1. Introduction

In today's society, with the profound reconstruction of family structure and the comprehensive innovation of marriage concept, the divorce rate in China basically shows a trend of increasing year by year. According to data released by the China Social Security Association, China's divorce rate rose from 0.96 ‰ in 2000 to 3.1 ‰ in 2020[1]. In 2023, There were 3,605,300 pairs of divorce procedures nationwide in accordance with the law, Women filed for divorce than men, The former accounts for more than 73%, At the same time, relevant scholars point out that, During the 33 years of 1982-2015, women's divorce status increased faster than men [2], The above set of data reflects the advancement of women in modern marriage, Even appeared the phenomenon of female-led marriage dissolution [3], But it has also sparked a new debate: the remarriage of divorced women. In recent years, the remarriage of divorced women has increasingly become the focus of attention from all walks of life. Marriage behavior is not only related to individual emotional destination and family reconstruction, but also profoundly affects the stability of social structure and family function. For divorced women with children, remarriage is not only an emotional choice, but also a repositioning of their living status, social role and family responsibilities.

In the complicated process of remarriage, the influence of children's factors and personal factors on remarriage behavior has been verified by relevant scholars at home and abroad to a certain extent. On the one hand, Zhang Xiaomin and other domestic scholars revealed the subtle influence of children on stepfamily relations through empirical analysis, and pointed out that factors such as the acceptance of children and the relationship between stepparents and children play a significant role in the stability and harmony of stepfamilies [4]. On the other hand, internationally, the studies of Silverstein and Bengtson similarly emphasized the differences in the provision of intergenerational social support, which may affect the psychological well-being and willingness to remarry [5]. Kalmijn, M. From the perspective of psychological resilience, social support and educational type marriage, deeply discussed the key role of personal resources in remarriage success and family happiness [6]. It can be seen that the above studies jointly constructed a multi-dimensional perspective, which to some extent confirmed that the factors of children and personal factors as the core variables, and their influence is particularly significant.

However, the above studies also have obvious limitations. Specifically, the scope of these studies is often limited to a specific region or based on foreign social background, which fails to fully reflect the complexity and diversity of China. In view of the uniqueness of Chinese society, including cultural traditions, values, family structure, etc., there may be deviations if foreign research results are directly applied to the Chinese situation. Therefore, it is urgent to deeply explore the influencing factors of the remarriage behavior of divorced women in the local background of China.

Based on the above research background and reality, this paper selects the Chinese Family Panel Studies (CFPS) 2010-2020 data, through the empirical analysis method, the system research children factors and personal factors of divorce women remarried behavior, and by constructing logical regression model, reveals how these factors independently and combined in remarriage decision, and then explore the social machine behind it.

2. Theoretical Perspective and Research Hypothesis

2.1. Social Gender Theory

According to the social gender theory, gender is not only a biological attribute, but also a social construction [7]. The society will give him (her) different expectations, requirements and limit according to the physiological differences between men and women[8]. For example, under the traditional division of gender roles, women are often given more family care responsibilities. Therefore, divorced women may pay more attention to how to balance family and work and how to take care of their children when considering remarriage. Social gender theory provides a theoretical perspective for us to understand the remarriage decision of divorced women, which reveals the dual social expectation in discussing the relationship between social gender and remarriage behavior: on the one hand, the society often places specific expectations on their role transformation and re-socialization process; on the other hand, the social gender theory also deeply analyzes the different expectations and considerations exerted on children due to gender differences, which implies the role positioning and function expectations of different gender roles in the future society. Therefore, from the perspective of social gender theory, it is helpful for us to comprehensively analyze the gender of children and the influence of divorced women on remarriage behavior.

2.2. Structural Family Theory

In the unique cultural and social context of China, the understanding and analysis of women's remarriage behavior cannot be separated from the perspective of family [9]. Women's decision to remarry often contains a multi-dimensional and deep and detailed consideration of the family. Therefore, when exploring the remarriage behavior of divorced women, it is necessary to consider its influence on the reconstruction of family structure and the adjustment of family relations, as the structural family theory elucidates the close connection between internal family dynamics and individual decision-making [10]. Based on the above analysis, it is observed that most of the existing studies are grounded in these two theoretical perspectives.

