Work-to-family conflict and parenting practices: Examining the role of working from home among lone and partnered working mothers

Objective: This study investigates associations between work-to-family conflict and parenting practices among lone and partnered working mothers and the role of working from home as a potential resource gain or drain for acting empathetically and supportively towards their children. Background: Emerging evidence suggests that work-to-family conflict reduces responsive parenting practices, yet prior studies have rarely examined disparities by family structure. Although working from home has recently gained in importance in the workforce, there is still little research on its implications for the relationship between work-to-family conflict and the quality of parenting practices. If working from home is not used to do supplemental work during overtime hours, it may free up mothers’ time and emotional resources. In turn, this may either buffer the harmful impact of work-to-family conflict on parenting practices or indirectly enhance the quality of parenting practices by reducing work-to-family conflict. This could be particularly beneficial for lone mothers, who experience more role and time strain. Method: Analyses were based on 1,723 working mothers and their reports on 2,820 schoolchildren drawn from a German probability sample that was collected in 2019 (i.e., before the outbreak of the COVID-19 pandemic). Using OLS regression models, we first examined whether work-to-family conflict was associated with four dimensions of verbal parenting practices (i.e., responsive and hostile communication, responsive decision-making, and school involvement at home). Second, we conducted moderation analyses to test differences by working from home (within contract hours and for supplemental work) and family structure with two-way and three-way interactions. Third, we performed mediation analyses to examine the indirect effect of working from home on each parenting dimension mediated by work-to-family conflict. Results: Higher levels of work-to-family conflict were associated with less responsive and more hostile parenting practices. The moderation analyses did not indicate a buffering effect of working from home. Instead, the mediation analyses showed that compared to mothers who worked from home within their contract hours, those who did not work from home or who did supplemental work from home tended to report less empathic parenting practices transmitted through higher levels of work-to-family conflict. Results showed no significant associations for mothers’ school involvement at home. Furthermore, no major differences emerged between lone and partnered mothers. Conclusion: Our pre-pandemic results challenge the buffering hypothesis and suggest that working from home can be either a resource gain or drain for the mother-child relationship regardless of family structure, but depending on mothers’ opportunity to work from home within the scope of contract hours .


Introduction
Work-to-family conflict has detrimental consequences for the well-being of working parents and their families. When work interferes with family responsibilities, the resulting role conflicts (Greenhaus & Beutell, 1985) may deplete parents' resources. Consequently, they can lead to serious health problems (Borgmann et al., 2019), conflicts in couple's relationships (Fellows et al., 2016), and psychosocial maladjustment among children (Dinh et al., 2017;Vahedi et al., 2019). One important but still rarely examined aspect concerning the negative ripple effects of work-to-family conflict are parenting practices, which have long-lasting consequences for children's development and well-being (e.g., Kaiser et al., 2019;Nomaguchi & Milkie, 2020). Emerging evidence in the work-family literature suggests that working parents, who experience higher levels of work-to-family conflict, tend to report parenting practices that are characterized by less warmth, higher irritability, and more hostile communication (Haines et al., 2020;Hess & Pollmann-Schult, 2020).
Several workplace-focused strategies that may ease parents' exposure to high levels of work-to-family conflict have been widely discussed, such as implementing flexible work arrangements that include flexible work schedules and working from home (Allen et al., 2013;Chung & van der Lippe, 2020;Kim et al., 2020;Perry-Jenkins & Gerstel, 2020). Fueled by the increased use of mobile devices, both at home and at work (Radesky et al., 2016), and, more recently, due to social distancing measures in response to the COVID-19 pandemic (Arntz et al., 2020), working from home has come into focus as a strategy that may allow parents to have more control over how they handle work and family demands. Consequently, parents who work from home may have more time and emotional resources to act attentively, patiently, and supportively towards their children. For this reason, working from home could have beneficial effects on parents' interactions with their children (Kim, 2020).
However, the implications of working from home for parenting practices have been rarely examined, and the role it plays in the relationship between work-to-family conflict and parenting practices is not clear yet. Theories on job stress (Demerouti et al., 2001;Demerouti et al., 2017) and work-home resources (Brummelhuis & A. B. Bakker, 2012) have provided reasonable arguments for two competing hypotheses: Working from home, if not used for supplemental work during overtime hours (Duxbury et al., 1996;Kim et al., 2020;Ojala et al., 2014), may protect and even enhance parents' resources, particularly in high-workdemand situations. Thus, working from home during contract hours may buffer (i.e., moderate) the harmful impact of work-to-family conflict on parenting practices, whereas supplemental work from home during overtime hours may amplify this link. Alternatively, because studies have found direct links between working from home and work-to-family conflict, particularly if parents work from home to perform supplemental work (Abendroth & Reimann, 2018;Kim et al., 2020), working from home may have an indirect effect on parenting practices through the mediating impact of work-to-family conflict. Compared to working from home during contract hours, doing supplemental work from home during overtime hours may increase workto-family conflict because of the additional workload and blurred work-family boundaries. This could reduce mothers' resources for supportive parenting practices.
Because lone parents have to cope with the demands of work and childcare on their own, they tend to experience higher levels of financial and parenting strain and suffer from poorer health as well (Brady & Burroway, 2012;Bull & Mittelmark, 2009;Cooper et al., 2009;Nomaguchi & Milkie, 2020;Pollmann-Schult, 2018). Work-to-family conflict may thus have an even more harmful impact on parenting practices among working lone parents compared to partnered ones. Lone parents also tend to experience more time pressure and higher levels of family-to-work conflict than partnered parents (Nieuwenhuis & Maldonado, 2018;Reimann et al., 2020) and they less frequently engage in enriching interactions with their children (Kim, 2020). Working from home during contract hours could therefore be more beneficial for lone parents by freeing up resources for warm and supportive parenting practices; by contrast, doing supplemental work from home during overtime hours may impose additional demands on lone parents. However, there is still a lack of studies on the differential impact of working from home on parenting practices by family structure.
Our study aims to fill these research gaps using large-scale German survey data collected shortly before the outbreak of the COVID-19 pandemic. We examined how work-to-family conflict was associated with supportive and hostile parent-child communication, as well as with parental school involvement at home, which have been identified as crucial aspects of parenting practices in previous research. We further aimed to test whether (a) working from home moderated the link between work-to-family conflict and parenting practices, or (b) working from home had an indirect impact on parenting practices through the mediating impact of work-to-family conflict. Because previous research suggested that working from home may have different implications depending on how it is used (Abendroth & Reimann, 2018;Kim et al., 2020;Ojala et al., 2014), our study differentiated between working from home during contract hours and supplemental work from home during overtime hours (Abendroth & Reimann, 2018;Kim et al., 2020).
Our study focused explicitly on mothers and examined differences by family structure because mothers still perform most childcare in two-parent families (Klünder & Meier-Gräwe, 2018) and because the vast majority of lone-parent families are female-headed (Bernardi et al., 2018). This is particularly true in the German context, where legislation that underpins a male breadwinner model-oriented welfare state has fostered a rather traditional division of labor within couples (Grunow et al., 2018), even during the COVID-19 pandemic, when many working parents switched to working from home (Zoch et al., 2020). The data for this study was gathered in 2019 and therefore reflects working mothers' situation before the COVID-19 pandemic and its ripple effects on families (e.g., closures of daycare and schools, lockdowns, and parents' increased use of work-from-home arrangements).

