aged 16–18 years (14.9%), ensuring comprehensive coverage across different school-age stages. Measures This study utilized two types of measurement tools: scales originally developed in Chinese, and rigorously translated foreign instruments. The back-translation method proposed was employed for the latter. The English items were translated into Chinese by bilingual experts, and other translators re-translated the Chinese version back into English. To ensure consistency , the research team compared the two English versions. All the instruments were pretested with families of children with ID to ensure their cultural relevance and comprehensibility. The details of these scales are as follows. Social responsiveness scale–short form (SRS-SF) The SRS-SF [ 47 ] was adapted to Chinese culture using a back-translation method. This scale includes 18 items across three dimensions: social cognition (5 items, example item: “Is unable to pick up on any of the meaning of conversations of older children or adults”), social communication (8 items, example item: “Is slow or awkward in turn-taking interactions with peers”), and autistic mannerisms (5 items, example item: “Has more difficulty than other children with changes in his/her routine”). Each item is rated on a 4-point Likert scale ranging from 1 (never) to 4 (always), with higher scores indicating poorer social skills. In this sample, Cronbach’s α was 0.840, composite reliability (CR) was 0.901, and average variance extracted (AVE) was 0.752, demonstrating the reliability and construct validity of the scale. Parental involvement questionnaire (PIQ) The PIQ was developed for parents of Chinese children with special needs [ 48 ]. It includes 15 items across four dimensions: parenting education (3 items, example item: “You will pay attention to information on how to educate children through media such as TV, mobile phone or newspaper”), home-school communication (4 items, example item: “You will keep in touch with the teacher by phone or social tools such as Wechat”), home learning involvement (4 items, example item: “You will take the time to train and improve your child’s language and communication skills”), and school activity involvement (4 items, example item: “You will attend parents’ Open Day, watch or participate in teacher teaching and rehabilitation training”). Items are rated on a 5-point Likert scale, ranging from 1 (never) to 5 (always), with higher scores indicating greater parental involvement. In this sample, Cronbach’s α was 0.685, CR was 0.811, and AVE was 0.522, indicating acceptable reliability and construct validity of the scale. Parenting stress index–short form-15 (PSI-SF-15) The PSI-SF-15 is a revised version of the Parenting Stress Index–Short Form, adapted to the Chinese context [ 49 ]. It contains 15 items across three dimensions : parenting distress (5 items, example item: “Unable to do new and different things”), parent-child interaction disorder (5 items, example item: “Child does not like me or want to be close”), and difficult child (5 items, example item: “Child does things that bother me a great deal”). Items are rated on a 5-point Likert scale ranging from 1 (strongly disagree) to 5 (strongly agree), with higher scores reflecting greater parenting stress. In this sample, Cronbach’s α was 0.674, CR was 0.821, and AVE was 0.610, suggesting reasonable reliability and construct validity of the scale. Multidimensional scale of perceived social support (MSPSS) The MSPSS [ 50 ] includes 12 items across three dimensions: family support (4 items, example item:“ I can talk about my problems with my family”), friend support (4 items, example item: “I can rely on my friends when I am in trouble”), and important others support (4 items, example item: “I can share happiness and sadness with some people (leaders, relatives, and colleagues)”). Items are rated on a 7-point Likert scale ranging from 1 (strongly disagree) to 7 (strongly agree), with higher scores indicating greater perceived social support. This scale has been validated in Chinese parents of children with disabilities [ 12 ]. In this study, the Cronbach’s α, CR, and AVE were 0.500, 0.747, and 0.500, respectively. Although the internal consistency coefficient was slightly below the ideal threshold (0.7), the research team retained this scale because of its established validation history in the Chinese cultural context and acceptable values for other reliability and validity indices. Data analysis Data processing and scoring The total and mean scores were calculated for all scales, with mean scores used to maintain comparability across scales with different item counts. For PIQ, PSI-SF-15, and MSPSS, reverse coding was not required because higher scores indicated higher levels of the respective constructs. For SRS-SF, higher scores reflected poorer social skills, and this scoring direction was consistent across the analysis. Statistical analyses Data analysis was conducted using SPSS 29.0 and SmartPLS 4.0. First, common method bias was assessed using SmartPLS, followed by descriptive statistics and correlation analysis using SPSS software. All analyses were standardized to three decimal places to ensure consistency. Child ’s age and sex were included as control variables. Preliminary analyses revealed a significant correlation between child age and social skills (r = 0.077, p 0.05). Partial least squares structural equation modeling (PLS-SEM) was used to evaluate the research model. A bootstrapping method with 10,000 resamples was used to calculate 95% confidence intervals, with intervals that did not overlap with zero deemed statistically significant (p < 0.05). Following the recommendations of Sarstedt et al. [ 51 ], a two-stage approach was adopted for the higher-order constructs. In Stage 1, the model included only first-order constructs and their scores were recorded. These scores were then added to the dataset as new variables. In Stage 2, these scores were used as indicators of higher-order constructs. Based on the scale developers’ perspectives [ 47 – 50 ], all four latent constructs in this study were modeled as reflective indicators. Following Hair et al. ’s guidelines, the measurement model was first evaluated (assessing construct reliability, convergent validity, and discriminant validity), followed by an analysis of the structural model to verify the relationships between the constructs and test the research hypotheses [ 52 ]. Results Common method bias assessment In this study, the data collected via parent al self-reports may have been prone to common method bias. To a ddress this issue, we employed the variance inflation factor (VIF). Generally, a VIF value under 3.3 indicates the absence of significant common method bias [ 53 ]. As presented in Table 1 , all VIF values in this study were below 3.3, suggesting that common method bias was not significant. Table 1 VIF testing SCOG SCOM AM PE HSC HLI SAI PD PCID DC FAS FRS IOS VIF 1.730 2.399 2.040 1.390 1.549 1.474 1.088 1.189 1.727 1.536 1.292 1.370 1.071 Note: Social Cognition (SCOG); Social Communication (SCOM); Autistic Mannerisms (AM); Parenting Education (PE); Home-School Communication (HSC); Home Learning Involvement (HLI); School Activity Involvement (SAI); Parenting Distress (PD); Parent-Child Interaction Disorder (PCID); Difficult Child (DC); family Support (FAS); friend Support (FRS); Important Others Support (IOS). the same applies below. Descriptive statistics and correlations analysis of variables Table 2 presents the descriptive statistics and correlations of the main variables. It should be noted that the SRS-SF scale had a reverse score. Therefore, when social skills are related to other variables, a positive correlation coefficient indicates a negative correlation and a negative correlation coefficient indicates a positive correlation. Pearson’s correlation analysis revealed that social skills were negatively correlated with parenting stress (r = 0.592, p < 0.001) and positively correlated with parental involvement (r = -0.208, p < 0.001) and social support (r = -0.237, p < 0.001). Furthermore, parenting stress was negatively associated with parental involvement (r = -0.137, p < 0.05) and social support (r = -0.191, p < 0.001). Parental involvement was positively related to social support (r = 0.400, p < 0.001). Table 2 presents the descriptive statistics and correlations between the variables. Table 2 Descriptive statistics and correlations of variables Variables M ± SD Correlations 1 2 3 4 1.Social Skill 2.632 ± 0.41 1 2.Parental Involvement 3.410 ± 0.50 -0.208 *** 1 3.Parenting Stress 3.351 ± 0.49 0.592 *** -0.137 * 1 4.Social Support 4.490 ± 0.72 -0.237 *** 0.400 *** -0.191 **** 1 Note. * p<0.05 *** p<0.001 Measurement model assessment The reliability, convergent validity, and discriminant validity of the measurement models were evaluated. Following the criteria of Hair et al. [ 52 ], the acceptable thresholds for indicator loadings, CR, and AVE were set at ≥ 0.5, ≥ 0.7, and ≥ 0.5, respectively. As shown in Table 3 , all indicator loadings exceeded 0.5, AVE values were ≥ 0.5, and CR values surpassed 0.7, indicating good reliability and convergent validity. For the discriminant validity assessment, the heterotrait-monotrait (HTMT) ratio was applied, adopting a stricter threshold of 0.85 [ 52 ]. Table 4 demonstrates that all the HTMT values between the variables met this criterion, confirming robust discriminant validity. Overall, the measurement model demonstrates satisfactory psychometric properties. Table 3 Estimation of the measurement model Construct Item Loading CR AVE Social Skill (SS) SCOG 0.830 0.901 0.752 SCOM 0.904 AM 0.866 Parental Involvement (PI) PE 0.733 0.811 0.522 HSC 0.815 HLI 0.765 SAI 0.551 Parenting Stress (PS) PD 0.610 0.821 0.610 PCID 0.879 DC 0.828 Social Support (SSU) FAS 0.624 0.747 0.500 FRS 0.815 IOS 0.668 Table 4 Discriminant validity assessment (HTMT) PI SSU PS SS SSU 0.698 - - - PS 0.252 0.330 - - SS 0.273 0.359 0.779 - SSU * PS 0.082 0.099 0.313 0.228 Structural model assessment Following confirmation of the measurement model’s quality, we conducted a structural model analysis to evaluate the significance of the hypothesized relationships and overall model quality. In PLS-SEM, structural model quality is assessed through predictive and explanatory powers. The explanatory power was evaluated using the coefficient of determination (R²) and effect size (f²), whereas the predictive power was assessed using the significance of the path coefficients and predictive relevance (Q²). As shown in Table 5 and Fig. 2 , parental involvement, parenting stress, social support, and control variables collectively explained 38.4% of the variance in social skills (R² = 0.384), indicating a moderate explanatory power [ 52 ]. Cohen suggested that f² values above 0.02, 0.15, and 0.35 represent small, medium, and large effects, respectively [ 46 ]. The f² metric quantifies the change in R² after a specific exogenous variable is removed from the model. The effect size of parenting stress on social skills was significant (f² = 0.432), whereas the effects of parental involvement on social skills (f² = 0.013) and parenting stress (f² = 0.019) were small. The interaction between social support and parenting stress was minimal (f² = 0.007). Q² reflects the model’s ability to predict reflective and endogenous constructs accurately. Only endogenous variables had Q² values. In this study, all Q² values exceeded zero, confirming that the exogenous constructs exhibited predictive relevance for the endogenous constructs [ 58 ]. Hypothesis testing Regarding the control variables, the child’s age significantly predicted social skills (β = 0.080, p 0.05). After controlling for demographic characteristics, the data supported all research hypotheses: 1. Parental involvement had a significant positive effect on social skills (β = -0.099, p < 0.01; note the reversed scoring for the SRS-SF). 2. Parental involvement had a significant negative effect on parenting stress (β = -0.137, p < 0.01). 3. Parenting stress exerted a significant negative influence on social skills (β = 0.543, p < 0.001; note the reversed SRS-SF scoring). 4. The indirect effect of parenting stress on the relationship between parental involvement and social skills was significant (β = -0.074, p < 0.01), with a variance accounted for (VAF) of 42.775%, indicating a partial mediation by parenting stress. 5. The interaction between parenting stress and social support was significant (β = 0.056, p PS -0.137 3.190 0.001 Accepted 0.019 0.019 0.009 -0.224 -0.057 H1 PI -> SS -0.099 2.761 0.006 Accepted 0.384 0.013 0.282 -0.172 -0.029 H3 PS -> SS 0.543 19.118 0 Accepted 0.432 0.485 0.597 H4 PI -> PS -> SS -0.074 3.141 0.002 Accepted - -0.123 -0.031 H5 SSU x PS -> SS 0.056 2.232 0.026 Accepted 0.007 0.005 0.104 - gender -> SS -0.017 0.280 0.780 - 0 -0.135 0.101 - age -> SS 0.080 2.624 0.009 - 0.01 0.020 0.139 To clarify the moderating effect, social support was categorized into high/low groups (± 1 SD) for simple slope analysis (Table 6 and Fig. 3 ). The results revealed that the predictive effect of parenting stress on social skills was stronger for high social support (β = 0.655, p < 0.001) than for low social support (β = 0.539, p < 0.001). The moderated mediation analysis demonstrated that the mediating effect of parenting stress was more pronounced under high social support (effect = -0.093, 95% CI: [-0.159, -0.032]) than under low social support (effect = -0.077, 95% CI: [-0.132, -0.027]). Table 6 Simple Slope Analysis Results β t P 95% CI Lower Limit Upper Limit PS -> SS conditional on SSU at + 1 SD 0.655 17.621 0.000 0.579 0.725 PS -> SS conditional on SSU at -1 SD 0.539 10.840 0.000 0.436 0.632 PI -> PS -> SS conditional on SSU at + 1 SD -0.093 2.889 0.004 -0.159 -0.032 PI -> PS -> SS conditional on SSU at -1 SD -0.077 2.834 0.005 -0.132 -0.027 Discussion Direct effects of parental involvement on social skills in children with ID This study confirmed that parental involvement significantly enhances social skills in children with ID, a finding consistent with prior research in general [ 17 , 20 ] and special education settings [ 5 , 25 ]. Theoretically, this relationship can be explained through two complementary frameworks: the ecological systems theory and overlapping spheres of influence theory. Ecological systems theory emphasizes that child development is nested within multilayered interactive systems, where the family, as the core microsystem, directly shapes developmental trajectories through daily interactions [ 7 ]. For children with ID, coherence across microsystems (e.g., family and school) is critical for effectively acquiring and generalizing social skills [ 54 ], as these children often require consistent cross-environmental support to overcome learning barriers imposed by cognitive processing limitations. Epstein’s overlapping spheres of influence theory further supplement this understanding by positing that optimal education occurs at the intersection of the family, school, and community domains [ 22 ]. Our data demonstrate that active parental engagement in “communication” and “home learning” and home-learning activities significantly improves social skills in children with ID, validating the value of synergistic inter-domain collaboration. Parental involvement promotes social skill s development through three primary mechanisms. First, parents provide additional learning opportunities and practice scenarios, compensating for the temporal and contextual constraints of school-based education [ 12 ]. Second, active involvement enhances children’s sense of