2.2.1. Child Factors and Remarriage Behavior

In the influence of child age study, Koo, Suchindran, and Griffith found that as children increased, especially as they entered adolescence or adulthood, helping to increase their willingness and likelihood to remarry [11]. This finding suggests that responsibility allocation and role changes within the family influence individual marriage decisions, reaching a consensus with structured family theory. And before this, Espenshade has been in its related research to further explore the economic influence of children age on remarriage behavior [12], he points out from the perspective of economics, young children need more care and input, which often limits the divorced women in the economic and emotional resources, thus delaying their remarriage behavior. As their children grow older and their independence increases, these constraints gradually weaken, creating more favorable conditions for divorced women to remarry. Later, Lamanna and Riedmann also highlighted the profound impact of family structure changes on remarriage behavior through empirical analysis. They believe that the aging of their children not only changes the resource allocation and role positioning within the family, but also affects the divorced women's expectations and planning for the future life of [13].

In the study of the influence of children gender, zhang and Chen Xianshou in Hubei province 1% population sampling analysis pointed out that children gender to a certain extent affect the divorce women remarriage decision, especially social cultural expectations and bias, which may lead to divorced women in the face of different gender of children, there are different considerations on the remarriage choice [10]. This view is basically in line with Cherlin's emphasis on the solidified role of social gender roles in family life in his book Marriage, Divorce, Remarriage, which states that these role expectations not only affect the dynamics of the marital relationship, but also indirectly affect the remarriage behavior after divorce [14]. However, Silverstein and Bengtson found differences in child gender in the provision of intergenerational social support, and this difference may affect the psychological well-being and willingness to remarry of divorced women [5]. For example, the society has higher expectations for male children in family economic support, while female children play a role in emotional support. This different support mode may encourage divorced women to adjust their remarriage strategies according to their own needs and gender characteristics of their children.

2.2.2. Personal factors and remarriage behavior

In the influence of individual age research, the results show that young divorced women may be more inclined to remarry behavior, and with the growth of age, their willingness to remarry may be affected by many factors, namely the divorced women's personal age not only affect the possibility of remarriage, also profoundly affect the remarriage life satisfaction [15]. Moreover, age also affects women's economic independence and their ability to acquire social resources, and these factors together act on their remarriage decision-making process. In short, the individual age of a divorced woman will have a profound impact on her remarriage behavior by affecting many aspects, such as her social cognition, psychological needs and economic independence.

In the influence of personal income studies, divorced women with high income tend to have more autonomy and choice. England, P., & Farkas, G. pointed out that economic independence may reduce women's economic demand for remarriage, thus weakening their urgency of remarriage [16]. This view has also been tested in studies of Chinese women, especially those living in rural areas and with lower cultural occupations, and financial pressures tend to encourage them to consider remarriage more quickly.

2.3. Research Hypothesis

In the study of the influence of children's factors and personal factors on the remarriage behavior of divorced women, the research and findings of previous scholars are re-examined from the perspective of social gender theory and structural family theory, leading to the formulation of the following research hypothesis.

2.3.1. The Influence of Children's Age on Remarriage Behavior

The existence of young children not only requires mothers to invest more emotional and energy to support, but also often accompanied by economic, educational and emotional support and other aspects of responsibility and pressure. In this context, remarriage, as a way that may bring about family stability and resource convergence, is particularly attractive to many divorced women with young children. When their children are young, their presence encourages the divorce people to find new partners to jointly build a complete family environment out of care and responsibility for their children. However, as the child ages, the dynamics within the family also change. Older children may have developed independent personalities and living habits, with relatively low acceptance of new members. This requires that stepfamilies pay more attention to the redefinition of boundaries and the interactive adjustment between subsystems in the integration process. Based on the above analysis, the hypothesis H1 was established.

Hypothesis H1: The presence of young children increases the urgency of remarriage for divorced women to remarry, which may encourage divorced women to consider and make remarriage decisions.

2.3.2. The Influence of Children's Gender on Remarriage Behavior

Becker Research found that when divorced women take on the responsibility of raising their children alone, they may face greater economic pressure, especially in the case of raising their sons, the society often has higher expectations on the education and growth investment of male children, which virtually increases the economic burden of divorced mothers [17]. Psychologists Wallerstein and Blakeslee explored in detail the psychological impact of divorce on children and both parents. They point out that divorced women with sons may feel additional stress from the widespread "lack of fathers" anxiety, not only from concerns about their future development, but also from questions about whether single mothers can effectively fulfill their role of father [18]. These mothers may make different remarriage decisions because they feel that the society cares about and judges about whether they can provide a "complete" family structure for their sons. Based on the above analysis, the hypothesis H2 was established.