Parenting practices & work-to-family conflict
Parenting is broadly defined as what parents do to raise and support their children (Nomaguchi & Milkie, 2020) and consists of different types of parent-child interactions. Parenting can refer to the quantity of childcare-related tasks and their division between parents (Craig & Mullan, 2011), to specific parent-child activities (Kim, 2020), and to the quality of parenting practices (Belsky et al., 1984;Elam et al., 2019). In this study, we focus on parenting practices, which can be conceptualized as specific verbal or physical behaviors parents use to influence and socialize their children (Belsky et al., 1984;Darling & Steinberg, 1993). Parenting practices can be thought of as emotional and instrumental support that parents provide to their children. While emotional support refers to empathetic behaviors, instrumental support describes tangible or physical help and assistance (House, 1981). Empirical evidence suggests that responsive and hostile communication behaviors are crucial dimensions of parental emotional support (Baumrind, 1991), and parents' school involvement is a major area of instrumental support (Kohl et al., 2000). For example, supportive and childcentered communication, attentiveness and responsiveness to the child's needs, and involvement in school achievements have all been linked to higher levels of academic success and lower levels of behavioral problems among children (Amato & Fowler, 2002;Spera, 2005;Thompson, 2014). In contrast, harsh parenting practices, such as verbal aggression or physical punishments, have been linked to higher levels of child aggression and externalizing problems (Buehler, 2020;Hess & Pollmann-Schult, 2020). Overall, parenting practices have been described as one of the most influential forces that shape child development and adjustment (Buehler, 2020).
Parenting practices are further influenced by contextual factors, which are factors located outside of the individual (Baumrind, 1991). One influential contextual stressor linked to parenting practices is mothers' experiences of work-family conflict (Crouter & Bumpus, 2001;Perry-Jenkins & Gerstel, 2020). Scholars typically differentiate between two types of inter-role conflicts related to work-and family-role demands: family-to-work conflict and work-to-family conflict (Greenhaus & Beutell, 1985). Such conflicts are thought to arise because of time pressure, psychological strain, or competing behavioral role expectations from different life domains (Carlson et al., 2000). Empirical studies have indicated that family-related factors, such as childcare demands, are important sources of family-to-work conflict, whereas poor working conditions, such as in jobs with high work pressure or low social support from supervisors and colleagues, are associated with work-to-family conflict (Bull & Mittelmark, 2009;Haines et al., 2019;Hwang & Jung, 2020;Perry-Jenkins & Gerstel, 2020;Reimann et al., 2020). From a resource perspective, work-family conflicts arise due to an imbalance between demands and resources: To cope with high demands, parents deplete their resources (Demerouti et al., 2001). When parents have insufficient resources to meet demands in one domain, the resulting conflicts can spill over into the other domain through transmission processes that further drain parents' resources, increase stress, and consequently undermine their performance in the other domain (A. B. Bakker & Demerouti, 2013;Brummelhuis & A. B. Bakker, 2012;Voydanoff, 2005). Consistent with the aims of this study, we focused on spillover processes from work to family and specifically addressed the potential impact of work-to-family conflict on parenting practices.
Although few studies have investigated links between work-to-family conflict and parenting practices, there is some evidence for negative spillover processes. Studies examining spillover effects of work-to-family conflict have found a direct link between work-to-family conflict and reduced parental psychological availability for their children (Danner-Vlaardingerbroek et al., 2013;Matias et al., 2017). Such studies have also found less warm and more irritable parent-child interactions (Cooklin et al., 2015) and poorer quality parenting practices (Haines et al., 2020). In addition, some research has focused on crossover processes (A. B. Bakker et al., 2009;A. B. Bakker & Demerouti, 2013;Westman, 2001), arguing that the detrimental impact of work-to-family conflict on parent-child interactions may eventually also affect child well-being (Hess & Pollmann-Schult, 2020;Matias et al., 2017;Vahedi et al., 2019). These studies have shown that higher levels of work-to-family conflict are positively associated with mothers' use of harsher parenting practices and negatively associated with their level of attentiveness to the child. In sum, except for a study by van den Eynde and colleagues (2020), which did not find negative spillover effects of work-to-family conflict on parenting practices based on two waves of German survey data, most studies have suggested that high levels of workto-family conflict reduce parents' capacity to engage in empathetic and supportive parenting and increase their use of hostile parenting practices. We therefore expect higher levels of work-to-family conflict to be related to lower involvement in supportive parenting practices.

