The concept of parenting stress is generally understood to be a negative psychological reaction that occurs when parents are not able to meet their parenting needs and concerns about their role as parents (Deater-Deckard, 1998). Our study focuses on parenting stress in parents of preschoolers because this developmental period poses a number of challenges for them (Harmeyer et al., 2016). Although many parents experience parenting stress, multiple studies show that high parenting stress can lead to a range of child development problems (Fang et al., 2022). When parents are experiencing high levels of parenting stress, they may become less responsive, inconsistent, or harsh to the needs of their children (Crnic and Low, 2002). These negative parent–child interactions can result in a variety of children’s developmental problems, including difficulties with adjustment, problem behaviors, language delay, sleep problems, and negative emotions (Deater-Deckard, 1998; Baker et al., 2003; Horwitz et al., 2003; Martin et al., 2019). Additionally, children raised by parents with high parenting stress may have lower cognitive abilities and poor academic performance due to fewer positive learning interactions and stimulations in the family daily life (Tachibana et al., 2012). Furthermore, these negative effects caused by parenting stress during early childhood may influence preschoolers’ future development (Neece et al., 2012). According to a recent study, parents’ low perceived social support and negative emotions negatively affect their children’s ATL (Yan et al., 2022). Moreover, low perceived social support is generally associated with parenting stress (Huang et al., 2014). Further, parenting stress, which could cause more frequent negative emotions in parents, may adversely affect the development of preschoolers’ ATL (Fonseca et al., 2020). Hence, this study proposes the following hypotheses based on the information provided above:

When assessing parenting stress’ impact on preschoolers’ ATL, it is imperative to consider how parents respond to this stressful situation to reduce the negative impact on preschoolers. Multiple research suggests that parental parenting style is crucial to a child’s development, particularly during the preschool years (Tan et al., 2012; Hosokawa and Katsura, 2019). Additionally, a large number of studies suggest that parental stress influences children’s development through its effects on parenting (Crnic et al., 2005; Tan et al., 2012). Interestingly, a substantial amount of literature has examined that parents with lower parenting stress are more likely to adopt authoritative parenting (Park and Walton-Moss, 2012; Gouveia et al., 2016; Fonseca et al., 2020). Most studies have described authoritative parenting as more likely to include a higher degree of restriction, responsiveness, warmth, developmental appropriateness, and support than other parenting styles (Baumrind, 1971; Robinson et al., 1995; Park and Walton-Moss, 2012; Gouveia et al., 2016). Authoritative parents pay close attention to their children’s feelings and communicate with them frequently. In addition to granting their children reasonable autonomy, authoritative parents also teach them how to make wise decisions (Pinquart, 2017). Moreover, ample research has demonstrated that authoritative parenting is a type of positive parenting that fosters children’s development, such as prosocial engagement, cooperation, social competence, peer acceptance, school achievement, etc. (Crnic and Low, 2002; Cheah et al., 2009). Furthermore, a recent Chinese study found that authoritative parenting can positively predict preschoolers’ ATL (Xia, 2023). In addition, a systematic review indicates that parental supportive and warm behaviors can act as protective factors to increase preschoolers’ appropriate behaviors and decrease problematic behaviors when parents face high levels of economic stress (Masarik and Conger, 2017). Based on the above, authoritative parenting may serve as a protective factor buffering the negative impact of parenting stress on preschoolers’ ATL development. However, to date, only a few studies have explored the relationship between authoritative parenting style in terms of parenting stress and preschoolers’ ATL. As such, this study proposes the following hypothesis:

In recent years, as the Chinese economy has developed rapidly and urbanization has accelerated, the number of Chinese migrants from rural areas to urban areas has increased (Yang, 2013). Although migrants are generally defined as having crossed national borders, it is necessary to examine the impact of rural–urban migration on the development of preschoolers due to the enormous urban–rural divide in China (Yan et al., 2022). In this study, a migrant family is one in which both parents have rural residency and have lived in the city for more than half a year without obtaining a long-term residence permit. Moreover, there is considerable literature arguing that migrant and native parents have different parenting beliefs and behaviors, especially when it comes to their children’s education (Fibbi and Truong, 2015). Specifically, migrants may differ from native parents in terms of parenting self-efficacy, attitudes toward their children’s education, expectations, resources, involvement in their children’s daily activities, provision of cognitive stimulation, attitudes toward their children’s abilities and performance, etc. (Barglowski, 2019). Further, it has been demonstrated in previous studies that these differences can impact children’s development, particularly their ATL development (Padilla and Ryan, 2020). Accordingly, parenting outcomes and preschoolers’ ATL development may be significantly different in these two household residencies. Furthermore, according to Mistry and colleagues’ study, household residency can also serve as a moderator (Mistry et al., 2008). Thus, the present study predicts household residency might moderate the association between authoritative parenting and preschoolers’ ATL and proposes the following hypothesis:

