Parental repartnering and child well-being: What role does coresidence play?

Objective: The paper examines the effects of parental repartnering (including residential and nonresidential partnerships) on children’s well-being. Background: An increasing number of children experience the repartnering of their parents. While previous research has focused on coresidential repartnering, this paper also considers the transition to a steady nonresidential (living apart together – LAT) partnership of formerly single parents. Specifically, the paper examines whether these transitions differ in their effect on children. Method: This study uses data from the German Family Panel (pairfam) to analyze the effects of parental repartnering on children’s emotional and behavioral well-being. The children in the sample were seven to 16 years old. Individual fixed effects regressions were estimated for two types of parental partnership transitions: the formation of a LAT partnership and the formation of a coresidential partnership. Results: The results show that children’s emotional symptoms increased in response to both parental LAT repartnering and coresidential repartnering, whereas children’s conduct problems increased only in response to parental coresidential repartnering. Conclusion: These findings suggest that the formation of a nonresidential partnership by a parent can affect children’s emotional well-being, and thus should be considered when analyzing post-separation family development.


Introduction
In recent decades, family life has changed considerably. Although two-biological-parent families are still the most common family structure, single parenthood and parental repartnering are becoming increasingly common. In Germany, the share of children who live in a household with a stepparent before age 18 increased from 6% for the 1971-73 birth cohort to 11% for the 1991-93 birth cohort (Kleinschlömer & Krapf, 2021). Previous studies have shown that children whose parents are divorced are disadvantaged with regard to their educational success (Francesconi et al., 2010), their psychological health (Amato, 2010), and their relationships with their parents (Amato, 2005). Similar disadvantages have been observed for children who live with a parent who has repartnered (Brown, 2006;Gennetian, 2005;Ginther & Pollak, 2004;King, 2009). It has also been shown that these negative effects often persist into adulthood (Amato, 2014;Heintz-Martin & Langmeyer, 2019). Given that families with lower socioeconomic status are at increased risk of experiencing a change in structure or having an alternative structure (Conger et al., 2010;Raley & Sweeney, 2020), the negative effects of such family transitions appear to play a role in the intergenerational reproduction of social inequality (Raley & Sweeney, 2020).
Prior research on the impact of parental repartnering focused on the effects of sharing a household with the parent's new partner on children's well-being. However, most parental relationships start with a living apart together (LAT) phase, during which the partners are in a steady relationship, but live in two separate households (Krapf, 2018;Wagner et al., 2019). The effects on children's well-being of this first phase of a parent's new partnership are often ignored, because many datasets focus on households and coresidential partnerships, and do not contain information on partners outside the household. Prior research shows that the start of a LAT relationship affects the well-being of the partners (Langlais et al., 2016). However, it is much less clear whether a parent's transition to a LAT relationship also affects the well-being of children. On the one hand, a parent's transition to a LAT relationship might affect the children's well-being because it occupies the parent's time and energy. On the other hand, a LAT partner might be perceived more as a visitor (instead of a social parent) who does not strongly affect the well-being of the children of the partner. By contrast, the transition to a coresidential relationship affects the children's well-being because it is accompanied by changes in daily routines and the establishment of new family roles. This paper examines the effects of parental repartnering on children's psychological well-being in Germany. With a focus on the biological parent in the household, we distinguish between the effects of a parent forming a LAT partnership and a parent forming a coresidential partnership. We analyze data from the German Family Panel (pairfam) (Brüderl et al., 2020) that provide us with information about LAT and coresidential partnerships. We analyze partnership information about the child's resident parent (and joint physical custody is still of minor importance in Germany (Walper, 2018, p. 17)). While most prior research used cross-sectional data, pairfam allows us to use a longitudinal research design. We estimate individual fixed effects regressions and thus reduce potential selection bias. The pairfam survey collects detailed data about the partnership histories of parents and the well-being of children. We analyze two separate samples. Using the first sample, we examine the effects of a parent transitioning to a LAT relationship on children's well-being (490 observations of which 76 have a parent with a LAT partnership). Using the second sample, we analyze the effects of a parent transitioning to a coresidential partnership on children's well-being (996 observations of which 107 have a parent in a coresidential partnership).