Working from home as a resource gain or drain for supportive parenting practices
Working from home-also referred to as telework, remote work, or flexplace-is a type of flexible work arrangement, which is an umbrella term for work options that allow workers some degree of autonomy and control over where and/or when they work (Allen et al., 2013). Although most workers in Europe and North America perform their jobs outside of the home, working from home has gained importance because of the increased use of mobile devices both at home and work (Radesky et al., 2016). More recently, it has grown in significance because many working parents switched to working from home during the height of the COVID-19 pandemic (Arntz et al., 2020).
Work-family research still has not definitely answered the question of whether working from home represents a job resource or demand for parents, that is, whether it improves or diminishes their performance in other life domains (for a discussion, see Chung & van der Lippe, 2020). Job resources can be understood as contextual resources that are located outside of the individual and refer to physical, psychological, social, or organizational job characteristics (Brummelhuis & A. B. Bakker, 2012;Demerouti et al., 2017). An important example of a job resource is autonomy, which allows individuals some discretion in their task performance and can therefore enhance motivation and help parents to manage work and family roles more flexibly (Allen et al., 2013). Resource approaches have posited that contextual resources in general and job resources, in particular, can help individuals to maintain or even enrich personal resources-that is, physical (e.g., energy), psychological (e.g., focus), intellectual (e.g., skills), affective (e.g., mood), and financial assets. This is because job resources can help individuals to achieve work goals, reduce job demands, or stimulate personal development. According to the work-home resources model, personal resources saved or gained through job resources can then be invested in family relationships-a process called work-home enrichment (Brummelhuis & A. B. Bakker, 2012).
Research studying the implications of working from home for parenting practices is relatively new (Kim, 2020), and it is still unclear what role this flexible work arrangement plays in the relationship between workto-family conflict and the quality of parenting practices. Previous studies have largely focused on the consequences of working from home and other flexible work arrangements for work-family reconciliation and parental well-being and revealed mixed findings (Allen et al., 2013;Chung & van der Lippe, 2020). Recent contributions to the field have found that working from home has different effects on work-to-family conflict and well-being depending on whether parents worked from home during or outside their contract hours (Abendroth & Reimann, 2018;Kim et al., 2020). We therefore expect the type of work-from-home arrangement to be crucial for determining whether it represents a resource gain or drain for supportive parenting practices. Based on two research traditions, which suggest either direct or moderating effects of flexible work arrangements, we propose two competing models. On the one hand, working from home may moderate the deleterious effects of work-to-family conflict on parenting. On the other hand, working from home may affect parenting indirectly through its impact on work-to-family conflict.