The current study proposes a moderated mediation model (see Figure 1) on the basis of the theory of the family stress model. This study aimed to examine the relationship between parenting stress and preschoolers’ ATL. Furthermore, we also investigated how authoritative parenting plays a mediating role in parenting stress’ effect on preschoolers’ ATL. In this vein, how the influence of authoritative parenting on preschoolers’ ATL may differ based on household residency (migrant or native) was also explored.

Using the convenience sampling method, this study selected parents from preschools that comprised both migrant and native preschoolers in Guangzhou, Foshan, and Shenzhen cities in southern China. We distributed 5,400 questionnaires and collected 5,047 valid responses, resulting in an effective response rate of 93.46%. The valid subjects included 2,186 native parents and 2,861 migrants. We obtained informed consent from all participants, and the Guangzhou University School of Education and related research ethics committee evaluated and approved the research. Specific demographic information is shown in Table 1.

In this study, data were analyzed using SPSS24.0, which included reliability analysis, common method bias test, descriptive statistics, and correlation analysis. We used Mplus8.3 to test structural equation models. And we tested the mediation model and the moderated mediation model using Bootstrap and multi-group comparison. Model parameters were estimated using the maximum likelihood method (ML). To assess the goodness of the model fit, we selected the following fit indices: the Tucker-Lewis index (TLI), the Comparative Fit Index (CFI), the Root Mean Square Error of Approximation (RMSEA), and the Standardized Root Mean Square Residual (SRMR). Since this study had a large sample size, the chi-square values were not used as a reference for the model fit. The cutoff values of CFI and TLI ≥ 0.9, SRMR and RMSEA ≤0.08 were adopted as the criteria for a good fit in the current study. And p value (p) < 0.05 was regarded as statistically significant (Kline, 2005).

To test whether household residency (native/migrant) has a moderating effect in the latter half of the mediation model, we used multi-group comparison to test the differences between groups. First, we examined the tested model between the two groups. We tested the following invariance: (1) Configural Invariance, that is, the attribution of indicators is equal among different groups; (2) Metric Invariance, that is, the loading of the indicator on the latent variable is equal between different groups; (3) Scalar Invariance, which means that the intercept of indicators is equal between different groups. In general, if the fit indexes (CFI, TLI, and RMSEA) do not change by more than 0.01, the model has not significantly changed (Meade et al., 2008). Following the testing of measurement invariance of the tested models, pathways between variables were added to the models. To test whether the pathways between authoritative parenting and preschoolers’ ATL are different among two family types, this study let these pathways be freely estimated among the two groups and constrained the invariance of other pathways. To determine whether the difference is significant, the Wald Test was used to compare the difference between the two pathways. If the Wald Test result has a significance p-value of less than 0.05, it suggests that the paths are statistically different across groups.

Although this study uses a more mature measurement tool and emphasizes the confidentiality of personal information in data collection, according to previous studies on common method deviations, a Harman one-way test is required to confirm common method deviations statistically after data collection (Podsakoff et al., 2003). It was found that there were 13 factors with feature values greater than one. The variance explained by the first principal factor was 21.54%, which was less than the critical criterion of 40%. Thus, there is no common method bias in this study.

Table 2 presents the descriptive statistics (standard deviations and means), and correlations for the main study variables. Based on the data analysis results, parenting stress was negatively correlated with preschoolers’ ATL (r = −0.45, p < 0.01). In addition, parenting stress was also negatively associated with authoritative parenting (r = −0.37, p < 0.01). Further, authoritative parenting was positively associated with preschoolers’ ATL (r = 0.35, p < 0.01). Moreover, household residency was significantly associated with preschoolers’ ATL, parenting stress, and authoritative parenting (r = −0.09, p < 0.01; r = 0.16, p < 0.01；r = −0.09, p < 0.01, respectively).