Theoretical framework
In our analyses, we are interested in investigating the effects on children of two separate repartnering events: (a) a parent transitioning to a LAT relationship and (b) a parent forming a joint household with a new partner. In the literature, two main mechanisms have been cited to explain the association between family structure and children's wellbeing. These mechanisms concern the availability of family resources and psychological distress (Amato, 2000;Brown, 2004;Sweeney, 2010;Thomson et al., 1994). The two mechanisms are of varying importance for the two repartnering transitions. As parental repartnering usually occurs in the aftermath of a parental separation (Andersson et al., 2017), we start our theoretical considerations with the situation after parental break-up.
The literature has emphasized that one-parent families tend to have fewer economic and time resources than two-biological-parent families (McLanahan & Sandefur, 1994). Thus, one-parent families face an increased risk of poverty (Brown, 2004;Heintz-Martin & Langmeyer, 2019), which is closely linked to a decline in child well-being (McLanahan & Sandefur, 1994). In addition, a single parent must take on the role of the breadwinner (Thomson et al., 1994), as well as the roles of both parents at home (Bastaits & Mortelmans, 2016;Cherlin, 1992). Because the time single parents are able to spend with their children is limited, they tend to devote less time than married parents to controlling and supervising their children (Brown, 2004;Wu & Thomson, 2001). When parents experience high levels of distress due to a lack of resources following a separation, the well-being of both the parents and the children is reduced (Amato & Booth, 1997).
Repartnering after separation changes this situation. However, the theoretical arguments for why this is the case have been contradictory. When parents repartner (regardless of whether they are or are not coresiding with the new partner), they may be more or less involved with their children from a prior union than they would be if they remained single. On the one hand, being in a new partnership can positively affect the well-being of parents by reducing their post-separation loneliness and depression (Gloor et al., 2021;Soons et al., 2009), which might, in turn, positively affect their parenting and the well-being of their children. On the other hand, repartnering may lead to a reduction in the amount of time parents spend with their children because they shift their attention to the new partner and new children (Manning & Smock, 2000). Moreover, children may find it difficult to accept that their parent has a new partner, or they may have conflicting loyalties because they do not want to upset the other biological parent by having a positive relationship with the new partner (Bastaits & Mortelmans, 2016).
While a child whose parent has started a new LAT relationship might have little contact with the parent's partner, the child's life changes considerably as soon as the new partner is living in the same household with the child. Theoretical perspectives on coresidential repartnering have suggested that family transitions are stressful for parents and children (Amato, 2000;Bray & Easling, 2005;Sandefur & Mosley, 1997;Wu & Thomson, 2001). Both children and parents need to adjust to new circumstances, which can produce stress and a decline in children's well-being (Brown, 2006;Cherlin et al., 1991). For instance, the formation of a coresidential stepfamily might involve moving, which can result in considerable changes in a child's living arrangements and daily routines, and in a change of schools . After a parent has formed a household with a new partner, the new couple tends to be occupied with their own problems, which might lead to a deterioration in parenting quality, and to inconsistencies in parenting (Brown, 2006;Hetherington, 2003;Sandefur & Mosley, 1997). Additionally, children might have difficulties accepting the stepparent's authority as a parent (Brown, 2006).
As well as having negative effects, the formation of a joint household with a new partner can improve a family's living situation. Coresiding with the new partner of the parent increases the household's economic resources through, for example, the reduction in costs associated with living in a joint household (Bray & Easling, 2005;Hetherington & Elmore, 2003;Lopoo & DeLeire, 2014). On the other hand, the amount of time the resident biological parent can spend with the child does not necessarily increase, since the parent also spends time with the new partner (Bastaits & Mortelmans, 2016;Brown, 2004;Thomson et al., 2001). However, the new partner can share household responsibilities as well as spend time with the child (Koster et al., 2021;Sweeney, 2010;Thomson et al., 2001). Thus, the child may benefit because the parent has greater access to resources that enable him/her to spend more time with the child (Bjarnason et al., 2012;Hetherington, 2006). In addition, having access to more resources can reduce the parent's distress, which could in turn increase the well-being of both the parent and the child (Amato & Booth, 1997). Overall, having access to more economic resources and sharing parenting and household responsibilities with the stepparent reduces the stress levels and increases the well-being of the parent, which should in turn be beneficial for the child's well-being.