Working from home as a moderator in the relationship between work-to-family conflict and parenting practices
Theories on job stress have emphasized the importance of resources for how individuals cope with stressors such as work-to-family conflict (Bliese et al., 2017). An influential model is the job demands-resources model, which posits that job resources can buffer the negative impacts of high job demands on well-being and performance (A. B. Bakker & Demerouti, 2007;Demerouti et al., 2001). Empirical studies have indicated that high job control, high schedule control, and reasonable opportunities to participate in decision-making dampened the adverse effects of work-to-family conflict on well-being and health (Badawy & Schieman, 2020;Demerouti et al., 2001;Mauno et al., 2006). Research examining strategies for using flexible work arrangements has suggested that mothers seek increased schedule control in situations of high work-tofamily conflict (Waples & Brock Baskin, 2021;Young & Schieman, 2018). However, little is known about how parents may use working from home as a strategy to counteract the potentially detrimental effect of work-to-family conflict on supportive parenting practices. Some studies have provided evidence for the resource hypothesis, showing that working from home was associated with increased autonomy and control (Arntz et al., 2019;Grunau et al., 2019;Schieman & Young, 2010). In addition, a study by Kim (2020) found that mothers who worked from home reported more frequent engagement in enrichment activities with their children. Research informed by the job demands-resources model has suggested that "job resources help employees manage and deal more effectively with their job demands" and have the potential to "boost employee motivation and work engagement particularly under demanding conditions" (Demerouti et al., 2017, 269, 272). According to the work-home resources model, utilizing job resources can satisfy basic needs for autonomy and lead to feelings of self-efficacy, fulfillment, and a positive mood. This should increase individuals' energy, attention, and patience, as well as other physical or psychological resources, which can, in turn, strengthen positive family relationships (Brummelhuis & A. B. Bakker, 2012).
Taken together, working from home could buffer the spillover of work-to-family conflict to responsive and supportive parenting practices by allowing parents to maintain-and even boost-the personal resources they need to provide emotional and instrumental support to their children, even when parents face high work demands. However, whether or not working from home can actually be used as a resource that increases parents' latitude, energy, and psychological availability to engage in responsive and supportive interactions with their children may also depend on how they use this work arrangement. For example, parents could use working from home to expand work activities by working even harder and longer hours or to expand childcare activities by shifting around work and care demands (Chung & van der Lippe, 2020). Stress research has suggested that coping with high levels of work-to-family conflict owing to intensified work demands can result in intensified burnout (Haar, 2006). Studies showed that working from home during informal overtime was connected to working more intensely and neglecting home issues (Ojala et al., 2014), as well as to increased stress and lower levels of well-being (Duxbury et al., 1996;Kim et al., 2020). In contrast, working from home as part of one's job was associated with lower levels of job stress and daily fatigue and higher levels of job satisfaction .
Working from home may therefore be a beneficial job resource that enables supportive parenting practices in high-work-demand situations only if mothers can use this work option during contract hours. Working from home may thus only have the potential to protect and enhance mothers' physical, cognitive, and emotional resources to act attentively and patiently, to show their children more support and to display less hostility, under such circumstances. In contrast, in situations with already-high work demands, when mothers take work home to perform supplemental overtime work, this is likely to deplete their personal resources for supportive parenting practices even further. In line with the stress-buffering hypothesis, we therefore anticipate that working from home, if used within the scope of contract hours, will buffer the negative impact of work-to-family conflict on mothers' parenting practices, whereas working from home to do supplemental overtime work will exacerbate the negative impact of work-to-family conflict on mothers' parenting practices.