This study tested the mediating effect of authoritative parenting based on the test procedure for mediation analysis of structural equations. Further, we estimated confidence intervals for each coefficient by the Bias-Corrected Bootstrap method (Bootstrap = 5,000), with 95% confidence intervals that do not contain zero indicating statistical significance (Shrout and Bolger, 2002). First, a simple regression model of latent variables was established to test whether parenting stress directly predicted preschoolers’ ATL. The results showed that the model fitted well with RMSEA = 0.05, CFI = 0.99, TLI = 0.98, and SRMR = 0.02. It was found that parenting stress negatively and significantly predicted preschoolers’ ATL after controlling for preschoolers’ gender and age (b = −0.30, p < 0.001). And the amount of preschoolers’ ATL explained by parenting stress was 37.3%. Hence, hypothesis 1 was supported.

Second, the original model also fitted well by including authoritative parenting as a mediating variable, with various fit indices of RMSEA = 0.06, CFI = 0.95, TLI = 0.94, SRMR = 0.05. Parenting stress negatively significantly predicted authoritative parenting (b = −0.52, p < 0.001) with a 95% confidence interval of [−0.56, −0.48], and authoritative parenting significantly positively predicted preschoolers’ ATL (b = 0.10, p < 0.001) with the 95% confidence interval was [0.08, 0.11], indicating that a mediating effect holds. The mediating effect size was 0.12, p < 0.001, with 95% confidence intervals of [0.10, 0.13], none of the 95% confidence intervals included 0, showing significance, and the mediating effect accounted for 54% of the total effect (0.22). As a result, authoritative parenting mediated the relationship between parenting stress and preschoolers’ ATL. Hypothesis 2 was supported. Figure 2 shows the findings.

We used multi-group comparison to test whether household residency moderates the relationship between authoritative parenting and preschoolers’ ATL. The result shows that in the tested model, both household residency (natives and migrants) pass the tests of measurement invariance, including Configural Invariance, Metric Invariance, and Scalar Invariance sequentially (Table 3 presents detailed analysis results). Therefore, the model can be applied to different groups. Further, we added pathways between the variables based on the tested model. In order to test whether there are differences between the two groups in the latter half of the mediation model, the pathway between authoritative parenting and preschoolers’ ATL was freely estimated between the two groups. Conversely, the pathway between parenting stress and authoritative parenting as well as the pathway between parenting stress and preschoolers’ ATL were constrained between different groups. Then, the Wald Test is used to compare the difference between the two freely estimated paths. As a result of the Wald Test (Wald test = 23.45, df = 1, p < 0.001), the results indicated that native and migrant families showed significant differences on these two freely estimated paths.

In native families, the mediating effect value of authoritative parenting between parenting stress and preschoolers’ ATL was −0.13, 95%CI was [−0.15, −0.11], and the mediating effect was significant, accounting for 21.2%. Among migrant families, the mediating effect was −0.08, 95%CI was [−0.09, −0.06], which was also significant, accounting for 12.8%. The difference in the mediating effect between the two types of families was 0.03, p < 0.001. Furthermore, the results show that the mediating effect of native families was significantly greater than that of migrant families. This indicates that household residency moderated authoritative parenting’s mediating effects in the relationship between authoritative parenting and preschoolers’ ATL. Thus, hypothesis 3 was supported.

In this study, it was found that parenting stress negatively affected preschoolers’ ATL. The family stress model also emphasizes the impact of family or parental stress on children’s development (Masarik and Conger, 2017). According to the model, parental stress can contribute to a stressful home atmosphere, which can adversely affect the children (Schmiedeberg and Bozoyan, 2021). That is, when children are exposed to such a stressful family environment, they also experience more negative emotions such as feeling neglected, anxious, or depressed. Additionally, these negative feeling can hinder their concentration, flexibility, and creativity, discourage their passion for learning, and further impact their academic performance. Moreover, a parent who is stressed out by parenting tends to behave less affectionately and less patiently toward his or her children and becomes less engaged in their daily routine (Conger and Donnellan, 2007). It is conceivable that low-frequency and low-quality parent–child interactions have a negative impact on children’s performance (Burchinal et al., 2002). Further, when parents experience high levels of parenting stress, children may not receive positive emotional support and responses from parent–child interactions but rather receive more negative feedback (Fonseca et al., 2020). Preschoolers often receive negative feedback or punishment, resulting in a lack of self-confidence, curiosity, exploration motivation, etc. Further, all these factors will inhibit preschoolers’ ATL development. As such, reducing parental stress levels can improve not only the psychological well-being of parents but also the ATL of preschoolers as well (Deater-Deckard, 1998).