belonging and self-esteem, which are psychological factors that serve as critical catalysts for social development [ 8 ]. Third, highly engaged parents are more likely to create diverse social interaction opportunities, such as organizing peer activities and community participation, offering authentic environments for practicing social skills [ 27 ]. Notably, effect size comparisons warrant further attention. The observed effect of parental involvement on social skills (β = -0.099, p < 0.01; negative coefficient under reversed scoring indicates a positive effect) aligns with Zhang et al.’s findings (β = 0.130, p < 0.05) [ 5 ] but is significantly smaller than the results reported for typically developing children (for example, β = 0.370 in Yue et al. [ 6 ]). This discrepancy highlights the unique challenges of social learning for children with ID, as deficits in cognitive processing, attention, and memory may constrain the efficacy of environmental interventions [ 1 ]. These children may require more explicit and structured social skill s instruction [ 23 ], as naturalistic parental involvement alone may be insufficient to overcome their developmental barriers. Despite the relatively small effect size, the positive impact of parental involvement is substantively significant given the social learning challenges faced by children with ID. This finding underscores the need to design family engagement strategies specifically tailored to these children. Such strategies should be structured and focused on overcoming specific cognitive barriers to maximize their potential for social development. The mediating role of parenting stress between parental involvement and social skills This study demonstrated that parenting stress plays a significant partial mediating role in the relationship between parental involvement and social skill development in children with ID. Specifically, higher parental involvement is associated with lower parenting stress, which correlates with better social skill s outcomes in children. This mediation effect accounted for 42.775% of the total effect, indicating that parental involvement not only directly influenced children’s social skills, but also indirectly promoted development by reducing parenting stress. These findings are consistent with existing empirical evidence. A randomized controlled trial by Williams et al. revealed that parents participating in supportive playgroups experienced significant reductions in parenting stress alongside marked improvements in their children’s social interaction skills [ 55 ]. This causal validation strengthens support for the mediation mechanism proposed in this study. Similarly, Kim et al. identified a partial mediation by maternal parenting stress in the relationship between paternal involvement and early infant neurodevelopment [ 56 ]. Although Kim’s study focused on neurodevelopment rather than social skills, both studies highlight ed the universal applicability of parenting stress as a mediator across developmental domains. Within the cultural context of China, this mediation mechanism may have unique significance. Traditional Chinese culture emphasizes family harmony and collectivist values, with high parental investment in education and emotional dependency on children. This heightened dependency may amplify the effects of parenting stress on child ren’s development. Furthermore, limited societal support for families with children with ID, particularly in rural and underserved communities, renders the optimization of internal family resources critical. Therefore, the quality of parental involvement is a pivotal factor in enhancing the developmental environment of these children. Notably, a bidirectional interaction may exist between parenting stress and social skill s development. Although the cross-sectional design of this study precludes definitive causal conclusions, this mutual influence is supported by both theoretical and empirical studies. For example, Neece et al.’s longitudinal research identified reciprocal temporal predictions between maternal stress and child behavioral issues, suggesting cyclical rather than unidirectional dynamics [ 30 ]. Future studies should employ longitudinal designs to explore this bidirectional relationship and its implications for mediation mechanisms. The moderating role of social support between parenting stress and social skills This study confirmed the significant moderating effect of social support on the relationship between parenting stress and social skills in children with ID (β = 0.056, p < 0.05). Specifically, under equivalent levels of parenting stress, children from families with higher social support levels exhibited better social skills. This result not only validates Cohen and Wills’stress-buffering hypothesis [ 14 ] but also extends it to families of children with ID, demonstrating that social support mitigates the direct impact of parenting stress and fosters protective environments for social development. Our findings are consistent with those in the existing literature. For instance, Yıldız and Uzundağ found that social support significantly buffered the negative effects of parenting stress on effortful control in preschoolers [ 57 ], while Park and Lee identified social support as a moderator between stress and depression in mothers of children with disabilities [ 58 ]. However, this study uniquely focused on school-aged children with ID in China, offering novel insights into the role of social support in special education contexts. A key innovation lies in identifying a threshold effect: the buffering role of social support is more pronounced in high-stress families (greater moderation path coefficients in high-support groups than in low-support groups). This suggests that limited special education resources in China should be strategically prioritized for high-stress families to maximize intervention efficacy. Culturally, the acquisition and use of social support in China reflect s distinct dynamics. Collectivist values and familial honor norms often discourage parents from disclosing their children’s developmental challenges [ 59 ], while traditional stigma toward disabilities further hinders help-seeking behaviors [ 60 ]. Our results show ed that when social support successfully overcomes these cultural barriers, its stress-buffering effects are particularly strong. This underscores the need for culturally sensitive interventions that integrate internal family networks (e.g., grandparent caregiving) with professional support. Theoretical and practical implications This study has significant theoretical and practical implications, particularly for elucidating the interactive mechanisms between parental involvement and social skill development in children with ID in the Chinese cultural context. Theoretical contributions At the theoretical level, this study integrates the family systems theory with the social support buffering model, first integrating parental involvement, parenting stress, and social support into a unified analytical framework. Constructing a moderated mediation model to explore family level mechanisms influencing social skill development in children with ID transcends prior studies that focused on singular variable pathways, such as the direct effects of parental involvement [ 24 ] or independent impacts of parenting stress [ 33 ]. The validation of parenting stress as a mediator and social support as a moderator provides cross-cultural empirical support for applying Bronfenbrenner’s ecological systems theory to special populations, deepening our understanding of the dynamic equilibrium between family environment and child development. Practical implications Practically, the se findings offer evidence-based guidance for developing differentiated family support programs. The mediating role of parenting stress suggests that parent training initiatives should not only enhance caregiving skills, but also incorporate stress management strategies. The moderating effect of social support highlights the need to prioritize community resource linkages or peer support networks for high-stress families in order to enhance intervention efficacy. These insights inform the development of “family-school-community” collaborative intervention systems, such as integrating mental health assessments into parent training and establishing teacher-social worker partnerships. Limitations and future directions While this study advances the field, several limitations warrant attention. 1. Design Constraints: The cross-sectional design limits causal inferences about the relationships among parental involvement, parenting stress, social support, and social skill development. Future longitudinal tracking studies should systematically examine these dynamic and bidirectional interactions, as well as temporal patterns. 2. Measurement limitations: Reliance on parental self-reports risks common method bias, potentially inflating the observed associations. Multisource data (e.g., teacher evaluations and behavioral observations) should be incorporated to enhance objectivity. 3. Sample representativeness: Underrepresentation of diverse socioeconomic backgrounds restricts generalizability. Stratified sampling based on household registration type, parental education level, and family structure is recommended. 4. Lack of dimensional specificity: The study did not differentiate between subtypes of parental involvement (e.g., academic support and emotional guidance) or social support dimensions (e.g., informational, emotional, and instrumental). Future studies should refine the variable classifications to identify precise mechanisms and multifactorial interactions. Declarations Supplementary Information The online version contains supplementary material available at “web address”. Supplementary Material 1 Acknowledgements We thank Sudan Idris Education University and all participants. Author contributions Yuting Han: Research conceptualization and design, methodology design, data collection, statistical analysis, and writing and finalizing the initial draft. Eng Hock Kway: Questionnaire revision, literature review support, results visualization, and writing of partial sections. Tingzhao Wang: Research supervision and guidance, funding acquisition, validated result interpretation, reviewed and edited the manuscript, and managed the overall project. All three authors participated in quality control of the questionnaire survey data and reviewed and approved the final version of the manuscript. Funding This work was funded by the Major Project of the National Social Science Foundation of China in 2021 (grant number: 21 & ZD293) and the National Social Science Fund Item of China in 2023 (grant number: CHA230303). Data availability The datasets during and/or analyzed during the current study available from corresponding author upon reasonable requests. Ethics approval and consent to participate This study was approved by the Human Research Ethics Committee of Sultan Idris Education University (approval no. 2024033001). All participants received detailed information about the study and provided written informed consent with the right to withdraw at any time, without providing a reason. Data collection was anonymized and securely stored with password protection and was accessible only to the research team. Competing interests The authors declare no conflicts of interest. Author details 1 School of Teacher Education, Heze University, Heze, Shandong, China 2 Faculty of Human Development, University Pendidikan Sultan Idris, Tanjong Malim, Malaysia 3 School of Education, Shaanxi Normal University, Xi’an, Shaanxi, China. References Sigafoos J, Lancioni GE, Singh NN, et al. Intellectual disability and social skills. In: Matson JL, editor. Handbook of social behavior and skills in children. Cham: Springer International Publishing; 2017. pp. 249–71. Gül SO. The combined use of video modeling and social stories in teaching social skills for individuals with intellectual disability. 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The moderating effect of social support on parental stress and depression in mothers of children with disabilities. Occup Ther Int. 2022;2022:5162954. Ren L, Edwards CP. Pathways of influence: Chinese parents’ expectations, parenting styles, and child social competence. Early Child Dev Care. 2015;185(4):614–30. Wang P, Michaels CA. Chinese families of children with severe disabilities: Family needs and available support. Res Pract Pers Severe Disabil. 2009;34(2):21–32. Supplementary Material Supplementary Material 1 is not available with this version. 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. 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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-5474664","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":440220519,"identity":"bcdec913-bb6d-454f-a353-362f06faf707","order_by":0,"name":"Yuting Han","email":"","orcid":"","institution":"Heze University","correspondingAuthor":false,"prefix":"","firstName":"Yuting","middleName":"","lastName":"Han","suffix":""},{"id":440220520,"identity":"d8404dd5-4025-458c-b0e4-03642c4c3405","order_by":1,"name":"Eng Hock Kway","email":"","orcid":"","institution":"University Pendidikan Sultan Idris","correspondingAuthor":false,"prefix":"","firstName":"Eng","middleName":"Hock","lastName":"Kway","suffix":""},{"id":440220521,"identity":"a3764092-13b1-4efa-b30e-bb69b0cb3e7a","order_by":2,"name":"Tingzhao Wang","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABAUlEQVRIiWNgGAWjYNACAyCWAOIPUL4EQR0HoFoYZxCvBaqMmYcYLQbHzx5+/aHgjt382c0PH9v8uZNncID54G0eBrs8nFrO5KVZHDB4ltw455ixcW7bs2KDA2zJ1jwMycW4tJgdyDEzOGBwOJlZIsFMOrfhcOKGAzxm0jwMBxIbcGk5/waihU0i/Zu0xR+QFv5v+LXcyDF+ANRixyORYybNwAa2hQ2vFvsbb8wYzhgcTpCQyCk27G07nDjzMJux5RyDZJxaJPtzjD9U/DlsLz8jfeODH0CH9R1vfnjjTYUdTi1AwAaKBSQFzCDCALd6kBJQMrHHq2QUjIJRMApGNgAA/c5dxNIHb5UAAAAASUVORK5CYII=","orcid":"","institution":"Shaanxi Normal University","correspondingAuthor":true,"prefix":"","firstName":"Tingzhao","middleName":"","lastName":"Wang","suffix":""}],"badges":[],"createdAt":"2024-11-18 09:38:26","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-5474664/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-5474664/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":80276278,"identity":"65c9f7fd-e5de-4af5-92f9-2ebae069f725","added_by":"auto","created_at":"2025-04-10 05:04:15","extension":"jpeg","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":96982,"visible":true,"origin":"","legend":"\u003cp\u003eThe conceptual model\u003c/p\u003e","description":"","filename":"floatimage1.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-5474664/v1/8ac368adb5c5b52e2686da9f.jpeg"},{"id":80277397,"identity":"06fd7780-bcd5-4a21-80a0-8ba71d1c5af2","added_by":"auto","created_at":"2025-04-10 05:12:15","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":1377192,"visible":true,"origin":"","legend":"\u003cp\u003eHypothesis testing\u003c/p\u003e","description":"","filename":"floatimage2.png","url":"https://assets-eu.researchsquare.com/files/rs-5474664/v1/2a1c0f64a3eb9b3e0c946e74.png"},{"id":80276281,"identity":"f076a751-ac3e-40f5-9d99-d1c674f39ab1","added_by":"auto","created_at":"2025-04-10 05:04:15","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":1772989,"visible":true,"origin":"","legend":"\u003cp\u003eThe simple slope for the interaction effect of parenting stress and social support on social skill\u003c/p\u003e","description":"","filename":"floatimage3.png","url":"https://assets-eu.researchsquare.com/files/rs-5474664/v1/8d762676a9197acd8279800f.png"},{"id":84658748,"identity":"597d03ff-5009-459e-879a-8485949e0089","added_by":"auto","created_at":"2025-06-16 03:31:40","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1902071,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-5474664/v1/bab39bfc-d3d7-4daa-be0e-d570a9a5ad32.