Indirect associations of working from home with parenting practices through the mediating impact of work-to-family conflict
Research informed by boundary and role theories has stressed that working from home changes how individuals manage the boundaries between work and family domains (Kossek et al., 2012). Boundaries, which can be thought of as mental fences (Zerubavel, 1991) between different social roles (Ashforth et al., 2000), become more flexible and permeable when parents work from home (Desrochers & Sargent, 2004). The greater flexibility of boundaries arises because working from home generally means fewer restrictions concerning when and where work needs to be completed. The greater permeability of boundaries arises because working from home reduces the physical boundaries between work and family spheres (Allen et al., 2014;Clark, 2000). Flexible and permeable boundaries can increase parents' latitude for organizing work and care demands more effectively by reducing the time, mental, or emotional demands associated with work, thereby reducing the level of work-to-family conflict. For example, working from home means that employees do not spend time commuting and help them reduce or reschedule interactions and focus on their work (Allen et al., 2013;Arntz et al., 2019). At the same time, work demands may be intensified and extended when boundaries become flexible and permeable. Working from home can, for instance, blur temporal and spatial boundaries between work and family spheres and increase work-family multitasking (Schieman & Young, 2010). Thus, this arrangement can also become a work demand, absorbing time and psychological resources and increasing levels of work-to-family conflict. Empirical research examining direct links between flexible work arrangements and work-to-family conflict has found consistent evidence that autonomy over working hours was associated with reduced levels of work-to-family conflict; yet, the implications of working from home as a specific type of flexible arrangement are still not fully understood (Abendroth & Reimann, 2018;Allen et al., 2013;Chung & van der Lippe, 2020;Kim et al., 2020;Perry-Jenkins & Gerstel, 2020;Schieman & Young, 2010;van der Lippe & Lippényi, 2020). Some studies have found that working from home can improve work-family balance and parental well-being (Allen et al., 2013;Kim et al., 2020). Other studies have found that working from home can also increase levels of work-to-family conflict, particularly if employees perform supplemental overtime work from home (Abendroth & Reimann, 2018;Kim et al., 2020). Conceptual research has argued that supplemental work from home expands employees' working time and workload on that specific day (Eichberger & Zacher, 2021). Empirical studies have shown that bringing work home to perform supplemental overtime work can increase time pressure and psychological distress (Duxbury et al., 1996;Ojala et al., 2014). Organizational research has found connections between supplemental work from home and team-level response expectations, suggesting that people do supplemental work at home because of work pressure and, at the same time, this intensifies work pressure (Zoonen et al., 2021).
From the perspective of the work-home resources model, this evidence suggests that supplemental work from home outside regular working hours may be part of a loss spiral (Brummelhuis & A. B. Bakker, 2012): Employees may use this arrangement as a coping strategy in response to high work pressure, which blurs boundaries, reduces family time, and depletes energy. Eventually, this process may lead to increased levels of work-to-family conflict and adversely affect parenting practices. The role of working from home for work-tofamily conflict and parenting practices may therefore depend on whether mothers work from home during or outside their contract hours. The gains in time savings, flexibility, and autonomy associated with working from home may only apply during contract hours because this arrangement would decrease work demands, reduce work-to-family conflict, and free up resources that would increase mothers' capacity for empathetic and supportive interactions with their children. In contrast, working from home for supplemental overtime work is likely to increase work-to-family conflict due to mothers' increased workload and blurred boundaries, which then reduce their resources for implementing supportive parenting practices.

The role of family structure
Due to the growing number of union dissolutions and the variety of family structure, minors are less likely to grow up with both biological parents in one household in many Western nations (Smock & Schwartz, 2020;Sobotka & Toulemon, 2008). Children are also far more likely to live with their mothers after a divorce or separation (Bernardi et al., 2018), despite trends toward increased rates of paternal post-separation involvement (Schoppe-Sullivan & Fagan, 2020). Lone mothers have become a more heterogeneous group in terms of age, education, and socioeconomic status over the last decades (Bernardi et al., 2018). Yet being a lone mother is still a strong predictor of poverty and financial strain, fragmented work histories, lower life satisfaction, and poorer health due to the exposure to chronic stressors in multiple life domains (Brady & Burroway, 2012;Bull & Mittelmark, 2009;Pollmann-Schult, 2018;Recksiedler et al., 2021). Furthermore, employed lone mothers tend to experience more time pressure and higher levels of family-to-work conflict (Kendig & Bianchi, 2008;Nieuwenhuis & Maldonado, 2018;Reimann et al., 2020). This can be attributed to the fact that lone mothers face more contraints in balancing the demands related to being responsible for earning the family income, managing work and family duties, and organizing childcare without or with only limited support of the other parent.
Prior studies have examined differences in work-to-family conflict and parenting practices by family structure, but rarely linked these issues. For instance, most studies have found similar levels of work-to-family conflict among lone and partnered mothers (Bull & Mittelmark, 2009;Minnotte, 2012;Reimann et al., 2020). Some studies also revealed no substantive differences in parenting practices between lone and partnered mothers (Dermott & Pomati, 2015;Kohl et al., 2000). Yet other studies found that lone mothers reported fewer enrichment interactions with their children and lower levels of school involvement and attributed this to their higher levels of role strain and time pressure (Kendig & Bianchi, 2008;Kim, 2020). Research has further shown that lone mothers are more likely to face greater parenting strain (Cooper et al., 2009) and that work-to-family conflict is positively associated with parenting stress among lone mothers (Hwang & Jung, 2020). To address the research gap on linkages between work-to-family conflict and parenting practices by family structure, we ask whether the direction and magnitude of these associations vary between lone and partnered mothers. This may occur because lone mothers tend to have fewer psychological, social, and economic resources than partnered mothers to cope with the demands from multiple life domains on their own (W. Bakker & Karsten, 2013;Dziak et al., 2010;Recksiedler et al., 2021). Likewise, when lone mothers have to cope with high work demands, their limited amount of resources may also hinder their capacity for supportive parenting more strongly. We therefore expect the links between work-to-family conflict and supportive parenting practices to be greater among lone compared to partnered mothers.
Furthermore, in line with the two competing hypotheses of moderation and mediation discussed above, we ask whether the relationship between working from home, work-to-family conflict, and parenting differs by family structure in one of the following ways. First, in line with the moderation hypothesis, the buffering effect of working from home during contract hours could be stronger among lone mothers. Mothers with higher family responsibilities may value working from home more because it may help them to deal with work demands more effectively (Waples & Brock Baskin, 2021). In contrast, supplemental work from home during overtime is likely to drain lone mothers' scarce resources, which could reinforce the negative link between work-to-family conflict and lone mothers' capacity to use supportive parenting practices. Second, in line with the mediation hypothesis, lone mothers stand to benefit more from reduced work demands when working from home during contract hours and to suffer more from increased work demands when doing supplemental work from home. For example, research comparing male and female workers showed that supplemental work from home was more strongly associated with higher levels of work-to-family conflict among women than men-possibly due to women's higher load of caregiving responsibilities in couple relationships . Because lone mothers have an even higher care workload compared to partnered mothers, the indirect effects of working from home on parenting through work-to-family conflict may be amplified among lone mothers.