Hypothesis H2: A divorced woman with a son may face greater social pressure and financial responsibility, prompting her to remarry.

2.3.3. The Influence of Individual Age on Remarriage Behavior

With the growth of age, individual yearning for a stable life increases, and remarriage becomes an important way for older divorced women to pursue emotional support, life partner and spiritual sustenance; at the same time, the demand for social belonging urges them to reintegrate into the family role through remarriage to gain social recognition; in addition, as their children become independent, the reduction of family responsibility provides them with more personal space and time to consider and decide the possibility of remarriage. Based on the above analysis, the hypothesis H3 was established.

Hypothesis H3: Older divorced women are more likely to remarry than younger divorced women.

2.3.4. The Influence of Personal Income on Remarriage Behavior

Higher personal income not only enhances the economic independence and confidence of divorced women, makes them more independent and picky in mate selection, and can choose partners based on spiritual fit and values rather than purely economic considerations. Meanwhile, high income also broadens their social circle, which provides them with a wider range of mate selection and allows them to have higher expectations and requirements for future quality of life. Economic independence reduces the social prejudice and pressure on divorced women and makes them more free in their remarriage decisions. Based on the above analysis, the hypothesis H4 was established.

Hypothesis H4: Divorce women with higher personal income are more competitive in the remarriage market and less constrained by social concepts and economic pressures, making them more likely to be successfully remarried.

3. Data, variables, and methods

3.1. Data Source and Variable Manipulation

The data for this study were obtained from the database of the China Family Panel Studies(CFPS, 2010-2020) hosted by the China Center for Chinese Social Sciences Survey of Peking University. First, the relevant variables in the database were cleaned and merged, including child sex, child age, maternal age, income, marital status, number of children, type of residence, and maternal education level, in order to control for biases arising from individual heterogeneity. This means that the time-invariant properties of each individual are controlled, thus more focused on explaining the relationships between variables. Furthermore, the data were deweighted to ensure that each individual appeared only once in one year, avoiding the effect of individuals with repeated observations on the regression results. Then, based on this, four key independent variables were selected: child's age, child's sex, mother's age, and income, along with one dependent variable: remarriage behavior. Marriage behavior is a binary variable, said whether divorced women remarry, to test the influence of children factors on remarriage behavior, but at the same time considering that the level of education, living area, the number of family members and year variables may affect remarriage behavior, but does not belong to the core research problem, so treat them as control variables, so that the model results more explanatory power, and reduce the deviation.

3.2. Analysis Methods and Strategies

In this study, the logistic regression model was used as the main analysis tool, and the main influencing factors of remarriage behavior were studied through this model, and the influence strength of the variables was revealed through the marginal effect. The robustness test, which includes the annual Logit regression, the former model to check whether the agreement with Probit years, and the latter to verify the agreement with the Logit results. Finally, considering the existence of the endogeneity problem, the issue was addressed through the use of instrumental variable regression.

4. Results and Analysis

4.1. Descriptive Analysis of The Sample Data

In this study, Stata17.0 was used to manipulate the data and to perform a descriptive analysis of the relevant variables. From the results of the descriptive statistics, the mean remarriage status of the respondents in the sample was 0.930, indicating that the majority of the respondents had remarried, while the proportion of respondents who had not remarried was only 7%. This phenomenon shows that remarriage behavior is very common in this sample. In terms of maternal age, the mean age was 54.84 years, indicating that the respondents in the sample were older and the age distribution was relatively scattered, with the minimum age of 16 years and the maximum age of 103 years. This wide age distribution is beneficial to reflect the difference in remarriage behavior of mothers in different age groups. The corresponding mean age of the children was 10.49 years, ranging from newborns to 59 years, reflecting the diversity of the children in the respondent's family. In terms of the gender of children, the gender distribution in the sample was relatively uniform, with 52% male and 48% female, and the gender difference was small. Meanwhile, the average educational level of the respondents was about 2.9 (in the range of 1 to 9), reflecting that the majority of the respondents had a moderate level of education. The standard deviation of education level was 1.46, indicating that there were some differences in educational level between respondents, including both groups with higher education and those with lower education level. The descriptive statistics of income showed that the average annual income of the respondents was 54,157 yuan, but the standard deviation was as high as 172,840 yuan, and the maximum income reached 11.4 million yuan, indicating that the income distribution in the sample was very uneven. Such an income gap can reflect the remarriage situation under different economic backgrounds. Finally, the year variable shows data covering multiple years between 2010 and 2020, which provides the context for subsequent years annual Logit regression analysis.