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Parental involvement and social skills of school-aged children with intellectual disabilities: the role of parenting stress and social support","fulltext":[{"header":"Introduction","content":"\u003cp\u003eChildren with intellectual disabilities (ID) navigate unique developmental pathways, with social adaptation being an important area of growth for them. Their distinctive cognitive processing styles and emotional regulation approaches may lead to different social interaction patterns within school, family, and community contexts [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e]. Existing research has extensively examined intrinsic factors affecting children’s social skills, including cognitive impairment [\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e], age-related differences [\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e], and gender differences [\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e]. However, a growing body of evidence suggests that the family environment is a key external factor in promoting the social development of children with ID [\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e–\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e]. According to Bronfenbrenner’s ecological systems theory, children’s development is influenced by \u003cspan type=\"SmallCaps\" class=\"SmallCaps\" name=\"Emphasis\"\u003ethe interactions between individuals and their environment.\u003c/span\u003e Among these, the family, as the most direct microsystem, shapes children’s behavioral patterns and directly and indirectly influences their social functioning development through interactions with other systems such as schools and communities [\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eParental involvement, \u003cspan type=\"SmallCaps\" class=\"SmallCaps\" name=\"Emphasis\"\u003eas a direct means of supporting childre\u003c/span\u003en’s development, \u003cspan type=\"SmallCaps\" class=\"SmallCaps\" name=\"Emphasis\"\u003ehas significant research value.\u003c/span\u003e Previous studies have confirmed that parental involvement can significantly enhance self-efficacy and social skills among typically developing children [\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e]. However, due to the need for long-term and intensive caregiving [\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e], parents of children with ID often experience higher levels of parenting stress [\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e], emotional exhaustion, and role conflicts [\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e]. Such high-stress conditions may lead to negative parenting behaviors, thereby weakening the positive effects of parental involvement [\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e]. Consequently, it is necessary to clarify the specific mechanisms by which parental involvement influences the development of social skills in children with ID.\u003c/p\u003e \u003cp\u003eSocial support, an important external resource that moderates parenting stress, can potential\u003cspan type=\"SmallCaps\" class=\"SmallCaps\" name=\"Emphasis\"\u003ely\u003c/span\u003e improve the quality of parental involvement in children’s education. Research indicates that parents who receive adequate social support can cope with parenting stress more effectively and demonstrate more positive parental involvement behaviors [\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e]. Based on this, the current study attempts to integrate the stress process model [\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e] and social support buffering model [\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e] to propose a new moderated mediation model that hypothesizes that parenting stress mediates the process by which parental involvement affects children’s social skills, whereas social support moderates the relationship between parenting stress and children’s social skills, thereby forming an integrated pathway of family system influence.\u003c/p\u003e \u003cp\u003eFurthermore, cultural context profoundly affects parental involvement patterns and their effectiveness. Compared with Western cultures, which emphasize children’s independence and self-expression, Chinese culture emphasizes collectivism and relationship orientation [\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e]. Deeply influenced by Confucian culture, Chinese parents typically hold high educational expectations for their children and support their development through structured guidance and control [\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e, \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e]. These cultural characteristics may lead Chinese families to adopt more protective involvement strategies than autonomy-promoting ones when raising children with ID.\u003c/p\u003e \u003cp\u003eThe current study addresses the significant limitations of the existing literature. Previous research has tended to examine factors such as parental involvement and parenting stress in isolation, overlooking the complex dynamic interactions among these variables. However, many findings based on Western cultural contexts fail to effectively explain the impact of the unique protective parenting style characteristic of China's collectivist culture on the social development of children with intellectual disabilities (ID). This study aimed to construct an integrated model and, through a questionnaire-based approach, systematically investigate how parental involvement, parenting stress, and social support\u003c/p\u003e \u003cp\u003eThe theoretical contributions of this study are as follows: ① deepening the applicability of ecological systems theory and family systems theory in the field of special education; ② constructing a dynamic integrated model to reveal the mechanisms within the family system of children with ID; and ③ exploring culturally specific influencing factors to enrich cross-cultural research in special education. On a practical level, this study provides empirical evidence for designing scientifically informed and precise family support programs, thereby promoting the social functioning and long-term development of children with ID.\u003c/p\u003e\n\u003ch3\u003eLiterature review and hypotheses\u003c/h3\u003e\n\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003eParental involvement and social skills\u003c/h2\u003e \u003cp\u003eSocial skills refer to a series of learned behavioral abilities that individuals display in social interactions, enabling them to interact effectively with others and adapt to various social environments [\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e]. Operationally, these abilities typically manifest as measurable behavioral expressions such as cooperation, self-assertion, self-control, and responsibility [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e]. For children with ID, Social skills have special significance \u003cspan type=\"SmallCaps\" class=\"SmallCaps\" name=\"Emphasis\"\u003efor children with ID, primarily encompassing three core dimensions: social orientation (e.g., initiating greetings and maintaining eye contact), emotional regulation (e.g., identifying and expressing emotions and managing conflicts), and environmental adaptation (e.g., following rules, sharing, and cooperating)\u003c/span\u003e [\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e, \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e, \u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e]. Children with ID face unique challenges in \u003cspan type=\"SmallCaps\" class=\"SmallCaps\" name=\"Emphasis\"\u003etheir\u003c/span\u003e development \u003cspan type=\"SmallCaps\" class=\"SmallCaps\" name=\"Emphasis\"\u003eof these skills. Cognitive processing limitations make it difficult to understand social cues, and they have relatively limited opportunities to experience diverse social situations\u003c/span\u003e [\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e]. However, these social skills are crucial for successful integration into educational environments and broader society. Dean and Chang [\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e] confirmed that social skill levels directly predicted the quality of social inclusion and psychological adaptation of children with autism in mainstream educational environments, emphasizing the critical role of these abilities in their educational success.\u003c/p\u003e \u003cp\u003eParental involvement refers to the time, energy, and resources parents invest in their children’s education and development [\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e], manifested in activities within the home environment (e.g., shared reading and emotional support) and extending to the school and community levels (e.g., home-school communication and volunteer service) [\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e]. Epstein systematizes parental involvement into six types: parenting, communication, volunteering, learning at home, decision-making participation, and community collaboration [\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e]. This provides a theoretical foundation for understanding the multidimensional nature of parental involvement in education.\u003c/p\u003e \u003cp\u003eParental involvement presents unique patterns and greater significance in children with ID. Compared to typically developing children, children with ID require more intensive and continuous support, demanding parental involvement across multiple dimensions [\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e]. Zhang et al. [\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e] found that parents of Chinese children with ID not only need to directly assist with learning tasks, \u003cspan type=\"SmallCaps\" class=\"SmallCaps\" name=\"Emphasis\"\u003ebut also more actively provide emotional support, facilitate teacher-student communication and peer interaction, and construct a holistic developmental environment.\u003c/span\u003e This multilevel involvement, which targets the special needs of children with ID, is crucial for social skill development [\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eThe impact of parental involvement on the social skill development of children with ID can be understood using two complementary theoretical frameworks. Bronfenbrenner’s ecological systems theory provides a multilevel analytical perspective that explains how child development is embedded within interacting environmental systems [\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e]. Within this framework, parents create structured social learning contexts through direct interactions at the micro\u003cspan type=\"SmallCaps\" class=\"SmallCaps\" name=\"Emphasis\"\u003e-system level.\u003c/span\u003e At the mesosystem level, they ensure consistency in educational goals and support strategies by connecting family and school environments, which is particularly crucial for children with ID who have limited cognitive processing abilities.\u003c/p\u003e \u003cp\u003eComplementary to this, Epstein’s theory of overlapping spheres of influence emphasizes how the three main influential domains—family, school, and community—overlap and work together [\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e]. When these three systems collaborate closely, they form the most advantageous “overlapping influence zone” for child development. This collaboration is especially important for children with ID, who experience difficulties in recognizing social cues and generalizing skills. Parents create learning continuity across environments by maintaining close communication with teachers and reinforcing the social skills taught at school in their daily lives [\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eTogether, these theoretical frameworks indicate that in promoting the social skill development of children with ID, parents serve as both direct constructors of the social environment and key facilitators of school-based social education. They effectively addressed these children’s inherent challenges in acquiring and generalizing \u003cspan type=\"SmallCaps\" class=\"SmallCaps\" name=\"Emphasis\"\u003etheir social skills by establishing a consistent and coherent support system.\u003c/span\u003e\u003c/p\u003e \u003cp\u003eCross-cultural research has provided rich evidence \u003cspan type=\"SmallCaps\" class=\"SmallCaps\" name=\"Emphasis\"\u003eto support\u003c/span\u003e the positive impact of parental involvement on the social skills of various groups of children. Multiple studies have consistently found \u003cspan type=\"SmallCaps\" class=\"SmallCaps\" name=\"Emphasis\"\u003ethat parental involvement\u003c/span\u003e play\u003cspan type=\"SmallCaps\" class=\"SmallCaps\" name=\"Emphasis\"\u003es a key role in\u003c/span\u003e typically developing children. Dekker and Kamerling’s large-sample study in the Netherlands showed that parents not only enhance children’s social abilities through modeling, motivation, and guidance but also partially alleviate social challenges arising from school ethnic diversity [\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e]. Similarly, LaRosa et al. found that family educational involvement and home-school communication quality significantly predicted children’s social-emotional development [\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e]. Notably, Magaly et al.’s research in Peru revealed the unique contribution of fathers’ involvement, particularly in boys’ social development, emphasizing the necessity for diverse caregiver participation [\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eThis positive influence was verified in groups of children with special needs and was consistent across disability types. Bennett and Hay’s research on children with physical disabilities [\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e] and Calderon’s study on children with hearing impairments found that high levels of parental educational involvement were significantly \u003cspan type=\"SmallCaps\" class=\"SmallCaps\" name=\"Emphasis\"\u003ecorrelated with better social skill development\u003c/span\u003e [\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e]. \u003cspan type=\"SmallCaps\" class=\"SmallCaps\" name=\"Emphasis\"\u003eMost relevantly, Zhang et al. ’s findings in a sample of Chinese children\u003c/span\u003e with ID further confirmed this relationship; in an environment of home-school collaboration, high-quality parental involvement can significantly promote the social ability development of children with ID [\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eThe above research spans different cultural backgrounds (European, Latin American, and Asian) and encompasses typically developing children and various groups with special needs. These results suggest that parental involvement may be a universal protective factor for children’s social development and that this protective effect is particularly important for children with limited cognitive abilities. Based on this empirical evidence, this study proposes the following hypothesis:\u003c/p\u003e \u003cp\u003e \u003cb\u003eH1: Parental involvement has a significant positive predictive effect on the social skills of school-aged children with ID.