Prior research
Prior research on the effects of parental repartnering on children focused on children who were living with a (married or unmarried) stepparent, i.e., with the parent's new coresidential partner. These studies found that stepchildren tend to fare worse than children with two biological parents in the household on a wide range of educational, cognitive, emotional, and behavioral outcomes (Raley & Sweeney, 2020). While many studies have compared stepchildren to children in two-biological-parent households, our theoretical explanations speak more directly to questions of how child well-being changes after a child has experienced the repartnering of a formerly single parent. The existing studies that explicitly compared the outcomes of children living in (coresidential) stepfamilies to those living in one-parent families yielded mixed results. Some studies found that children fare better in stepfamilies than in one-parent families (Bachman et al., 2011;Hao & Xie, 2002;Langton & Berger, 2011;Magnuson & Berger, 2009;Ryan & Claessens, 2013;Wen, 2008), while others reached the opposite conclusion (Brown, 2006;Tillman, 2007), and still others found no differences between these two groups (Bachman et al., 2009;Fomby et al., 2021;Ganong & Coleman, 2017;Ram & Hou, 2003). Most of these studies used cross-sectional data from the US. In a cross-sectional analysis of the German pairfam data (the same source that we use in this paper but with a focus on anchor respondents while we use the child data), Walper, Thönnissen, and Alt (2015) found no differences in the well-being of adolescents depending on whether they were living in a stepfather family or with both biological parents. Based on the cross-sectional German AID:A-data, Heintz-Martin and Langmeyer (2019) showed that children living in a one-parent family or a blended stepfamily had a significantly higher probability of exhibiting behavioral problems than children living in a two-biological-parent family. Another study based on the AID:A-data showed that compared to children living in a nuclear family, children living in a one-parent family or a stepfamily were more likely to attend the lowest school track in Germany (Hauptschule), and were less likely to attend the highest school track (Gymnasium) (Steinbach & Knüll, 2016).
To our knowledge, no previous study has analyzed the effects on children's well-being of a parent transitioning from being single to being in a non-residential relationship using an explicitly longitudinal approach. Prior research based on cross-sectional data largely supports the hypothesis that a parents' LAT relationship has a negative effect on children. One paper studied the effect of the number of the parents' non-residential partnership transitions on child well-being (Cooper et al., 2011). The authors showed that the number of the parents' dating transitions was negatively associated with child well-being. However, sensitivity analyses indicated that these findings were likely driven by omitted variables (Cooper et al., 2011, p. 255). Using a measure for family instability that included parental transitions to both coresidential and non-residential partnerships, one study found that the number of transitions was negatively related to child well-being, and that this finding was robust even when counting only transitions to coresidential partnerships (Osborne & McLanahan, 2007). The authors concluded that coresidential and nonresidential partnerships had similar effects on child well-being. A study on the effects of maternal dating on children's sexual debut indicated that a higher number of maternal dating partners was associated with early sexual initiation among girls but not among boys (Zito & De Coster, 2016). One longitudinal study examined dating and coresidential transitions and their effects on mothers' parenting (Beck et al., 2010). The authors found that while both types of transitions increased mothers' parenting stress and harsh parenting, coresidential transitions seemed to have a stronger effect on harsh parenting than dating transitions. All the mentioned studies analyzed families in the US. Two studies of European countries did not find support for a negative effect of a parents' LAT relationship compared to single parent families. A Belgian study analyzed adolescents' well-being based on their parents' partnership trajectories (Bastaits et al., 2018), and found that the effects on adolescents' depression levels of living in a stable single-mother family and of living with a mother who had a LAT relationship were negative and similar in size (reference: two-biological-parent families). For the outcome variable of adolescents' life satisfaction, the effects differed for the two groups. However, the authors did not test whether these differences were statistically significant. For stable single-father families, no effects on child outcomes were found (Bastaits et al., 2018, p. 104). A Dutch study that analyzed the impact of the non-residential partnerships of parents on their children showed that having a non-residential relationship did not affect the frequency of the parents' care and leisure activities (Koster et al., 2021).

Hypotheses
The aim of this study is to identify the effects on children's well-being of the resident parent repartnering compared to the resident parent staying single. While most previous research on this topic focused on the effects of a parent forming a coresidential partnership (i.e., a married or an unmarried stepfamily), we are also interested in the question of whether a parent forming a LAT relationship affects children's outcomes. As we discussed above, the potential effects of a parent having a LAT partner on the lives of the parent's children are ambiguous. On the one hand, parents who are in a new relationship might be happier, and the children might therefore benefit from improved parenting. On the other hand, parents may have to divide their time and emotional resources between their children and their new LAT partner. In light of prior research results, the negative effect of parental repartnering on children seems to outweigh the positive effect. Therefore, we expect to find that the formation of a LAT relationship is associated with a reduction in child well-being (Hypothesis 1). The formation of a joint household with the parent's new partner further changes a child's life, because the prior family system is discontinued, and the role of each family member must be adapted or (re-)established. As the process of adaptation might be stressful, we expect to observe that the start of the period of coresidence with the parent's new partner has negative effects on child well-being (Hypothesis 2).