Table 1: Descriptive statistical analysis.

4.2. The Logit Regression Model

Next, Logit regression analysis was performed on the relevant variables. From the results of the analysis, maternal age had a significant positive effect on remarriage behavior, older mothers were more likely to remarry, and for each additional year, the probability of maternal remarriage increased by about 0.18%, which is consistent with hypothesis H3.

Child age has a negative effect on mother's remarriage behavior, and the probability of mother's remarriage decreases by about 0.58%, which also confirms hypothesis H1.

However, child sex did not show a significant effect in this analysis, suggesting that sex has less effect on remarriage behavior, which violates hypothesis H2.

Income also had no significant effect on remarriage behavior in this data set, and the coefficients were very small and not significant, indicating that income level has a limited impact on maternal remarriage decision-making, which also negates hypothesis H4.

It is worth noting that in terms of time, the year coefficient from 2012 to 2020 was negative and significant, indicating that the possibility of remarriage gradually decreased over time compared to the baseline year, especially in 2018, the probability of remarriage decreased significantly by 53.68%.

In conclusion, maternal age and child age are important determinants of remarriage behavior, while income and gender have a limited impact. Furthermore, the time effect showed a significant reduction in remarriage behavior in 2018, which may reflect a specific social or economic context at the time.

Table 2: Logistic regression analysis.

4.3. Edge Effect

Next, the marginal effect was used to explain the actual impact of each variable on remarriage behavior.

The results showed that maternal age had a significant positive effect on remarriage behavior. Specifically, each annual increase in maternal age increased the probability of remarriage by 0.18%. This is consistent with the positive relationship of maternal age in the regression analysis. However, the effect of the age of the child is opposite. For each year increase, the probability of the mother remarrying decreases on average by about 0.58%. This result is equally significant, indicating that the possibility of the mother remarrying is significantly reduced with the age of the child. The effect of child sex on remarriage behavior was not significant, and children with male sex had little significant effect on maternal remarriage behavior, indicating that gender is not an important factor in remarriage decisions in this model. The marginal effect of income was very small and non-significant, indicating that the effect of income on remarriage behavior was not statistically significant in this sample.

It is worth noting that in the year variable, the marginal effect from 2012 to 2020 showed that the remarriage probability decreased year by year, especially in 2018, the probability of maternal remarriage significantly decreased by about 53.68%. This result may reflect the presence of some social or economic factors influencing remarriage decisions in that year.

The marginal effect analysis further validates the results of the regression analysis, indicating that maternal age and child age were the main influencing factors of remarriage behavior.

Table 3: Marginal effect analysis.

4.4. Roubustness Test

4.4.1. Logit Regression Performed by Years

Based on the above operations, the robustness test of the Logit regression was then performed by years.

The robustness test of annual Logit regression showed that the effect of maternal age on remarriage behavior had a significant positive effect in most years, especially in 2012,2014 and 2016, when each year increase in maternal age significantly increased the likelihood of remarriage significantly. However, in 2010 and 2018, the influence of mother age is not significant, especially in 2018, based on the realistic background, 2018 global economic environment is complex, including trade friction, economic slowdown, and these factors greatly increased the uncertainty of family life, cause people considering remarriage, compared with age factors, more balance the economic situation and the stability of the future life, so also explains the weakening of the correlation between age and remarriage behavior. However, the influence of children's age is mostly negative, especially in 2012,2014 and 2016. The older the child is, the lower the less likely the mother is to remarry, indicating that the remarriage decision may be restricted by the child's age of the child. However, in 2010 and 2018 and the offspring age effect was not significant. In terms of gender, it did not show significant effects in all years, and this result suggests that child gender is not a key factor in maternal remarriage decisions. In terms of income, the results also showed consistent regression results across years, whether in the better years or worse years, the income level had a significant impact on remarriage decisions.

In conclusion, maternal age and child age are important influencing factors of remarriage behavior in most years, and income and child sex did not show a significant role in each year, at the same time, the determinants of remarriage behavior changed in different years, but maternal age and child age is still the core variables in the remarriage decision in most cases.

Table 4: Logit regression analysis performed by years.