\u003c/b\u003e \u003c/p\u003e \u003c/div\u003e\n\u003ch3\u003eParental involvement and parenting stress\u003c/h3\u003e\n\u003cp\u003eParenting stress is a complex state shaped by multiple factors, including child characteristics, parental psychological resources, and environmental support [\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e]. Although traditional research has explored how parenting stress influences parental involvement, recent theoretical and empirical studies have revealed that parental involvement can actively reduce parenting stress through two key pathways. On one hand, high levels of involvement create more frequent positive interaction opportunities, optimizing parents’ emotional experiences of their parental role. Crnic and Ross [\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e] showed that positive father\u003cspan type=\"SmallCaps\" class=\"SmallCaps\" name=\"Emphasis\"\u003es’ involvement was significantly associated with lower levels of parenting stress, indicating that direct participation in parenting practices enhances parents’ perceived competence, and that this improvement in self-efficacy is closely linked to stress reduction. However, parents can improve their children’s behavioral performance through quality involvement\u003c/span\u003e [\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e]. \u003cspan type=\"SmallCaps\" class=\"SmallCaps\" name=\"Emphasis\"\u003eA longitudinal study by Goodrum et al. demonstrated that when mothers actively participated in their children’s education and daily activities, their reported levels of parenting stress decreased significantly over time\u003c/span\u003e [\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e]. This may be because the reduction in children’s behavioral problems serves as positive feedback, further dissolving parents’ stress experiences [\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e] and forming a virtuous cycle of stress reduction. This bidirectional reciprocal process not only reflects the dynamic nature of member interactions in the family system but also provides a theoretical foundation for understanding how parental involvement buffer\u003cspan type=\"SmallCaps\" class=\"SmallCaps\" name=\"Emphasis\"\u003es stress in families with children with\u003c/span\u003e ID.\u003c/p\u003e \u003cp\u003eThese findings align with the stress-buffering model [\u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e], indicating that positive involvement as an adaptive coping strategy can alleviate stress in the family system. \u003cspan type=\"SmallCaps\" class=\"SmallCaps\" name=\"Emphasis\"\u003eQuality involvement is particularly important\u003c/span\u003e for parents of children with ID, as it provides problem-solving tools and emotional resources to help parents address special parenting challenges more effectively. Based on the above analysis, this study proposes the following hypothesis:\u003c/p\u003e \u003cp\u003e \u003cb\u003eH2: Parental involvement significantly and negatively affects parenting stress.\u003c/b\u003e \u003c/p\u003e\n\u003ch3\u003eParenting stress and social skills\u003c/h3\u003e\n\u003cp\u003eMultiple studies have supported the negative impact of parenting stress on children’s social skills. Crum and Moreland confirmed that high levels of parenting stress significantly reduced social competence and emotional regulation abilities in children aged 2–6 by increasing abuse potential [\u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e]. This suggests that high parenting stress may lead parents to adopt inappropriate parenting behaviors, thereby hindering their children’s \u003cspan type=\"SmallCaps\" class=\"SmallCaps\" name=\"Emphasis\"\u003edevelopment of social skill\u003c/span\u003es. More compelling evidence has been provided by longitudinal studies. Using cross-lagged analysis, Neece and Baker found that parenting stress at age six significantly predicted social skill deficits at age eight, while the reverse predictive path (from early social skills to later parenting stress) was not statistically significant [\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e]. This finding strongly supports the unidirectional causal relationship between parenting stress and social skills, establishing early parenting stress as a key predictor of children’s social development.\u003c/p\u003e \u003cp\u003eIntervention studies have further validated this association. Neece’s study of parents of children with developmental delays demonstrated that mindfulness intervention programs that reduced parental stress significantly improved children’s social behavior. When parents’ stress levels decrease, they can provide more consistent and positive parenting environments, thus promoting the development of \u003cspan type=\"SmallCaps\" class=\"SmallCaps\" name=\"Emphasis\"\u003etheir children’s social skills\u003c/span\u003e [\u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e]. \u003cspan type=\"SmallCaps\" class=\"SmallCaps\" name=\"Emphasis\"\u003eFor children with\u003c/span\u003e ID, this relationship may be even more critical, as they need more structured guidance in social learning; when parents reduce positive interactions due to stress, these children lose valuable social learning opportunities [\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e]. Based on this empirical evidence, this study proposes the following hypothesis:\u003c/p\u003e \u003cp\u003e \u003cb\u003eH3: Parenting stress significantly negatively impacts the social skills of school-aged children with ID.\u003c/b\u003e \u003c/p\u003e\n\u003ch3\u003eThe Mediating Role of Parenting Stress\u003c/h3\u003e\n\u003cp\u003eThe stress process model [\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e] and family systems theory [\u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e35\u003c/span\u003e] jointly establish a theoretical framework for understanding the relationships between parental involvement, parenting stress, and children’s social skills. The “resource-stress-outcome” chain proposed by the stress process model complements the dynamic cyclical characteristics of family interaction systems emphasized in family systems theory. These theoretical perspectives suggest that parental involvement, as a positive resource, can alleviate parenting stress, while reduced stress can promote children’s social development by optimizing the quality of parent-child interactions. Although existing research has not directly examined the complete mediation model, strong support exists for each link: parental involvement has been proven to strengthen family functioning and effectively reduce parenting stress, with mothers’ deep involvement in childcare significantly reducing role stress and improving parent-child relationships [\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e]. Parenting stress affects children’s social skill development by influencing their emotional regulation, parenting behavior choices, and interaction sensitivity [\u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eThe current study shows a notable gap in the population of children with ID. Most studies examine these relationships separately. In particular, while Neece and Baker’s longitudinal study confirmed the predictive effect of parenting stress on social skills [\u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e36\u003c/span\u003e], it did not include parental involvement. This mediating mechanism is especially crucial for children with ID as they rely more heavily on structured parental support to compensate for their social deficits. When parental stress is low, parents can provide targeted social guidance and practice opportunities, which are vital for the social development of children with cognitive limitations.\u003c/p\u003e \u003cp\u003eThe Chinese cultural context offers a unique perspective for understanding this mediation mechanism. In the Chinese context, parents of children with ID face dual pressure due to concerns about their children’s development and gaps in social expectations. In a culture that emphasizes “face” and family continuity, children are viewed as symbols of social status, which gives parenting stress a significant social characteristic. Chinese parents must frequently respond to judgments from their social networks, and this social pressure may further strengthen the impact of parenting stress on parent-child interactions [\u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e36\u003c/span\u003e]. Based on theoretical integration, existing evidence, cultural specificity, and the unidirectional relationships established in H2 and H3, this study proposes the following hypothesis:\u003c/p\u003e \u003cp\u003e \u003cb\u003eH4: Parenting stress plays a significant mediating role between parental involvement and social skills in school-aged children with ID.\u003c/b\u003e \u003c/p\u003e\n\u003ch3\u003eThe Moderating Role of Social Support\u003c/h3\u003e\n\u003cp\u003eParenting stress is typically directly associated with negative developmental outcomes in children, such as deficiencies in social skills and increased behavioral problems. However, this relationship is influenced by complex protective factors, including parent-child relationships and family learning environments [\u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e37\u003c/span\u003e–\u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e38\u003c/span\u003e]. Among many protective factors, social support is a critical external resource that can buffer the adverse effects of parenting stress. Although previous research has explored the profound impact of parental stress on child development [\u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e39\u003c/span\u003e] and the positive effects of social support on parental emotional adjustment and behavioral optimization [\u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e40\u003c/span\u003e], research on how social support moderates the relationship between parenting stress and social skills in children with ID is limited. This research gap restricts understanding and implementation of precise intervention strategies.\u003c/p\u003e \u003cp\u003eSocial support refers to various forms of assistance that individuals receive from their social networks, including emotional, informational, and instrumental support [\u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e41\u003c/span\u003e]. According to the stress-buffering model, social support serves as a protective resource that can buffer the effects of significant stress, thereby mitigating the negative impact of stress on psychological health and behavior [\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e]. Particularly for parents raising children with ID who generally face higher levels of parenting stress and complex challenges, social support plays an important role in promoting positive parenting behaviors, optimizing psychological health, and improving child developmental outcomes [\u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e42\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eThe social support buffering model supports the theory that social support acts as a moderating variable. This model suggests that economic and psychological stress adversely affect child development by influencing family functioning and parent-child interactions. Social support can also function as a protective external resource to mitigate negative pathways [\u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e43\u003c/span\u003e]. Although research \u003cspan type=\"SmallCaps\" class=\"SmallCaps\" name=\"Emphasis\"\u003ethat specifically examin\u003c/span\u003ees the moderating effects of social support is relatively scarce, few studies have provided empirical evidence for this hypothesis. For example, Lee et al. demonstrated that social support could moderate the relationship between economic stress and parental emotional distress, thereby reducing disruptive parenting behaviors and improving child developmental outcomes [\u003cspan citationid=\"CR44\" class=\"CitationRef\"\u003e44\u003c/span\u003e]. Notably, Hooper et al. ’s study of families participating in the Early Head Start program found that children demonstrated optimal social-emotional skills in families with low stress and high family functioning (including higher levels of social support) [\u003cspan citationid=\"CR45\" class=\"CitationRef\"\u003e45\u003c/span\u003e]. This study directly supported the moderating role of social support in the relationship between family stress and children’s socioemotional development.\u003c/p\u003e \u003cp\u003eBased on the above theoretical and empirical analyses, this study proposes the following hypotheses:\u003c/p\u003e \u003cp\u003e\u003cb\u003eH5: Social support moderates the relationship between parenting stress and social skills in children with ID. Specifically, among parents with high levels of social support, the negative correlation between parenting stress and children’s social skills was significantly weakened.\u003c/b\u003e\u003c/p\u003e \u003cp\u003eThis study fills an important gap by providing a theoretical foundation for developing family intervention strategies. These findings will help us \u003cspan type=\"SmallCaps\" class=\"SmallCaps\" name=\"Emphasis\"\u003eto better design supportive programs to ensure that children with\u003c/span\u003e ID receive more support and developmental opportunities within complex parenting contexts.\u003c/p\u003e \u003cp\u003eThe conceptual framework is illustrated in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e.\u003c/p\u003e "},{"header":"Methods","content":"\u003ch2\u003eResearch design and sampling procedure\u003c/h2\u003e\u003cp\u003eThis study employed a cross-sectional survey design using convenience sampling to select special education schools in Heze City (northern China) and Zhongshan City (southern China) as survey sites. These locations were chosen to represent different geographical regions and levels of economic development in China, thereby enhancing the generalizability of our findings.\u003c/p\u003e\u003cp\u003eThe selected special education schools serve school-aged children who have been formally diagnosed with ID and hold nationally recognized disability certificates. The inclusion criteria for parents were as follows: (1) cohabitation with a child with ID for more than three months; (2) absence of severe cognitive impairments or mental illness that would prevent understanding \u003cspan type=\"SmallCaps\" class=\"SmallCaps\" name=\"Emphasis\"\u003eof the questionnaire content; and (3) voluntary participation in the research.\u003c/span\u003e\u003c/p\u003e\u003cp\u003eTo prevent stigmatization during the research process, this study implemented multilevel protective measures: sampling exclusively from special education schools to avoid labeling that might occur in integrated environments; establishing collaborative relationships with school principals to leverage existing trust foundations and increase acceptance of participation; using capability-oriented expression frameworks in all research communications, emphasizing that the purpose of the research was to enhance support systems rather than focus on deficits; and ensuring destigmatizing language in research materials and interaction processes. These measures created a research environment that respected participants’ dignity and protected their family privacy while enhancing the effectiveness of data collection.