Data and analytic strategy
Our analyses are based on data from ten waves of the German Family Panel (pairfam), (release 11.0 (Brüderl et al., 2020)). A detailed description of the study can be found in Huinink et al. (2011). The main respondents (so-called anchors) were randomly selected from the German population of three cohorts (born in 1971-73, 1981-83, or 1991-93) and were interviewed yearly from 2008 to 2018, along with their parents, partners, and selected resident children in a multi-actor design. In the first wave, 12,004 persons participated. Anchor respondents provided detailed information on their relationships. Resident children between seven and 16 years were surveyed from the second wave onward, and their participation was conditional on parents' consent. In our analyses, we combined waves two to eleven of the child data and the anchor data including the anchors' relationship histories. Because a considerable share of anchor respondents is childless and because only a subset of children was surveyed, the child dataset contains information on 3,507 children who completed the questionnaire.
The unit of analysis was the child. Because our theoretical argumentation is based on parent-child dyads, children who were associated with an anchor who was not their biological parent were excluded. Given our dynamic perspective in a fixed effects regression analysis, we also excluded children who participated in the survey only once, and those who experienced the anchor's repartnering before the start of the panel study. At their first observation, each child in the sample was living with one parent only, since children living in one-parent families are the ones at risk of parental repartnering. Only eleven children experienced the transition from a two-biological-parent family to a coresidential stepfamily between two waves (i.e., we did not have a measurement of children's well-being when the child lived in a single parent household) and were thus excluded.
We examined the effects of two different transitions. To identify the effects on children of having a parent who transitioned to (a) a LAT relationship or to (b) a coresidential partnership, we use two different samples. In our analysis of sample (a), we are interested in examining the changes in children's well-being after their parent transitioned to a LAT relationship (n=490). Therefore, the sample contains all children who were living with a single parent at time t. In our analysis of sample (b), we are interested in assessing children's well-being after their parent entered a coresidential partnership (n=996). Here, we start with one-parent families and parents who have a LAT partner at time t. Pooling these two groups resembles the approach in prior research that did not have information about LAT relationships. Clearly, it would be an advantage to distinguish between children who saw the transition from a single parent family to a coresidential stepfamily and those who saw their parent's transition from a LAT to a coresidential partnership. However, for some children, the transition from a single parent family to the parent's LAT relationship and the transition to a coresidential partnership occur in the same year. Because of the small number of transitions, we decided to consider both groups as they are at risk to transition to a joint household. We focus on the parent's first repartnering the child experiences during the panel for each transition. This means that in the coresidential repartnering sample, we look at the first cohabitation with a stepparent the child experiences in the prospective data. Children who experienced the start of their anchor's relationship with a new partner and the beginning of coresidence with that stepparent in the same year were only included in the coresidential repartnering sample (14 children), and not in the LAT repartnering sample. For the LAT transition, about half of the children experience the dissolution of the repartnering in focus, whereas for the coresidential transition the dissolution of the partnership in focus happens only in about 15% of the cases. We analyzed only this first repartnering event and censored the observations after the first repartnering union dissolved.
In the first wave, the response rate of anchor respondents in pairfam was 37% (Brüderl et al., 2021, p. 11), and the panel attrition rates ranged between 23% in wave 2 and levelled off at 7% in waves 9 to 12 (Brüderl et al., 2021, p. 37). In case a child between eight and 15 years was living in the same household, the anchor person was asked for their consent to the child interview. The coverage rate was around 60% in all waves (Brüderl et al., 2021, p. 39) and the response rate of children whose respective anchor person had given consent was high with 76% (Brüderl et al., 2021, p. 32) to 96% (Brüderl et al., 2021, p. 21) in different survey waves. We discuss potential bias due to selective sample dropout in the Discussion section below.