4.4.2. Probit Model

Meanwhile, the Probit model was also utilized to test the robustness of the marital status. The results showed that the results of the Probit model were very similar to those of the previous Logit models, which verified the robustness of the model, showing that the effects of child age, income and education level on female remarriage behavior were consistent in both models, and the significance and direction were consistent. In particular, the negative influence of the child's age and the reduced probability of remarriage due to the higher education level were verified in both models. Gender, maternal age, area of residence, and number of members were not significantly affected in both models, suggesting that these variables did not have much effect on remarriage behavior.

Table 5: Probit model.

4.4.3. Dealing with endogenous problems

Here, instrumental variable regression (2SLS) was employed to address the endogeneity of income. Specifically, the effectiveness of education as an instrumental variable and its impact on the regression results were examined. The results indicated that income has a significant negative effect on remarriage behavior, with a regression coefficient of -4.13e-07, which is statistically significant. This means that mothers are less likely to remarry with increasing income, which may be due to higher income mothers who are more financially independent and have a lower need for remarriage. Second, maternal age had a significant positive effect on remarriage behavior with a regression coefficient of 0.0022, suggesting that the likelihood of maternal remarriage increased with increasing age. This result is consistent with previous analyses suggesting that maternal age plays a key role in remarriage behavior. The effect of child age was negative on remarriage behavior with a regression coefficient of-0.0039, which indicated that the older the child is, the less the mother was likely to remarry. The results showed that the influence of the child sex on the remarriage behavior was not significant, indicating that the child sex is not a key factor in the mother's remarriage decision, that is, the gender has less influence on the remarriage behavior regardless of whether the children are male or female. However, among the year variables, years in 2012 and 2018 had significant negative effects on remarriage behavior, especially in 2018, the possibility of maternal remarriage was significantly reduced, while the possibility of remarriage in 2020 increased, indicating that the socioeconomic background of different years had a significant impact on remarriage behavior.

In conclusion, the use of education as an instrumental variable successfully addressed the endogeneity of income, and the results further verified the negative effect of income level on remarriage behavior, while reinforcing the importance of factors such as maternal age and family structure.

Table 6: Tool variable regression.

5. Conclusion and Thinking

5.1. Conclusion

This study deeply explores how children, as key independent variables, influence the remarriage behavior of divorced women. This issue is not only related to the choice of individual emotions, but also reflects the complex interweaving of family dynamics, social and cultural factors and gender roles. From the perspective of social gender theory and family function theory, a series of research hypotheses are proposed. Subsequently, data analysis is utilized to elucidate how these factors interact and collectively influence the remarriage decision-making process of divorced women.

It was found that maternal age has a significant positive effect on remarriage behavior, especially in specific years such as 2012,2014 and 2016, with each increase in maternal age, the likelihood of remarriage increases significantly. This finding is consistent with the conclusions of existing studies, further validating the important effect of age on remarriage behavior. The age of children generally has a negative effect, that is, the older the child, the lower the less likely the mother is to remarry. This suggests that child age is an important constraint in remarriage decision-making and that mothers may abandon the remarriage plan by considering issues such as their child's life and education. However, the results show that the influence of income and gender of children on remarriage behavior is relatively limited. Although high-income women may be more competitive in the remarriage market, overall, the impact of income on remarriage behavior is not significant. However, the role of child sex in remarriage decision is not obvious and shows no significant difference.

5.2. Thinking

Upon reviewing the entire research process, potential limitations and future research directions are also identified. First, the data sources of this study, although extensive and representative, still have the limitations of sample selection. For example, the sample in the CFPS database may fail to fully cover all types of divorced women, especially those with low socioeconomic status or poor access. Therefore, the universality of the study results is somewhat affected.

Secondly, this study mainly adopts the logistic regression analysis model, although the model has advantages in dealing with the binary dependent variables, but can not fully capture the complexity of remarriage behavior, especially mentioned above in particular years, the social background of specific years. The author believes that future studies can try to introduce more analytical methods and models to explore the influencing factors and mechanisms of remarriage behavior.

Finally, it is of great significance to explore and reveal the internal mechanism of remarriage behavior, which is conducive to guiding the society to provide more accurate and personalized guidance and services for divorced women and their families. At the same time, it is recommended that all sectors of society provide greater understanding, respect, and support to divorced women, and jointly strive to create a more inclusive and harmonious social environment.