\u003c/p\u003e\u003ch3\u003eData collection procedures\u003c/h3\u003e\u003cp\u003e \u003cspan type=\"SmallCaps\" class=\"SmallCaps\" name=\"Emphasis\"\u003eThe\u003c/span\u003e G * Power software was used to calculate the minimum required sample size. Considering that the research model involved five predictor variables (parenting stress, parental involvement, social support, interaction between parental involvement and parenting stress, and interaction between parenting stress and social support) with a medium effect size (0.15), desired statistical power of 0.90, and \u003cspan type=\"SmallCaps\" class=\"SmallCaps\" name=\"Emphasis\"\u003ea significance level of 0.05, the minimum requirement was 116 respondents.\u003c/span\u003e\u003c/p\u003e\u003cp\u003eData were collected from May to July, \u003cspan type=\"SmallCaps\" class=\"SmallCaps\" name=\"Emphasis\"\u003e2024. The researchers first obtained approval and support from the principals of the special education schools in\u003c/span\u003e Heze and Zhongshan. Subsequently, the teachers introduced the research purpose to the parents and obtained informed consent, emphasizing questionnaire anonymity and the principle of voluntary participation. With parental consent, teachers distributed electronic questionnaires through class WeChat groups, and the researchers communicated with the teachers to track the progress of the questionnaire submissions. A total of 774 questionnaires were collected, with 22 incomplete questionnaires or questionnaires with obvious response patterns eliminated. Following Cohen’s recommendation [\u003cspan citationid=\"CR46\" class=\"CitationRef\"\u003e46\u003c/span\u003e], responses falling outside three standard deviations from the mean were considered outliers, resulting in the exclusion of 60 outliers. The final sample included 692 valid questionnaires, representing an effective response rate of 89.4%, which far exceeded the minimum requirement and was sufficient to support data analysis.\u003c/p\u003e\u003cp\u003eAmong the valid responses, children with ID included 341 \u003cspan type=\"SmallCaps\" class=\"SmallCaps\" name=\"Emphasis\"\u003ewere boys (49.3%) and 351 were girls (50.7%). The age distribution of\u003c/span\u003e children with ID was 190 aged 6–9 years (27.5%), 232 aged 10–12 years (33.5%), 167 aged 13–15 years (24.1%), and 103 aged 16–18 years (14.9%), ensuring comprehensive coverage across different school-age stages.\u003c/p\u003e\u003ch2\u003eMeasures\u003c/h2\u003e\u003cp\u003eThis study utilized two types of measurement tools: scales originally developed in Chinese, \u003cspan type=\"SmallCaps\" class=\"SmallCaps\" name=\"Emphasis\"\u003eand rigorously translated foreign instruments.\u003c/span\u003e The back-translation method proposed was employed \u003cspan type=\"SmallCaps\" class=\"SmallCaps\" name=\"Emphasis\"\u003efor the latter. The\u003c/span\u003e English items were translated into Chinese by bilingual experts, and other translators re-translated the Chinese version back into English. \u003cspan type=\"SmallCaps\" class=\"SmallCaps\" name=\"Emphasis\"\u003eTo ensure consistency\u003c/span\u003e, the research team compared the two English versions. All \u003cspan type=\"SmallCaps\" class=\"SmallCaps\" name=\"Emphasis\"\u003ethe instruments were pretested with families of children with\u003c/span\u003e ID to ensure their cultural relevance and comprehensibility. The details of these scales are as follows.\u003c/p\u003e\u003ch2\u003eSocial responsiveness scale–short form (SRS-SF)\u003c/h2\u003e\u003cp\u003eThe SRS-SF [\u003cspan citationid=\"CR47\" class=\"CitationRef\"\u003e47\u003c/span\u003e] was adapted to Chinese culture using a back-translation method. This scale includes 18 items across three dimensions: social cognition (5 items, example item: “Is unable to pick up on any of the meaning of conversations of older children or adults”), social communication (8 items, example item: “Is slow or awkward in turn-taking interactions with peers”), and autistic mannerisms (5 items, example item: “Has more difficulty than other children with changes in his/her routine”). Each item is rated on a 4-point Likert scale ranging from 1 (never) to 4 (always), with higher scores indicating poorer social skills. In this sample, Cronbach’s α was 0.840, composite reliability (CR) was 0.901, and average variance extracted (AVE) was 0.752, demonstrating the reliability and construct validity of the scale.\u003c/p\u003e\u003ch2\u003eParental involvement questionnaire (PIQ)\u003c/h2\u003e\u003cp\u003eThe PIQ was developed for parents of Chinese children with special needs [\u003cspan citationid=\"CR48\" class=\"CitationRef\"\u003e48\u003c/span\u003e]. It includes 15 items across four dimensions: parenting education (3 items, example item: “You will pay attention to information on how to educate children through media such as TV, mobile phone or newspaper”), home-school communication (4 items, example item: “You will keep in touch with the teacher by phone or social tools such as Wechat”), home learning involvement (4 items, example item: “You will take the time to train and improve your child’s language and communication skills”), and school activity involvement (4 items, example item: “You will attend parents’ Open Day, watch or participate in teacher teaching and rehabilitation training”). Items are rated on a 5-point Likert scale, ranging from 1 (never) to 5 (always), with higher scores indicating greater parental involvement. In this sample, Cronbach’s α was 0.685, CR was 0.811, and AVE was 0.522, indicating acceptable reliability and construct validity of the scale.\u003c/p\u003e\u003ch2\u003eParenting stress index–short form-15 (PSI-SF-15)\u003c/h2\u003e\u003cp\u003eThe \u003cspan type=\"SmallCaps\" class=\"SmallCaps\" name=\"Emphasis\"\u003ePSI-SF-15 is a revised version of the Parenting Stress Index–Short Form, adapted to the Chinese context\u003c/span\u003e [\u003cspan citationid=\"CR49\" class=\"CitationRef\"\u003e49\u003c/span\u003e]. \u003cspan type=\"SmallCaps\" class=\"SmallCaps\" name=\"Emphasis\"\u003eIt contains 15 items across three dimensions\u003c/span\u003e: parenting distress (5 items, example item: “Unable to do new and different things”), parent-child interaction disorder (5 items, example item: “Child does not like me or want to be close”), and difficult child (5 items, example item: “Child does things that bother me a great deal”). Items are rated on a 5-point Likert scale \u003cspan type=\"SmallCaps\" class=\"SmallCaps\" name=\"Emphasis\"\u003eranging from 1 (strongly disagree) to 5 (strongly agree), with higher scores reflecting greater parenting stress. In this sample, Cronbach’s α was 0.674, CR was 0.821, and AVE was 0.610, suggesting reasonable reliability and construct validity of the scale.\u003c/span\u003e\u003c/p\u003e\u003ch2\u003eMultidimensional scale of perceived social support (MSPSS)\u003c/h2\u003e\u003cp\u003eThe MSPSS [\u003cspan citationid=\"CR50\" class=\"CitationRef\"\u003e50\u003c/span\u003e] includes 12 items across three dimensions: family support (4 items, example item:“ I can talk about my problems with my family”), friend support (4 items, example item: “I can rely on my friends when I am in trouble”), and important others support (4 items, example item: “I can share happiness and sadness with some people (leaders, relatives, and colleagues)”). Items are rated on a 7-point Likert scale \u003cspan type=\"SmallCaps\" class=\"SmallCaps\" name=\"Emphasis\"\u003eranging from 1 (strongly disagree) to 7 (strongly agree), with higher scores indicating greater perceived social support.\u003c/span\u003e This scale has been validated in Chinese parents of children with disabilities [\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e]. In this study, \u003cspan type=\"SmallCaps\" class=\"SmallCaps\" name=\"Emphasis\"\u003ethe Cronbach’s α, CR, and AVE were 0.500, 0.747, and 0.500, respectively. Although the internal consistency coefficient was slightly below the ideal threshold (0.7), the research team retained this scale because of its established validation history in the Chinese cultural context\u003c/span\u003e and acceptable values for other reliability and validity indices.\u003c/p\u003e\u003ch2\u003eData analysis\u003c/h2\u003e\u003ch2\u003eData processing and scoring\u003c/h2\u003e\u003cp\u003e \u003cspan type=\"SmallCaps\" class=\"SmallCaps\" name=\"Emphasis\"\u003eThe\u003c/span\u003e total and mean scores were calculated for all scales, with mean scores used to maintain comparability across scales with different item counts. For PIQ, PSI-SF-15, and MSPSS, reverse coding was not required because higher scores indicated higher levels of the respective constructs. For SRS-SF, higher scores reflected poorer social skills, and this scoring direction was consistent across the analysis.\u003c/p\u003e\u003ch2\u003eStatistical analyses\u003c/h2\u003e\u003cp\u003eData analysis was conducted using SPSS 29.0 and SmartPLS 4.0. First, common method bias was assessed using SmartPLS, followed by descriptive statistics and correlation analysis using SPSS \u003cspan type=\"SmallCaps\" class=\"SmallCaps\" name=\"Emphasis\"\u003esoftware.\u003c/span\u003e All analyses were standardized to three decimal places to ensure consistency. Child\u003cspan type=\"SmallCaps\" class=\"SmallCaps\" name=\"Emphasis\"\u003e’s age and\u003c/span\u003e sex were included as control variables. Preliminary analyses revealed a significant correlation between child age and social skills (r = 0.077, p \u0026lt; 0.01), whereas the relationship between child gender and social skills was not significant (r = -0.006, p \u0026gt; 0.05).\u003c/p\u003e\u003cp\u003ePartial least squares structural equation modeling (PLS-SEM) was used to evaluate the research model. A bootstrapping method with 10,000 resamples was used to calculate 95% confidence intervals, with intervals that did not overlap with zero deemed \u003cspan type=\"SmallCaps\" class=\"SmallCaps\" name=\"Emphasis\"\u003estatistically significant (p \u0026lt; 0.05).\u003c/span\u003e Following \u003cspan type=\"SmallCaps\" class=\"SmallCaps\" name=\"Emphasis\"\u003ethe recommendations of\u003c/span\u003e Sarstedt et al. [\u003cspan citationid=\"CR51\" class=\"CitationRef\"\u003e51\u003c/span\u003e], a two-stage approach was adopted for \u003cspan type=\"SmallCaps\" class=\"SmallCaps\" name=\"Emphasis\"\u003ethe higher-order constructs. In Stage 1, the model included only first-order constructs\u003c/span\u003e and their scores were recorded. These scores were then added to the dataset as new variables. In Stage 2, these scores were used as indicators of higher-order constructs.\u003c/p\u003e\u003cp\u003eBased on the scale developers’ perspectives [\u003cspan additionalcitationids=\"CR48 CR49\" citationid=\"CR47\" class=\"CitationRef\"\u003e47\u003c/span\u003e–\u003cspan citationid=\"CR50\" class=\"CitationRef\"\u003e50\u003c/span\u003e], all four latent constructs in this study were modeled as reflective indicators. Following Hair et al.\u003cspan type=\"SmallCaps\" class=\"SmallCaps\" name=\"Emphasis\"\u003e’s guidelines, the measurement model was first evaluated (assessing construct reliability, convergent validity, and discriminant validity), followed by an analysis of the structural model to verify the relationships between the constructs and test the research hypotheses\u003c/span\u003e [\u003cspan citationid=\"CR52\" class=\"CitationRef\"\u003e52\u003c/span\u003e].\u003c/p\u003e"},{"header":"Results","content":"\u003cdiv id=\"Sec20\" class=\"Section2\"\u003e \u003ch2\u003eCommon method bias assessment\u003c/h2\u003e \u003cp\u003eIn this study, the data collected via parent\u003cspan type=\"SmallCaps\" class=\"SmallCaps\" name=\"Emphasis\"\u003eal self-reports may have been prone to common method bias. To a\u003c/span\u003eddress this issue, we employed the variance inflation factor (VIF). Generally, a VIF value under 3.3 indicates the absence of significant common method bias [\u003cspan citationid=\"CR53\" class=\"CitationRef\"\u003e53\u003c/span\u003e]. As presented in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e, all VIF values in this study were below 3.3, suggesting that common method bias was not significant.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eVIF testing\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"14\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c9\" colnum=\"9\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c10\" colnum=\"10\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c11\" colnum=\"11\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c12\" colnum=\"12\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c13\" colnum=\"13\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c14\" colnum=\"14\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eSCOG\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eSCOM\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eAM\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003ePE\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eHSC\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003eHLI\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c8\"\u003e \u003cp\u003eSAI\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c9\"\u003e \u003cp\u003ePD\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c10\"\u003e \u003cp\u003ePCID\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c11\"\u003e \u003cp\u003eDC\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c12\"\u003e \u003cp\u003eFAS\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c13\"\u003e \u003cp\u003eFRS\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c14\"\u003e \u003cp\u003eIOS\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eVIF\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1.730\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e2.399\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e2.040\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1.390\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e1.549\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e1.474\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e1.088\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e1.189\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e1.727\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e1.536\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e1.292\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e1.370\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c14\"\u003e \u003cp\u003e1.071\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003ctfoot\u003e \u003ctr\u003e\u003ctd colspan=\"14\"\u003eNote: Social Cognition (SCOG); Social Communication (SCOM); Autistic Mannerisms (AM); Parenting Education (PE); Home-School Communication (HSC); Home Learning Involvement (HLI); School Activity Involvement (SAI); Parenting Distress (PD); Parent-Child Interaction Disorder (PCID); Difficult Child (DC); family Support (FAS); friend Support (FRS); Important Others Support (IOS). the same applies below.