In our analyses, we estimated individual linear fixed effects regression models in which we assessed the differences in the average well-being of children before and after they experienced a parental transition to a new LAT relationship or a coresidential partnership. Estimating fixed effects reduces the potential bias produced in conventional cross-sectional regression models (Gangl, 2010). This method allowed us to estimate the causal effects of each event on the children's well-being, as it controls for all unobserved time-constant heterogeneity (Brüderl & Ludwig, 2015). Only children between seven and 16 years participated in the child survey. The maximum number of observations one child contributed to our analyses was eight (3.45% of respondents in the coresidential repartnering sample, 1.41% of respondents in the LAT repartnering sample). Most children were observed twice (32.57% of respondents in the coresidential repartnering sample, 43.66% of respondents in the LAT repartnering sample). The number of waves in which we observe each child before and after the transition differs. In the LAT repartnering sample, most children participated in two waves before the transition (27%; maximum number of waves before transition: eight) and two waves after the transition (40%; maximum number of waves after transition: six). For the coresidential repartnering sample, most children were observed in two waves before the transition (21%; maximum number of waves before transition: eight) and four waves after the transition (22%; maximum number of waves after transition: seven).

Outcome variable: children's well-being
The dependent variable, children's well-being, was measured via two indicators: emotional symptoms and conduct problems. For each indicator, we used five items of the Strengths and Difficulties Questionnaire (SDQ (Goodman, 1997)) which is integrated in the pairfam question program (for the measurement items, see the Appendix). The children rated their own emotional and behavioral problems on a three-point scale from "not true" to "somewhat true" to "certainly true." The five emotional symptoms items included questions about self-esteem, psychosomatic symptoms, and anxiety, as well as happiness. The five items measuring conduct problems focused on anger, lying, physical aggression, and stealing. We combined the individual items to create two continuous measures, one for emotional symptoms and one for conduct problems, for all children who answered at least three of the items of the respective indicator. These measures ranged from zero to ten, with zero indicating that a child had no problems and high well-being, and ten indicating that a child had many problems and low well-being. The distribution of these variables was right-skewed. Skewed dependent variables might violate the homoscedasticity assumption in regression analyses. In order to assess whether there was inefficient estimation, we used in an alternative model specification the logarithm of our dependent variables (Kohler & Kreuter, 2012). We also estimated sensitivity models that assessed the short-term effects of each partnership transition. Here, we dropped all waves after the first wave in which repartnering was reported. We discuss the results of these additional analyses in the Results section below.

Explanatory variables
Our key explanatory variable was the repartnering of the resident parent. The measurement differed across the models. In the first analysis, we investigated the formation of a LAT relationship. For the formation of a LAT relationship, we coded a dummy variable that took a value of one as soon as the anchor reported the beginning of a LAT relationship with an individual who was not the child's parent, and a value of zero if the anchor remained single. In the second analysis, we examined the effects on children of the formation of a coresidential stepfamily. For coresidential repartnering, we coded a dummy variable that took a value of one if the anchor reported the beginning of a cohabitation with a partner who was not the child's parent. The indicator took a value of zero if the parent was single (33% of children) or was in a LAT relationship (63% of children) in wave t. The number of observations in which the formerly single parent had a LAT relationship was 76 (16% of observations in sample 1, see Table 1), and the number of observations in which the parent had started a coresidential relationship was 107 (11% of observations in sample 2, see Table 2). These relatively small numbers show that among the parents in our sample, repartnering was a rare event. The numbers differ because the number of children who experienced a transition and the time in each state differs across the types of transition.
Since individual fixed effects in our analyses control for all individual-level timeconstant heterogeneity (Brüderl & Ludwig, 2015), like the children's gender, parents' educational attainment, and region of residence, such characteristics were not included in our analyses. However, we controlled in our models for the children's time-varying confounders, i.e., characteristics that might affect both the probability of parental repartnering and children's well-being. Moreover, as has been suggested in the literature (see, e.g., Zinn et al., 2020), we controlled for characteristics that might be related to the probability of participating continuously in the survey. The variables we include in the models are children's physical health, their age, the time since their parents' separation, the number of children living in their household, their family household income, the quality of their relationship with their resident biological parent, and the depressive symptoms of their resident biological parent. The children's physical health was selfreported and was measured on a five-point Likert scale ranging from one (bad health) to five (excellent health). The children's age was measured in years. The time since the separation of the children's biological parents was measured in years based on the biopart dataset. The number of children living in the household was measured as a continuous variable based on the parents' reports of the number of children living in the main household residence in the given year. The monthly net household income was reported by the resident parents and was measured using three categories reflecting terciles of the distribution of household income in the sample.