The results showed that the authoritative parenting style mediated the relationship between parenting stress and preschoolers’ ATL. In other words, authoritative parenting buffers the negative impact of parenting stress on preschoolers’ ATL. As such, this pathway fits with the extension of the family stress model (Masarik and Conger, 2017; Lee et al., 2021). The family stress model indicates that parental stress and depression make it difficult for parents to maintain a positive relationship with their children and may lead to a variety of maladaptive parenting practices (Masarik and Conger, 2017). Consequently, children are at a higher risk of displaying problematic behaviors, achieving poor educational outcomes, and experiencing emotional difficulties (Schmiedeberg and Bozoyan, 2021). Firstly, consistent with previous studies, we have found that parenting stress negatively predicts authoritative parenting styles (Cheah et al., 2009). Parents may feel anxious and sullen under high levels of parenting stress, and these negative emotions may reduce their positive responses to their children (Fonseca et al., 2020). Moreover, parents who suffer from high parenting stress may experience self-doubt and low parenting self-efficacy, which leads them to be less involved in their children’s daily lives (Crnic and Low, 2002). Nevertheless, all these behaviors are contrary to authoritative parenting. Secondly, the present study confirmed previous findings by indicating that authoritative parenting was positively related to preschoolers’ ATL (Xia, 2023). Accordingly, authoritative parenting is more conducive to improving preschoolers’ ATL because it displays high levels of warmth, support, and responsiveness. Indeed, parents who adopt authoritative parenting can understand their children’s characteristics better and can help them maximize their strengths (Crnic and Low, 2002). Additionally, authoritative parents are better at communicating with their children, respecting and understanding their children’s feelings, maintaining a positive parent–child relationship, and caring about their children’s school lives. Consequently, children raised in this parenting style will be more independent, confident, and cooperative, as well as more proactive in their learning process, and will exhibit better ATL (Blair, 2002). Thus, parenting stress is not only directly related to preschoolers’ ATL, but it is also indirectly related to preschoolers’ ATL through authoritative parenting practices.

The results of this study showed that household residency can moderate the relationship between authoritative parenting and preschoolers’ ATL. Furthermore, compared with parents in migrant families, native parents’ authoritative parenting showed a stronger positive relationship with preschoolers’ ATL. In our opinion, several factors contributed to this finding. To begin with, economically, the data of the current study showed that migrant preschoolers’ parents in China tend to work in manual labor jobs and have lower household incomes than native families. Moreover, it is well known that capital is vital resource parents provide to their children. Low family income will reduce parents’ investment in their children’s education, including extracurricular books, tutoring, and other education services (Gong and Zhong, 2015). It is imperative to note that this situation is very different from that of native children living in the cities (Gong and Zhong, 2015). Secondly, the result may be explained by the difference in educational background between migrant and native parents. According to the data, it has been found that migrant parents tend to be less educated than parents from native families. However, parents with higher educational levels have a better educational concept and authoritative parenting behavior, which is helpful for the development of children’s ATL (Schady, 2011; Sung and Wickrama, 2018). Highly educated parents generally have effective approaches to supporting their children to learn and measuring their children’s progress positively (Schmiedeberg and Bozoyan, 2021). Further, migrant parents generally work intensively for long hours, which leaves less time for them to be involved in their children’s education (Gong and Zhong, 2015). Additionally, previous research has revealed that parents’ mental health significantly impacts the performance of young children (Herba et al., 2016). Due to the household registration system in China, migrants have difficulty accessing the same urban resources as natives (Knight and Gunatilaka, 2010). Therefore, parents of migrant families may suffer from a sense of deprivation (Xiong et al., 2021). This negative feeling may reduce the effectiveness of their authoritative parenting and further influence children’s ATL (Knight and Gunatilaka, 2010). Furthermore, Yan and colleagues indicated that parents’ perceived social support positively influenced their children’s ATL (Yan et al., 2022). However, migrant parents’ perceived social support is generally lower than native parents, which in turn negatively impacts the child’s ATL (Hashemi et al., 2021). Moreover, the family environment also plays an important role, since migrant families have low-quality housing and a chaotic home environment, which may negatively influence the development of preschoolers’ ATL (Zhao et al., 2023). Thus, native families’ authoritative parenting styles are more conducive to fostering preschoolers’ ATL than migrant families.