The present study
Our study had three goals. First, we aimed to analyze how mothers' work-to-family conflict was related to the frequency of different parenting practices (namely, responsive parenting, harsh parenting, and mothers' school involvement at home). Second, we tested two different models concerning the impact of working from home on mothers' parenting practices as illustrated in Figure 1. More specifically, we examined whether (a) working from home, particularly during contract hours, may dampen the adverse impact of work-to-family conflict on supportive parenting practices, while working from home to do supplemental overtime work may amplify these links (Figure A on the left); or whether (b) working from home may have an indirect effect on parenting practices mediated by work-to-family conflict. Working from home during contract hours could reduce mothers' work-to-family conflict and thereby increase their resources to engage in supportive interactions with their children, whereas doing supplemental work from home may have the opposite effect ( Figure B on the right). Third, in all three steps, we also investigated whether these relationships differed between lone and partnered mothers.

Figure 1:
Competing conceptual models of the potential role of working from home in the relationship between work-to-family conflict and parenting practices Note: WFC = work-to-family conflict; WFH CH = working from home during contract hours; WFH OH = working from home to do supplemental work during overtime hours.
Our study was set in Germany, which operates a modernized male breadwinner welfare model (Pfau-Effinger, 2005). Taxation and social insurance regulations, coupled with a shortage of childcare opportunities particularly in the Western federal states (Kelle et al., 2017), promote rather traditional arrangements in couple relationships: Fathers usually work full-time and mothers are employed part-time (Boll & Lagemann, 2019;Grunow et al., 2018;Zoch & Hondralis, 2017). Lacking state support for maternal family-workreconciliation may further elevate lone mothers' poverty risk in Germany because these mothers may be pushed into more precarious, and often lower-paying, part-time jobs (Hübgen, 2018). Nevertheless, studies have suggested that lone mothers in Germany experience similar levels of work-to-family conflict (Reimann et al., 2020). International comparisons further showed that the average level of work-to-family conflict in Germany ranks around the OECD average (Adema et al., 2016), and working from home is still less prevalent compared to the European average. For example, only about 7% of female workers in Germany worked from home several times a month compared to about 12% across 30 European countries in 2015 (Chung & van der Lippe, 2020).

Data
We used data from the third installment of the large-scale, representative German survey Growing up in Germany, which was collected via standardized computer-assisted personal interviews in 2019 (Kuger et al., 2020;Kuger & Walper, 2021). A sample of 0 to 32 year-olds was drawn in two steps. First, municipalities across Germany were sampled with inclusion probabilities proportional to the number of inhabitants. Second, a fixed-size sample was randomly drawn from municipal population registers. The target personsor, when these were minors, their primary caretaker-were then contacted by professional interviewers to schedule an interview. Once target persons-or their primary caretakers-had agreed to participate in the study, data were collected from the target person. In addition, modularized interviews were also conducted with other members of the household (e.g., parents, siblings, or others within the target age range), provided they were willing to participate in the study as well. Participants also received modest compensation for taking part in the study. The overall response rate was about 21% (Braun et al., 2021). The survey covered a wide range of topics, such as the socioeconomic circumstances of families, the quality of relationships within families, and indicators of well-being for each family member. The full sample included 7,291 interviews with target persons aged 9 to 32 years and 12,106 interviews with 6,606 parents (59.6% female) of minors, both (A) Working from home as a moderator in the relationship between work-to-family conflict and parenting (B) Indirect association of working from home with parenting through the mediating impact of work-to-family conflict nested in 4,371 households. After correcting for the fact that target persons in larger households had a higher probability of being included and adjusting for unit nonresponse by applying a combined weight, we obtained a sample that represented the target population well with respect to age, gender, German nationality, education, and regional factors (Braun et al., 2021).
For the purpose of this study, we restricted the sample to working mothers aged 18 to 65 years (i.e., inactive, unemployed, and mothers in vocational training were excluded). We further excluded self-employed mothers because we were interested in the impact of working from home during contract hours compared to overtime hours. These exclusion criteria resulted in a subsample of 2,311 mothers (about 59% of all mothers). Moreover, information on mothers' parenting practices was collected for minors of all ages (N = 4,200). However, information on the full range of parenting dimensions considered in this study were available only for schoolchildren (N = 2,905). We therefore restricted our sample to mother-schoolchildren dyads and provide sensitivity checks of our results for younger children as well. This reduced the sample to 1,779 mothers of 2,905 children aged 5 to 17 years (47.8% female). Among those were 270 lone mothers, who were separated from and did not live together with the biological father of their children. Furthermore, information on one or more parenting outcomes were missing for 18 children (nested within 12 mothers). After excluding these observations, we still had missing information on one covariate for 66 children (nested within 44 mothers); one child had missing values on two variables. In sum, information on all indicators was available for 97.1% of the sample, and 2,820 children of 1,723 mothers were included in the analyses. Table 1 provides descriptive statistics for all study variables of the analytic sample (for a description by family structure, see Table A1 in the online appendix).