In order to control for the resident biological parent-child relationship quality, we used two dimensions: conflict and intimacy. Both dimensions were measured via two items for which each child assessed the frequency of certain interactions with the anchor on a five-point Likert-scale. Conflict was measured with the items: "you and anchor are annoyed/angry with each other" and "you and anchor disagree and quarrel." Intimacy was assessed with the items: "you tell anchor what you are thinking" and "you share with anchor your secrets/private feelings" (Thönnissen et al., 2019). For each dimension, we took the rounded mean of both items that measured it. This produced the variables "conflict with the parent" and "intimacy with the parent," measured on a five-point scale (1 "never," 2 "rarely," 3 "sometimes,", 4 "often," and 5 "always"). The biological parent's mental health (for the anchor) was measured using depression scores from 10 items of the State-Trait-Depression Scales (STDS Form Y-2 (Spaderna et al., 2002)) with values ranging from ten to 40, with higher scores indicating stronger depressive symptoms. For both forms of repartnering, the mean values of the children's emotional and conduct problems were lower before (LAT repartnering emotional symptoms: mean=2.57; conduct problems: mean 1.58; coresidential repartnering emotional symptoms: mean=2.55; conduct problems: mean=1.59) than after the transition (LAT repartnering emotional symptoms: mean=2.71; conduct problems: mean=1.75; coresidential repartnering emotional symptoms: mean=2.90; conduct problems: mean=1.98). These findings indicate that the children's problems increased after the parent repartnered, i.e., that the family transition led to a reduction in the children's well-being. The descriptive statistics for both samples can be found in Tables 1 and 2.

Results
In our main analyses, we estimated four models: for each parental transition (LAT repartnering and coresidential repartnering), one model with the outcome variable emotional symptoms and one with the outcome variable conduct problems. The results of these multivariate fixed effects regressions are displayed in Table 3. For LAT repartnering, the results show that the parent starting a LAT partnership significantly (at a 10% significance level only) increased the children's emotional symptoms by a moderate amount (β = 0.45, p = .09), but did not seem to affect the children's conduct problems. The effect of the parent's LAT repartnering on conduct problems was very small and was statistically insignificant (β = -0.02, p = .92). The results also showed that the parent's coresidential repartnering was associated with significant increases in both the children's emotional symptoms (10% significance level) and their conduct problems (5% significance level). The coefficient for emotional symptoms was slightly larger (β = 0.51, p = .06) than the coefficient for conduct problems (β = 0.45, p = .02). These results indicate that the children's well-being was significantly reduced by the parent's coresidential repartnering. They are in line with both Hypotheses 1 and 2, which stated that a child's well-being is reduced after each of the two parental repartnering transition. With regard to our control variables, the children's physical health was found to be related only to the emotional component of the children's well-being, with better health significantly reducing emotional symptoms in both samples. Conflict with the resident biological parent was shown to be significantly and rather strongly associated with both indicators in both samples. This variable displayed the expected relationship: i.e., less conflict with the parent resulted in fewer problems, and more conflict with the parent fostered more problems. The level of intimacy with the resident biological parent was found to be significantly related to the children's conduct problems. In both samples, a higher level of intimacy in the parent-child relationship reduced the children's conduct problems. The number of children living in the same household had a moderate and significant decreasing effect on the children's emotional symptoms (10% significance level in LAT repartnering sample, 1% significance level in coresidential repartnering sample), while the years since the parents' separation had a strong positive and significant effect on the children's emotional symptoms only after the parent's coresidential repartnering. Finally, household income, the resident parent's depressive symptoms, and the child's age had small and insignificant effects on the children's well-being. Note: All models control for waves (not shown in the tables). + p < 0.10, * p < 0.05, ** p < 0.01, *** p < 0.001 Because children tend to adapt to their new family situation in the period after their parent has repartnered (Hetherington, 2003), we expected to find that the effect of repartnering was strongest immediately after the children experienced the transition from living in a one-parent family to living in a repartnered-parent family. In order to identify this immediate repartnering effect, we did additional analyses. In these short-term analyses, we censored our observations after the first wave in which the repartnering occurred. In other words, we compared the children's average level of well-being in the first year after the parent's repartnering to the children's average level of well-being before the parent's repartnering. The findings of these additional analyses were largely in line with the results presented in Table 3 (results are shown in Appendix Table 6). However, effect sizes were larger in this censored sample for the coresidential repartnering for both well-being indicators compared to the main sample (emotional symptoms: β = 0.62, p = .04, conduct problems: β = 0.52, p = .02), indicating that there occurs some kind of adjustment for the children that increases their well-being slightly as the transition lies further in the past, at least for the coresidential repartnering transition. It should, however, be noted that these analyses were based on rather small numbers of repartnering events. Therefore, we refrain from discussing them in greater detail.