\u003c/td\u003e\u003c/tr\u003e \u003c/tfoot\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec21\" class=\"Section2\"\u003e \u003ch2\u003eDescriptive statistics and correlations analysis of variables\u003c/h2\u003e \u003cp\u003eTable\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e presents the descriptive statistics and correlations of the main variables. It should be noted that the SRS-SF scale had a reverse score. Therefore, when social skills are related to other variables, a positive correlation coefficient indicates a negative correlation and a negative correlation coefficient indicates a positive correlation. Pearson\u0026rsquo;s correlation analysis revealed that social skills were negatively correlated with parenting stress (r\u0026thinsp;=\u0026thinsp;0.592, p\u0026thinsp;\u0026lt;\u0026thinsp;0.001) and positively correlated with parental involvement (r = -0.208, p\u0026thinsp;\u0026lt;\u0026thinsp;0.001) and social support (r = -0.237, p\u0026thinsp;\u0026lt;\u0026thinsp;0.001). Furthermore, parenting stress was negatively associated with parental involvement (r = -0.137, p\u0026thinsp;\u0026lt;\u0026thinsp;0.05) and social support (r = -0.191, p\u0026thinsp;\u0026lt;\u0026thinsp;0.001). Parental involvement was positively related to social support (r\u0026thinsp;=\u0026thinsp;0.400, p\u0026thinsp;\u0026lt;\u0026thinsp;0.001). Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e presents the descriptive statistics and correlations between the variables.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eDescriptive statistics and correlations of variables\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"6\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\"\u0026plusmn;\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eVariables\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eM\u0026thinsp;\u0026plusmn;\u0026thinsp;SD\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"4\" nameend=\"c6\" namest=\"c3\"\u003e \u003cp\u003eCorrelations\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003e4\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1.Social Skill\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c2\"\u003e \u003cp\u003e2.632\u0026thinsp;\u0026plusmn;\u0026thinsp;0.41\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2.Parental Involvement\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c2\"\u003e \u003cp\u003e3.410\u0026thinsp;\u0026plusmn;\u0026thinsp;0.50\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-0.208\u003csup\u003e***\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e3.Parenting Stress\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c2\"\u003e \u003cp\u003e3.351\u0026thinsp;\u0026plusmn;\u0026thinsp;0.49\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.592\u003csup\u003e***\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-0.137\u003csup\u003e*\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e4.Social Support\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c2\"\u003e \u003cp\u003e4.490\u0026thinsp;\u0026plusmn;\u0026thinsp;0.72\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-0.237\u003csup\u003e***\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.400\u003csup\u003e***\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e-0.191\u003csup\u003e****\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003ctfoot\u003e \u003ctr\u003e\u003ctd colspan=\"6\"\u003eNote. \u003csup\u003e\u003cem\u003e*\u003c/em\u003e\u003c/sup\u003e\u003cem\u003ep\u0026lt;0.05\u003c/em\u003e \u003csup\u003e\u003cem\u003e***\u003c/em\u003e\u003c/sup\u003e\u003cem\u003ep\u0026lt;0.001\u003c/em\u003e\u003c/td\u003e\u003c/tr\u003e \u003c/tfoot\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec22\" class=\"Section2\"\u003e \u003ch2\u003eMeasurement model assessment\u003c/h2\u003e \u003cp\u003eThe reliability, convergent validity, and discriminant validity of the measurement models were evaluated. Following the criteria of Hair et al. [\u003cspan citationid=\"CR52\" class=\"CitationRef\"\u003e52\u003c/span\u003e], \u003cspan type=\"SmallCaps\" class=\"SmallCaps\" name=\"Emphasis\"\u003ethe acceptable thresholds for indicator loadings, CR, and AVE were set at \u0026ge;\u0026thinsp;0.5, \u0026ge;\u0026thinsp;0.7, and \u0026ge;\u0026thinsp;0.5, respectively. As shown in\u003c/span\u003e Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e, \u003cspan type=\"SmallCaps\" class=\"SmallCaps\" name=\"Emphasis\"\u003eall indicator loadings exceeded 0.5, AVE values were \u0026ge;\u0026thinsp;0.5, and CR values surpassed 0.7, indicating good reliability and convergent validity.\u003c/span\u003e\u003c/p\u003e \u003cp\u003eFor \u003cspan type=\"SmallCaps\" class=\"SmallCaps\" name=\"Emphasis\"\u003ethe discriminant validity assessment, the\u003c/span\u003e heterotrait-monotrait (HTMT) ratio was applied, adopting a stricter threshold of 0.85 [\u003cspan citationid=\"CR52\" class=\"CitationRef\"\u003e52\u003c/span\u003e]. Table\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003e demonstrates that all the HTMT values between the variables met this criterion, confirming robust discriminant validity. Overall, the measurement model demonstrates satisfactory psychometric properties.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab3\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eEstimation of the measurement model\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"5\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eConstruct\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eItem\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eLoading\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eCR\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eAVE\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"2\" rowspan=\"3\"\u003e \u003cp\u003eSocial Skill\u003c/p\u003e \u003cp\u003e(SS)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eSCOG\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.830\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\" morerows=\"2\" rowspan=\"3\"\u003e \u003cp\u003e0.901\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\" morerows=\"2\" rowspan=\"3\"\u003e \u003cp\u003e0.752\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eSCOM\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.904\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eAM\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.866\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"3\" rowspan=\"4\"\u003e \u003cp\u003eParental Involvement\u003c/p\u003e \u003cp\u003e(PI)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003ePE\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.733\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\" morerows=\"3\" rowspan=\"4\"\u003e \u003cp\u003e0.811\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\" morerows=\"3\" rowspan=\"4\"\u003e \u003cp\u003e0.522\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eHSC\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.815\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eHLI\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.765\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eSAI\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.551\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"2\" rowspan=\"3\"\u003e \u003cp\u003eParenting Stress\u003c/p\u003e \u003cp\u003e(PS)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003ePD\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.610\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\" morerows=\"2\" rowspan=\"3\"\u003e \u003cp\u003e0.821\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\" morerows=\"2\" rowspan=\"3\"\u003e \u003cp\u003e0.610\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003ePCID\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.879\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eDC\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.828\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"2\" rowspan=\"3\"\u003e \u003cp\u003eSocial Support\u003c/p\u003e \u003cp\u003e(SSU)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eFAS\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.624\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\" morerows=\"2\" rowspan=\"3\"\u003e \u003cp\u003e0.747\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\" morerows=\"2\" rowspan=\"3\"\u003e \u003cp\u003e0.500\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eFRS\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.815\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eIOS\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.668\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab4\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 4\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eDiscriminant validity assessment (HTMT)\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"5\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003ePI\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eSSU\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003ePS\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eSS\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSSU\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.698\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePS\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.252\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.330\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSS\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.273\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.359\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.779\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSSU * PS\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.082\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.099\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.313\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.228\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cdiv id=\"Sec23\" class=\"Section3\"\u003e \u003ch2\u003eStructural model assessment\u003c/h2\u003e \u003cp\u003eFollowing confirmation of the measurement model\u0026rsquo;s quality, we conducted a structural model analysis to evaluate the significance of the hypothesized relationships and overall model quality. In PLS-SEM, structural model quality is assessed through predictive and explanatory powers. \u003cspan type=\"SmallCaps\" class=\"SmallCaps\" name=\"Emphasis\"\u003eThe\u003c/span\u003e explanatory power was evaluated using the coefficient of determination (R\u0026sup2;) and effect size (f\u0026sup2;), whereas \u003cspan type=\"SmallCaps\" class=\"SmallCaps\" name=\"Emphasis\"\u003ethe predictive power was assessed\u003c/span\u003e using the significance of the path coefficients and predictive relevance (Q\u0026sup2;).\u003c/p\u003e \u003cp\u003eAs shown in Table\u0026nbsp;\u003cspan refid=\"Tab5\" class=\"InternalRef\"\u003e5\u003c/span\u003e and Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e, parental involvement, parenting stress, social support, and control variables collectively explained 38.4% of the variance in social skills (R\u0026sup2; = 0.384), indicating a moderate explanatory power [\u003cspan citationid=\"CR52\" class=\"CitationRef\"\u003e52\u003c/span\u003e]. Cohen suggested that f\u0026sup2; values above 0.02, 0.15, and 0.35 represent small, medium, and large effects, respectively [\u003cspan citationid=\"CR46\" class=\"CitationRef\"\u003e46\u003c/span\u003e]. The f\u0026sup2; metric quantifies the change in R\u0026sup2; after a specific exogenous variable \u003cspan type=\"SmallCaps\" class=\"SmallCaps\" name=\"Emphasis\"\u003eis removed from the model. The effect size\u003c/span\u003e of parenting stress on social skills was significant (f\u0026sup2; = 0.432), whereas the effects of parental involvement on social skills (f\u0026sup2; = 0.013) and parenting stress (f\u0026sup2; = 0.019) were small. The interaction between social support and parenting stress was minimal (f\u0026sup2; = 0.007). Q\u0026sup2; reflects the model\u0026rsquo;s ability to predict reflective and endogenous constructs \u003cspan type=\"SmallCaps\" class=\"SmallCaps\" name=\"Emphasis\"\u003eaccurately.\u003c/span\u003e Only endogenous variables had Q\u0026sup2; values. In this study, all Q\u0026sup2; values exceeded zero, confirming that the exogenous constructs exhibited predictive relevance for the endogenous constructs [\u003cspan citationid=\"CR58\" class=\"CitationRef\"\u003e58\u003c/span\u003e].\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv id=\"Sec24\" class=\"Section2\"\u003e \u003ch2\u003eHypothesis testing\u003c/h2\u003e \u003cp\u003eRegarding the control variables, \u003cspan type=\"SmallCaps\" class=\"SmallCaps\" name=\"Emphasis\"\u003ethe child\u0026rsquo;s age significantly predicted social skills (β\u0026thinsp;=\u0026thinsp;0.080, p\u0026thinsp;\u0026lt;\u0026thinsp;0.01), whereas the child\u0026rsquo;s gender\u003c/span\u003e was no\u003cspan type=\"SmallCaps\" class=\"SmallCaps\" name=\"Emphasis\"\u003et statistically significan\u003c/span\u003et (β\u0026thinsp;=\u0026thinsp;0.280, p\u0026thinsp;\u0026gt;\u0026thinsp;0.05).\u003c/p\u003e \u003cp\u003eAfter controlling for demographic characteristics, the data supported all research hypotheses:\u003c/p\u003e \u003cp\u003e1. Parental involvement had a significant positive effect on social skills (β = -0.099, p\u0026thinsp;\u0026lt;\u0026thinsp;0.01; note the reversed scoring for \u003cspan type=\"SmallCaps\" class=\"SmallCaps\" name=\"Emphasis\"\u003ethe SRS-SF).\u003c/span\u003e\u003c/p\u003e \u003cp\u003e2. Parental involvement had a significant negative effect on parenting stress (β = -0.137, p\u0026thinsp;\u0026lt;\u0026thinsp;0.01).\u003c/p\u003e \u003cp\u003e3. Parenting stress exerted a significant negative influence on social skills (β\u0026thinsp;=\u0026thinsp;0.543, p\u0026thinsp;\u0026lt;\u0026thinsp;0.001; note the reversed SRS-SF \u003cspan type=\"SmallCaps\" class=\"SmallCaps\" name=\"Emphasis\"\u003escoring).\u003c/span\u003e\u003c/p\u003e\u003cp\u003e4. The indirect effect of parenting stress on the relationship between parental involvement and social skills was significant (β = -0.074, p\u0026thinsp;\u0026lt;\u0026thinsp;0.01), with a variance accounted for (VAF) of 42.775%, indicating \u003cspan type=\"SmallCaps\" class=\"SmallCaps\" name=\"Emphasis\"\u003ea partial mediation by parenting stress.\u003c/span\u003e\u003c/p\u003e\u003cp\u003e5. The interaction between parenting stress and social support was significant (β\u0026thinsp;=\u0026thinsp;0.056, p\u0026thinsp;\u0026lt;\u0026thinsp;0.05), confirming the moderating role of social support.