Measures
We used ten indicators to operationalize different dimensions of parenting practices. All dimensions focused on verbal parent-child interactions and referred either to emotional or instrumental aspects of parenting. All answers were given on a 6-point Likert scale ranging from 1 (always or almost always/daily) to 6 (never). Responses were reversed so that higher values represented more frequently reported behaviors on the respective parenting dimension. First, we measured responsiveness as an indicator of emotionally supportive parenting based on four items, such as "I talk to [child] about his/her experiences" and "I ask [child] for his/her opinion before I make a decision that concerns him/her" (Greenberger et al., 1994). Based on principal component factor analysis (PCFA), we divided the original scale into two subdimensions: responsive communication and responsive decision-making. Each subdimension consisted of two items, which were strongly correlated (Pearson's r = 0.71, p < 0.001 for responsive communication, and r = 0.68, p < 0.001 for responsive decision-making). For subsequent analyses, we formed two mean composite scores, which were only weakly correlated (r = 0.29, p < 0.001). Second, hostile parenting-also an indicator of emotionally supportive parenting-was assessed with two items of hostile communication toward the child, such as "If [child] is naughty or behaves inappropriately, I say nasty or hurtful things or swear at him/her" (Rhoades & O'Leary, 2007). The two items were moderately correlated (r = 0.42, p < 0.001), and a mean composite score was formed for subsequent analyses. In addition, we ran separate regression models for these two items to investigate the robustness of the results (see sensitivity analyses below). Lastly, we included mothers' school involvement at home as an important indicator of their instrumental support provided to the child (Kohl et al., 2000;Spera, 2005). These were four questions on the frequency of parent-child communication concerning homework, such as "How often do you talk with [child] about what he/she has to do for school?" Based on results of the PCFA confirming the underlying single-factor structure, and given the high internal consistency of the scale (Cronbach's alpha = 0.87), we calculated a mean composite score for subsequent analyses.
Work-to-family conflict has been measured in different ways in previous studies, for example, as a multidimensional construct, a one-dimensional multi-item global construct, or a single-item global assessment (see Min et al., 2021 for an overview). We used the following single-item indicator: "Because of my work, it is difficult for me to fulfill my family responsibilities" (1 = totally agree to 6 = totally disagree). This item generally assesses work-related conflicts with family life from the respondent perspective without considering the specific qualities of these conflicts, such as time-based, strain-based, or behavior-based aspects (Carlson et al., 2000). Comparative research evaluating associations between the different measurements of work-to-family conflict has found moderate to strong connections between the different scales and provided evidence of an underlying common latent construct of work-to-family conflict (Min et al., 2021). Thus, although this overall assessment of work-to-family conflict did not represent its multifaceted character, the indicator provided a solid and validated summary measure of the different qualities of conflict. The response scale was reversed such that higher values represented higher levels of conflict.
Working from home was based on two questions: whether employees worked from home and, if so, whether they did so (a) (mostly) during contract hours, (b) (mostly) for supplemental work, or (c) partly during contract hours and partly for supplemental work. We then created an indicator consisting of three categories: 1 = not working from home (Not WFH) applied when mothers reported that they did not use this work arrangement; 2 = working from home during contract hours (WFH CH) applied when mothers reported that they used this arrangement (mostly) for contractual working time; and 3 = working from home for supplemental work during overtime hours (WFH OH) applied when mothers reported that they used this arrangement at least partly for supplemental work. We combined the last two categories (b and c) to differentiate between working from home during contract hours and working from home during overtime hours in the best possible way. Note that overtime hours may be compensated in some form. What mattered for the purpose of our study was that overtime hours may limit mothers' capacity to engage in supportive parenting practices (for a discussion, see Eichberger & Zacher, 2021).

Analytic Approach
We conducted the empirical analyses in three main steps using Stata (v17.0).

Main associations
First, we examined the association between work-to-family conflict and the four parenting outcomes (i.e., we computed one regression model each, while controlling for working from home, family structure, and other relevant sociodemographic variables). We estimated OLS regression models using weighted data adjusted for the sample design and unit nonresponse and cluster-robust standard errors that accounted for the hierarchical structure of the data (i.e., children nested within mothers).