Sensitivity analyses
We have performed additional analyses with alternative model specifications. We used the logarithm of the dependent variables to adjust for potential heteroskedasticity due to the skewed distribution of the outcome variables (see Appendix Table 4). Moreover, we used the children's perceived economic situation as a control for the family's economic resources, instead of the anchor's report of household income (see Appendix Table 5). These alternative analyses confirmed the coresidential repartnering patterns reported in Table 3, most consistently for the dependent variable children's conduct problems. However, in these sensitivity analyses, the effects of the parent's transition to a LAT partnership on the outcome variable emotional symptoms turned insignificant. Given that the effect sizes found in these additional models are comparable in size to those reported in our main analyses, the differences were likely related to small sample sizes. For the children's conduct problems, the findings of the sensitivity analyses were in line with those of the main model, i.e., they show that the parent's LAT repartnering had no significant and very small effects on the children's conduct problems. These findings suggest that the results of our main analyses are largely robust to different model specifications. It would have been interesting to estimate our models for different subgroups, e.g., for different age groups, parents' educational levels, and for boys or girls separately. However, the numbers of repartnered-parent families were too small to allow for meaningful analyses of such subgroups.
In our samples, 87% of the resident biological parents are the children's mothers, while only 13% are the fathers. In order to identify whether the effects of repartnering change, we estimated our models for fathers and mothers separately. The results for mother's repartnering and the results of our main analyses are largely the same (see Appendix Table 7). However, in a separate model for fathers, our results deviated from the findings of our main models with a strong and negative effect of fathers' LATrepartnering on children's emotional symptoms and conduct problems. The analyses for fathers' coresidential repartnering show no significant effects (see Appendix Table 8). However, for the father analyses the number of repartnering events and observations after the event was very low (LAT events = 6, LAT repartnered observations = 8; coresidential transition events = 7, coresidential repartnered observations = 13). Potentially heterogeneous effects of repartnering by parents' gender should be analyzed in larger samples in the future.
In our fixed effects models, we only considered a limited number of potential timevarying confounders. Other potentially relevant characteristics like the involvement of the non-resident biological parent and the child's relationship to the non-resident parent are only surveyed bi-annually in the pairfam data. Taking into consideration these additional variables, results in a very small number of repartnering events. Hence, no meaningful analyses were possible.
With regard to our control variables, we argued that we wanted to reduce confounding effects in our models. However, some of the variables that might be confounders might also change with repartnering and affect child outcomes, i.e., they are confounders and mediators at the same time. Including intermediate variables can lead to overcontrol and/ or endogenous selection biases (Grätz, 2022). In Table 9 in the Appendix, we present the results of a model that we specified without potential mediators. The effects of the parent's partnership formation in this additional analysis were very similar to the results of our main model presented in Table 3. Merely the effect of the parent's LAT relationship on a child's emotional symptoms turned insignificant using this model specification.

Discussion
The goal of this investigation was to examine the effects of repartnering by single parents on their children's well-being. We examined two stages of the repartnering process: the transition (a) to a nonresidential steady partnership (a living apart together relationship -LAT) and (b) to a coresidential partnership. While most prior research on this topic focused on the effects of the transition to a coresidential partnership on children, we were also able to analyze the effects of the transition to a nonresidential partnership. Given that transitioning to a LAT partnership affects the life of the parent, we expected to find that it also has consequences for the parent's children. In order to identify the causal effects of single parents' partnership transitions, we specified individual fixed effects models using two measures of children's well-being: emotional symptoms and conduct problems.
In line with existing research and our Hypothesis 2, we found that coresidential repartnering negatively affected both conduct problems and emotional symptoms among the children in our sample. For the transition to a LAT partnership, we observed effects on emotional symptoms only, and not on conduct problems. Thus, our Hypothesis 1 was only partly supported. The findings for the transition to a parent's LAT relationship were sensitive to the model specification but were robust especially for families with a resident mother instead of a resident father.