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab5\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 5\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eResults of hypothesis testing\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"11\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c9\" colnum=\"9\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c10\" colnum=\"10\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c11\" colnum=\"11\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eHypothesis\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eRelationship\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eβ\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003et\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eP\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eDecision\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eR\u003csup\u003e2\u003c/sup\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c8\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003ef\u003csup\u003e2\u003c/sup\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c9\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eQ\u003csup\u003e2\u003c/sup\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c10\"\u003e \u003cp\u003e95%CI\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c11\"\u003e \u003cp\u003e95%CI\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c10\"\u003e \u003cp\u003eLL\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c11\"\u003e \u003cp\u003eUL\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eH2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003ePI -\u0026gt; PS\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e-0.137\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e3.190\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eAccepted\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.019\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0.019\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e0.009\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e \u003cp\u003e-0.224\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c11\"\u003e \u003cp\u003e-0.057\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eH1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003ePI -\u0026gt; SS\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e-0.099\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e2.761\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.006\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eAccepted\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\" morerows=\"5\" rowspan=\"6\"\u003e \u003cp\u003e0.384\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0.013\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\" morerows=\"5\" rowspan=\"6\"\u003e \u003cp\u003e0.282\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e \u003cp\u003e-0.172\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c11\"\u003e \u003cp\u003e-0.029\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eH3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003ePS -\u0026gt; SS\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.543\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e19.118\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eAccepted\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0.432\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e \u003cp\u003e0.485\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c11\"\u003e \u003cp\u003e0.597\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eH4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003ePI -\u0026gt; PS -\u0026gt; SS\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e-0.074\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e3.141\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.002\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eAccepted\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e \u003cp\u003e-0.123\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c11\"\u003e \u003cp\u003e-0.031\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eH5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eSSU x PS -\u0026gt; SS\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.056\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e2.232\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.026\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eAccepted\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0.007\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e \u003cp\u003e0.005\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c11\"\u003e \u003cp\u003e0.104\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003egender -\u0026gt; SS\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e-0.017\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.280\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.780\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e \u003cp\u003e-0.135\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c11\"\u003e \u003cp\u003e0.101\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eage -\u0026gt; SS\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.080\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e2.624\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.009\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0.01\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e \u003cp\u003e0.020\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c11\"\u003e \u003cp\u003e0.139\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eTo clarify the moderating effect, social support was categorized into high/low groups (\u0026plusmn;\u0026thinsp;1 SD) for simple slope analysis (Table\u0026nbsp;\u003cspan refid=\"Tab6\" class=\"InternalRef\"\u003e6\u003c/span\u003e and Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e). The results revealed that the predictive effect of parenting stress on social skills was stronger for high social support (β\u0026thinsp;=\u0026thinsp;0.655, p\u0026thinsp;\u0026lt;\u0026thinsp;0.001) than for low social support (β\u0026thinsp;=\u0026thinsp;0.539, p\u0026thinsp;\u0026lt;\u0026thinsp;0.001). \u003cspan type=\"SmallCaps\" class=\"SmallCaps\" name=\"Emphasis\"\u003eThe\u003c/span\u003e moderated mediation analysis demonstrated that the mediating effect of parenting stress was more pronounced under high social support (effect = -0.093, 95% CI: [-0.159, -0.032]) than under low social support (effect = -0.077, 95% CI: [-0.132, -0.027]).\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab6\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 6\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eSimple Slope Analysis Results\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"6\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colname=\"c2\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eβ\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003et\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eP\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c6\" namest=\"c5\"\u003e \u003cp\u003e95% CI\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eLower Limit\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eUpper Limit\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePS -\u0026gt; SS conditional on SSU at +\u0026thinsp;1 SD\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.655\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e17.621\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.579\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.725\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePS -\u0026gt; SS conditional on SSU at -1 SD\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.539\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e10.840\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.436\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.632\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePI -\u0026gt; PS -\u0026gt; SS conditional on SSU at +\u0026thinsp;1 SD\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e-0.093\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e2.889\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.004\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e-0.159\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e-0.032\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePI -\u0026gt; PS -\u0026gt; SS conditional on SSU at -1 SD\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e-0.077\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e2.834\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.005\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e-0.132\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e-0.027\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e"},{"header":"Discussion","content":"\u003cdiv id=\"Sec26\" class=\"Section2\"\u003e \u003ch2\u003eDirect effects of parental involvement on social skills in children with ID\u003c/h2\u003e \u003cp\u003eThis study confirmed that parental involvement significantly enhances social skills in children with ID, a finding consistent with prior research in general [\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e, \u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e] and special education settings [\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e, \u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e]. Theoretically, this relationship can be explained through two complementary frameworks: the ecological systems theory and overlapping spheres of influence theory.\u003c/p\u003e \u003cp\u003eEcological systems theory emphasizes that child development is nested within multilayered interactive systems, where the family, as the core microsystem, directly shapes developmental trajectories through daily interactions [\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e]. For children with ID, coherence across microsystems (e.g., family and school) is critical for effectively acquiring and generalizing social skills [\u003cspan citationid=\"CR54\" class=\"CitationRef\"\u003e54\u003c/span\u003e], as these children often require consistent cross-environmental support to overcome learning barriers imposed by cognitive processing limitations. Epstein\u0026rsquo;s overlapping spheres of influence theory further supplement this understanding by positing that optimal education occurs at the intersection of the family, school, and community domains [\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e]. Our data demonstrate that active parental engagement in \u0026ldquo;communication\u0026rdquo; and \u0026ldquo;home learning\u0026rdquo; \u003cspan type=\"SmallCaps\" class=\"SmallCaps\" name=\"Emphasis\"\u003eand home-learning activities significantly\u003c/span\u003e improves social skills in children with ID, validating the value of synergistic inter-domain collaboration.\u003c/p\u003e \u003cp\u003eParental involvement promotes social skill\u003cspan type=\"SmallCaps\" class=\"SmallCaps\" name=\"Emphasis\"\u003es development through three primary mechanisms. First, parents provide additional learning opportunities and practice scenarios, compensating for the temporal and contextual constraints of school-based education\u003c/span\u003e [\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e]. \u003cspan type=\"SmallCaps\" class=\"SmallCaps\" name=\"Emphasis\"\u003eSecond, active involvement enhances children\u0026rsquo;s sense of belonging and self-esteem, which are psychological factors that serve as critical catalysts for social development\u003c/span\u003e [\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e]. \u003cspan type=\"SmallCaps\" class=\"SmallCaps\" name=\"Emphasis\"\u003eThird, highly engaged parents are more likely to create diverse social interaction opportunities, such as organizing peer activities and community participation, offering authentic environments for practicing social skills\u003c/span\u003e [\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eNotably, effect size comparisons warrant further attention. The observed effect of parental involvement on social skills (β = -0.099, p\u0026thinsp;\u0026lt;\u0026thinsp;0.01; negative coefficient under reversed scoring indicates a positive effect) aligns with Zhang et al.\u0026rsquo;s findings (β\u0026thinsp;=\u0026thinsp;0.130, p\u0026thinsp;\u0026lt;\u0026thinsp;0.05) [\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e] but is significantly smaller than the results reported for typically developing children (for example, β\u0026thinsp;=\u0026thinsp;0.370 in Yue et al. [\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e]). This discrepancy highlights the unique challenges of social learning for children with ID, as deficits in cognitive processing, attention, and memory may constrain the efficacy of environmental interventions [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e]. These children may require more explicit and structured social skill\u003cspan type=\"SmallCaps\" class=\"SmallCaps\" name=\"Emphasis\"\u003es instruction\u003c/span\u003e [\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e], \u003cspan type=\"SmallCaps\" class=\"SmallCaps\" name=\"Emphasis\"\u003eas naturalistic parental involvement alone may be insufficient to overcome their developmental barriers.\u003c/span\u003e\u003c/p\u003e \u003cp\u003eDespite the relatively small effect size, the positive impact of parental involvement is substantively significant given the social learning challenges faced by children with ID. This finding underscores the need to design family engagement strategies specifically tailored to these children. Such strategies should be structured and focused on overcoming specific cognitive barriers to maximize their potential for social development.\u003c/p\u003e \u003cdiv id=\"Sec27\" class=\"Section3\"\u003e \u003ch2\u003eThe mediating role of parenting stress between parental involvement and social skills\u003c/h2\u003e \u003cp\u003eThis study demonstrated that parenting stress plays a significant partial mediating role in the relationship between parental involvement and social skill development in children with ID. Specifically, higher parental involvement is associated with lower parenting stress, which correlates with better social skill\u003cspan type=\"SmallCaps\" class=\"SmallCaps\" name=\"Emphasis\"\u003es outcomes in children.\u003c/span\u003e This mediation effect accounted for 42.775% of the total effect, indicating that parental involvement not only directly influenced children\u0026rsquo;s social skills, \u003cspan type=\"SmallCaps\" class=\"SmallCaps\" name=\"Emphasis\"\u003ebut also indirectly promoted development by reducing parenting stress.\u003c/span\u003e\u003c/p\u003e \u003cp\u003eThese findings are consistent with existing empirical evidence. A randomized controlled trial by Williams et al. revealed that parents participating in supportive playgroups experienced significant reductions in parenting stress alongside marked improvements in their children\u0026rsquo;s social interaction skills [\u003cspan citationid=\"CR55\" class=\"CitationRef\"\u003e55\u003c/span\u003e]. This causal validation strengthens support for the mediation mechanism proposed in this study. Similarly, Kim et al. identified \u003cspan type=\"SmallCaps\" class=\"SmallCaps\" name=\"Emphasis\"\u003ea partial mediation by maternal parenting stress in the relationship between paternal involvement and early infant neurodevelopment\u003c/span\u003e [\u003cspan citationid=\"CR56\" class=\"CitationRef\"\u003e56\u003c/span\u003e]. Although Kim\u0026rsquo;s study focused on neurodevelopment rather than social skills, both studies highlight\u003cspan type=\"SmallCaps\" class=\"SmallCaps\" name=\"Emphasis\"\u003eed the universal applicability of parenting stress as a mediator across\u003c/span\u003e developmental domains.\u003c/p\u003e \u003cp\u003eWithin the cultural context of China, this mediation mechanism may have unique significance. Traditional Chinese culture emphasizes family harmony and collectivist values, with high parental investment in education and emotional dependency on children. This heightened dependency may amplify the effects of parenting stress on child\u003cspan type=\"SmallCaps\" class=\"SmallCaps\" name=\"Emphasis\"\u003eren\u0026rsquo;s development.\u003c/span\u003e Furthermore, limited societal support for families with children with ID, particularly in rural and underserved communities, renders the optimization of internal family resources critical. Therefore, the quality of parental involvement is a pivotal factor in enhancing the developmental environment of these children.\u003c/p\u003e \u003cp\u003eNotably, a bidirectional interaction may exist between parenting stress and social skill\u003cspan type=\"SmallCaps\" class=\"SmallCaps\" name=\"Emphasis\"\u003es development.\u003c/span\u003e Although the cross-sectional design of this study precludes definitive causal conclusions, this mutual influence is supported by both theoretical and empirical studies. For example, Neece et al.