Our findings showed that parents' transitions to either a nonresidential partnership or a coresidential partnership had similar effects on children's emotional problems, but not on children's conduct problems. What might explain these differences? With regard to emotional problems, both partnership transitions might be emotionally demanding. A child may have to deal with feelings of rejection and emotional insecurity, and with the realization that his/her biological parents will never be a couple again. These feelings might be similar regardless of whether the parent is transitioning to a nonresidential or a coresidential partnership. With regard to conduct problems, only the transition to a coresidential partnership was found to be associated with increased problematic behavior in children. This might be because establishing a joint household may be accompanied by more changes for children, such as moving to a new neighborhood or to a new school . In addition, when a joint household is formed with the parent's new partner, the stepparent may act as a new authority figure, which can be challenging for children. They might feel guilt toward their second biological parent, or they may have problems accepting the parenting authority of the stepparent. This situation might ultimately result in children exhibiting more problematic behavior than after their resident parent had transitioned to a nonresidential partnership.
Our analyses have several limitations. The fixed effects analysis corrects for unobserved time-invariant covariates, but not for unobserved time-varying covariates. One potential confounder could be the characteristics of the non-resident biological parent, like their relationship status or their involvement in the child's life. Prior research indicates that more father-child contact is associated with positive child outcomes (especially if the father's level of involvement was high before the parental separation (Poortman, 2018)). At the same time, it has been shown that higher levels of paternal involvement decreases the probability of repartnering, especially for mothers who were neither married nor cohabiting when their child was born (Berger et al., 2018). Such potential selection into new partnerships on time-varying family characteristics might bias the results of our analyses. However, as this kind of information is collected only irregularly in pairfam, we were unable to control for the second parent's involvement with the child after the dissolution of the parents' union (and also other characteristics of the nonresidential parent).
Also, selective panel attrition might distort our findings. As has been suggested in the literature about attrition (Hoem, 1987;Zinn et al., 2020), we included a number of anchor respondents' characteristics, which might be associated with selective dropout, such as anchor's mental health and financial situation of the family, in our regression models. However, children's participation in the pairfam survey was contingent not only on anchors' participation but also on the anchor respondents' consent. Parents who have observed their child's well-being deteriorating might reject child participation, e.g., because they want to protect their child. Such a selective drop-out of children, especially if they have also experienced a parent's repartnering, could lead to a downward bias in our results.
Another drawback of our analytical strategy is related to the sequences of parents' partnership transitions. In most cases LAT repartnering precedes coresidential repartnering, i.e., the majority of children who saw the transition into their parent's coresidential relationship experienced the transition to a LAT repartnering before. Because of the small number of the event "start of coresidential partnership", we used the information of children who (1) lived in a single parent family and (2) in a household with a parent in a LAT relationship before the coresidence started. It might be that our analyses underestimate the effect in the second group because these children might already have seen a deterioration of well-being after the transition into a LAT relationship. Future studies should use larger samples to further disentangle the underlying processes. We did additionally analyze this, looking at the transition from a LAT to a coresidential stepfamily, however, the small case numbers did make such an analysis difficult.
This leads us to another limitation of our study, which is related to the sample size. Although a growing share of children experiences their parents' break-up, still most children live continuously with their two biological parents (Kleinschlömer & Krapf, 2021). This is reflected in the limited number of LAT and coresidential partnership formations. Thus, we were unable to analyze the potentially heterogeneous effects of repartnering on children's well-being, e.g., based on their socioeconomic group. The small time frame of our study in combination with the small sample size precluded also the analysis of children's adjustment to the new partnership of their resident parent over time. In order to further investigate the dynamic character of parents' partnership formation patterns and children's well-being, future data collections should include larger samples of children over a longer time period.
Furthermore, future research needs to take into account the mutual relationship of children's well-being and parents' repartnering decisions. If parents notice that their children's well-being is low, they might refrain from repartnering. In addition, the repartnering of parents of children who already had low levels of well-being might have less negative impact on these children's well-being due to a ceiling effect. In such a situation, we might underestimate the negative effect of parental repartnering. One possibility to account for such selection into repartnering would be to estimate a crosslagged panel model with fixed effects. This approach does not suffer from reverse causality bias (Leszczensky & Wolbring, 2022). For this approach, the data has to provide a sufficient number of observations before an event occurs. As this is not given in our dataset, we have to leave such an analytical approach for future studies.