\u0026rsquo;s longitudinal research identified reciprocal temporal predictions between maternal stress and child behavioral issues, suggesting cyclical rather than unidirectional dynamics [\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e]. Future studies should employ longitudinal designs to explore this bidirectional relationship and its implications for mediation mechanisms.\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv id=\"Sec28\" class=\"Section2\"\u003e \u003ch2\u003eThe moderating role of social support between parenting stress and social skills\u003c/h2\u003e \u003cp\u003eThis study confirmed the significant moderating effect of social support on the relationship between parenting stress and social skills in children with ID (β\u0026thinsp;=\u0026thinsp;0.056, p\u0026thinsp;\u0026lt;\u0026thinsp;0.05). Specifically, under equivalent levels of parenting stress, children from families with higher social support \u003cspan type=\"SmallCaps\" class=\"SmallCaps\" name=\"Emphasis\"\u003elevels exhibited better social\u003c/span\u003e skills. This result not only validates Cohen and Wills\u0026rsquo;stress-buffering hypothesis [\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e] but also extends it to families of children with ID, demonstrating that social support mitigates the direct impact of parenting stress and fosters protective environments for social development.\u003c/p\u003e \u003cp\u003eOur findings are consistent with those in the existing literature. For instance, Yıldız and Uzundağ found that social support significantly buffered the negative effects of parenting stress on effortful control in preschoolers [\u003cspan citationid=\"CR57\" class=\"CitationRef\"\u003e57\u003c/span\u003e], while Park and Lee identified social support as a moderator between stress and depression in mothers of children with disabilities [\u003cspan citationid=\"CR58\" class=\"CitationRef\"\u003e58\u003c/span\u003e]. However, this study uniquely focused on school-aged children with ID in China, offering novel insights into the role of social support in special education contexts.\u003c/p\u003e \u003cp\u003eA key innovation lies in identifying a threshold effect: the buffering role of social support is more pronounced in high-stress families (greater moderation path coefficients in high-support groups than in low-support groups). This suggests that limited special education resources in China should be strategically prioritized for high-stress families to maximize intervention efficacy.\u003c/p\u003e \u003cp\u003eCulturally, the acquisition and use of social support in China reflect\u003cspan type=\"SmallCaps\" class=\"SmallCaps\" name=\"Emphasis\"\u003es distinct dynamics.\u003c/span\u003e Collectivist values and familial honor norms often discourage parents from disclosing \u003cspan type=\"SmallCaps\" class=\"SmallCaps\" name=\"Emphasis\"\u003etheir children\u0026rsquo;s developmental challenges\u003c/span\u003e [\u003cspan citationid=\"CR59\" class=\"CitationRef\"\u003e59\u003c/span\u003e], \u003cspan type=\"SmallCaps\" class=\"SmallCaps\" name=\"Emphasis\"\u003ewhile traditional stigma toward disabilities further hinders help-seeking behaviors\u003c/span\u003e [\u003cspan citationid=\"CR60\" class=\"CitationRef\"\u003e60\u003c/span\u003e]. Our results show\u003cspan type=\"SmallCaps\" class=\"SmallCaps\" name=\"Emphasis\"\u003eed that when\u003c/span\u003e social support successfully overcomes these cultural barriers, its stress-buffering effects are particularly strong. This underscores the need for culturally sensitive interventions that integrate internal family networks (e.g., grandparent caregiving) with professional support.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec29\" class=\"Section2\"\u003e \u003ch2\u003eTheoretical and practical implications\u003c/h2\u003e \u003cp\u003eThis study has significant theoretical and practical implications, particularly for elucidating the interactive mechanisms between parental involvement and social skill development in children with ID in the Chinese cultural context.\u003c/p\u003e \u003c/div\u003e\n\u003ch3\u003eTheoretical contributions\u003c/h3\u003e\n\u003cp\u003eAt the theoretical level, this study integrates \u003cspan type=\"SmallCaps\" class=\"SmallCaps\" name=\"Emphasis\"\u003ethe family systems theory with the social support buffering model, first integrating parental involvement, parenting stress, and social support into a unified analytical framework.\u003c/span\u003e Constructing a moderated mediation model to explore family level mechanisms influencing social skill development in children with ID transcends prior studies that focused on singular variable pathways, such as the direct effects of parental involvement [\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e] or independent impacts of parenting stress [\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e]. The validation of parenting stress as a mediator and social support as a moderator provides cross-cultural empirical support for applying Bronfenbrenner\u0026rsquo;s ecological systems theory to special populations, deepening our understanding of the dynamic equilibrium between family environment and child development.\u003c/p\u003e \u003cdiv id=\"Sec31\" class=\"Section2\"\u003e \u003ch2\u003ePractical implications\u003c/h2\u003e \u003cp\u003ePractically, the\u003cspan type=\"SmallCaps\" class=\"SmallCaps\" name=\"Emphasis\"\u003ese findings offer evidence-based guidance for developing differentiated\u003c/span\u003e family support programs. The mediating role of parenting stress suggests that parent training initiatives should not only enhance caregiving skills, \u003cspan type=\"SmallCaps\" class=\"SmallCaps\" name=\"Emphasis\"\u003ebut also incorporate stress\u003c/span\u003e management strategies. The moderating effect of social support highlights the need to prioritize community resource linkages or peer support networks for high-stress families \u003cspan type=\"SmallCaps\" class=\"SmallCaps\" name=\"Emphasis\"\u003ein order to enhance intervention efficacy. These insights inform the development of \u0026ldquo;family-school-community\u0026rdquo; collaborative intervention systems, such as integrating mental health assessments into parent training and establishing teacher-social worker partnerships.\u003c/span\u003e\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec32\" class=\"Section2\"\u003e \u003ch2\u003eLimitations and future directions\u003c/h2\u003e \u003cp\u003eWhile this study advances the field, several limitations warrant attention.\u003c/p\u003e \u003cp\u003e1. Design Constraints: The cross-sectional design limits causal inferences about the relationships among parental involvement, parenting stress, social support, and social skill development. Future longitudinal tracking studies should systematically examine these dynamic and bidirectional interactions, as well as temporal patterns.\u003c/p\u003e \u003cp\u003e2. Measurement limitations: Reliance on parental self-reports risks common method bias, potentially inflating \u003cspan type=\"SmallCaps\" class=\"SmallCaps\" name=\"Emphasis\"\u003ethe observed associations.\u003c/span\u003e Multisource data (e.g., teacher evaluations and behavioral observations) should be incorporated to enhance objectivity.\u003c/p\u003e \u003cp\u003e3. Sample representativeness: Underrepresentation of diverse socioeconomic backgrounds restricts generalizability. Stratified sampling based on household registration type, parental education level, and family structure is recommended.\u003c/p\u003e \u003cp\u003e4. Lack of dimensional specificity: The study did not differentiate between subtypes of parental involvement (e.g., academic support and emotional guidance) or social support dimensions (e.g., informational, emotional, \u003cspan type=\"SmallCaps\" class=\"SmallCaps\" name=\"Emphasis\"\u003eand instrumental).\u003c/span\u003e Future studies should refine the variable classifications to identify precise mechanisms and multifactorial interactions.\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003c/ol\u003e \u003c/p\u003e \u003c/div\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eSupplementary Information\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe online version contains supplementary material available at \u0026ldquo;web address\u0026rdquo;.\u003c/p\u003e\n\u003cp\u003eSupplementary Material 1\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAcknowledgements\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eWe thank Sudan Idris Education University and all participants.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAuthor contributions\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eYuting Han: Research conceptualization and design, methodology design, data collection, statistical analysis, and writing and finalizing the initial draft. Eng Hock Kway: Questionnaire revision, literature review support, results visualization, and writing of partial sections. Tingzhao Wang: Research supervision and guidance, funding acquisition, validated result interpretation, reviewed and edited the manuscript, and managed the overall project. All three authors participated in quality control of the questionnaire survey data and reviewed and approved the final version of the manuscript.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eFunding\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThis work was funded by the Major Project of the National Social Science Foundation of China in 2021 (grant number: 21 \u0026amp; ZD293) and the National Social Science Fund Item of China in 2023 (grant number: CHA230303).\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eData availability\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe datasets during and/or analyzed during the current study available from corresponding author upon reasonable requests.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eEthics approval and consent to participate\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThis study was approved by the Human Research Ethics Committee of Sultan Idris Education University (approval no. 2024033001). All participants received detailed information about the study and provided written informed consent with the right to withdraw at any time, without providing a reason. Data collection was anonymized and securely stored with password protection and was accessible only to the research team.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCompeting interests\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe authors declare no conflicts of interest.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAuthor details\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\u003csup\u003e1\u0026nbsp;\u003c/sup\u003eSchool of Teacher Education, Heze University, Heze, Shandong, China\u003c/p\u003e\n\u003cp\u003e\u003csup\u003e2\u003c/sup\u003eFaculty of Human Development, University Pendidikan Sultan Idris, Tanjong Malim, Malaysia\u003c/p\u003e\n\u003cp\u003e\u003csup\u003e3\u0026nbsp;\u003c/sup\u003eSchool of Education, Shaanxi Normal University, Xi\u0026rsquo;an, Shaanxi, China.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eSigafoos J, Lancioni GE, Singh NN, et al. Intellectual disability and social skills. 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Pathways of influence: Chinese parents\u0026rsquo; expectations, parenting styles, and child social competence. Early Child Dev Care. 2015;185(4):614\u0026ndash;30.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eWang P, Michaels CA. Chinese families of children with severe disabilities: Family needs and available support. Res Pract Pers Severe Disabil. 2009;34(2):21\u0026ndash;32.\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"},{"header":"Supplementary Material","content":"\u003cp\u003eSupplementary Material 1 is not available with this version.\u003c/p\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":"Children with intellectual disabilities, Social skill, Parental involvement, Parenting stress, Social support","lastPublishedDoi":"10.21203/rs.3.rs-5474664/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-5474664/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003e\u003cstrong\u003eBackground\u003c/strong\u003e Children with intellectual disabilities (ID) require additional support for social skills development, with parental involvement being a key factor. However, the mechanisms underlying this relationship remain unclear.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eObjectives\u003c/strong\u003e This study aimed to examine the relationship between parental involvement and social skills in children with ID, assess the mediating role of parenting stress, and explore the moderating effect of social support on the relationship between parenting stress and children’s social skills.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eMethods\u003c/strong\u003e Using convenience sampling, 692 parents of children with ID (aged 6–18) from special education schools in Zhongshan and Heze, China (May-July 2024) were recruited. Participants completed the Social Responsiveness Scale-Short Form, Parental Involvement Questionnaire, Parenting Stress Index-Short Form-15, and Multidimensional Scale of Perceived Social Support. SPSS was used for descriptive statistics and SmartPLS was to examine the mediation and moderation effects.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eResults\u003c/strong\u003e Parental involvement had a significant positive direct effect on children’s social skills (β = -0.099, p \u0026lt; 0.01, due to the reverse scoring of the SRS-SF). Parenting stress partially mediated this relationship (indirect effect: β = -0.074, p \u0026lt; 0.01), with higher parental involvement significantly associated with lower parenting stress (β = -0.137, p \u0026lt; 0.01). Parenting stress partially mediated this relationship (indirect effect: β = -0.074, p \u0026lt; 0.01), with higher involvement being associated with lower stress (β = -0.137, p \u0026lt; 0.01) and lower stress predicting better social skills (β = 0.543, p \u0026lt; 0.001). Social support significantly moderated the negative relationship between parenting stress and children’s social skills (β = 0.056, p \u0026lt; 0.05), with higher levels of social support mitigating the negative effects of parenting stress.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eConclusions\u003c/strong\u003e: This study revealed a complex interplay between parental involvement, parenting stress, and social support in shaping social skills development in children with ID. These findings support an integrated intervention approach that enhances parental involvement, reduces parenting stress, and strengthens social support systems. However, the cross-sectional nature of this study precludes causal interpretations, warranting longitudinal investigation to establish temporal relationships.\u003c/p\u003e","manuscriptTitle":"Parental involvement and social skills of school-aged children with intellectual disabilities: the role of parenting stress and social support","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-04-10 05:04:10","doi":"10.21203/rs.3.rs-5474664/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":"0442e2f4-6b23-47df-8793-aefc13a5e6f2","owner":[],"postedDate":"April 10th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2025-06-16T03:23:31+00:00","versionOfRecord":[],"versionCreatedAt":"2025-04-10 05:04:10","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-5474664","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-5474664","identity":"rs-5474664","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}