Moderation analyses
Second, we used moderation analyses to test the modifying impact of working from home and differences between lone and partnered mothers in the relationship between (mean-centered) work-to-family conflict and parenting practices. Specifically, we tested two-way interactions between (1) work-to-family conflict and working from home, and (2) work-to-family conflict and lone-parent status. Lastly, we also examined threeway interactions to test whether the expected moderating effect of working from home on the link between work-to-family conflict and parenting practices varied between lone and partnered mothers.

Mediation analyses
Third, we conducted path analyses (a regression-based approach without latent variables) to test whether work-to-family conflict mediated the relationship between working from home and parenting practices and whether this process differed between lone and partnered mothers. For this purpose, we specified (1) a mediation model controlling for family structure and other potential confounders, and (2) a conditional process model (Hayes, 2018) with interactions between working from home and lone-parent status. We entered the same variables into the models as those in the OLS regressions in order to keep model specifications as parallel as possible between both types of analyses. Point estimates were calculated based on weighted data. Confidence intervals of the direct, indirect, and total effects were generated using bootstrapping with 5,000 replications (in which clusters of mothers were resampled), and we reported percentile intervals (Hayes, 2018). 1 Family structure 1 = lone mother, 0 = partnered mother 0.20 0 1 Notes: N (children) = 2,820; N (mothers) = 1,723; weighted data.

Controlling for confounders
All analyses controlled for potential confounders associated with either of the parenting outcomes on the one hand, and work-to-family conflict, working from home, or family structure on the other. Although there is still little evidence for the heterogeneity of parenting practices across work and family contexts, previous studies have suggested that mothers' occupation, having a full-time job, and their commuting time may impact the time and energy they have to invest in responsive and supportive parenting practices but also their level of work-to-family conflict and/or their likelihood of working from home (Abendroth & Reimann, 2018;Chung & van der Lippe, 2020;Kim, 2020). 2 In addition, we considered the gender and age of the child, the presence of younger or older siblings, the total number of children in the household, and the use of formal childcare options-characteristics that tend to differ between partnered and lone mothers (Reimann et al., 2020) and have proved to be relevant in the study of parent-child interactions in the context of working from home (Kim, 2020). 3 To control for structural and cultural heterogeneity in parenting, we further included mothers' age, educational attainment based on the Comparative Analysis of Social Mobility in Industrial Nations index (Brauns et al., 2003), whether they or their parent(s) had migrated to Germany, and whether they lived in Eastern or Western Germany (Nauck & Lotter, 2015). Table 2 shows the results of the OLS regression models for the relationship between work-to-family conflict (WFC) and each parenting outcome. The results indicate that work-to-family conflict was significantly related to three of the four parenting dimensions. On average, a one-unit increase in work-to-family conflict was associated with a 0.05 point decrease in responsive communication, a 0.04 point decrease in responsive decision-making, and a 0.04 point increase in hostile communication (all measured on a 6-point Likert scale). In order to assess and compare the magnitude of these associations, we calculated fully standardized coefficients of work-to-family conflict. An increase of one standard deviation (SD) in work-to-family conflict corresponded to a 0.08 SD decrease in responsive communication, a 0.06 SD decrease in responsive decisionmaking, and a 0.10 SD increase in hostile communication. Thus, the effect sizes of work-to-family conflict were very small across all parenting dimensions. Work-to-family conflict was most strongly related to hostile parenting, yet the differences in the effect sizes across the parenting dimensions were quite modest. To assess extreme differences, we also calculated partially standardized coefficients by comparing differences in parenting between the lowest and highest level of work-to-family conflict. An increase from the lowest to the highest level of work-to-family conflict corresponded to a 0.26 SD decrease in responsive communication, a 0.21 SD decrease in responsive decision-making, and a 0.31 SD increase in hostile communication. Thus, large differences in work-to-family conflict were associated with moderate differences in three of the four parenting dimensions. However, only small proportions of working mothers reported such extreme levels of work-to-family conflict. Nevertheless, the direction of these relationships was in line with our first hypothesis on the link between work-to-family conflict and parenting practices, which is thus supported for these three parenting outcomes. In contrast, the association between work-to-family conflict and school involvement at home was close to zero and not significant. For this reason, we rejected this hypothesis for parental school involvement at home.

Main associations: Work-to-family conflict and mothers' parenting practices
2 For example, longer commutes to the workplace are likely to increase levels of work-to-family conflict (van der Lippe & Lippényi, 2020) and decrease time for childcare. Individuals with longer commutes may therefore also be more likely to choose to work from home (Chung & van der Lippe, 2020). 3 For example, the availability of childcare is likely to affect both the likelihood of working from home and opportunities for parentchild interactions (Kim, 2020).

Moderation analyses: The role of working from home and family structure
Building on these base models, we specified different interaction models to test whether working from home served as a moderator of the relationship between work-to-family conflict and parenting, and to probe differences in the relationship by family structure. The full models are shown in Tables A2-4 in the online appendix. We started with two-way interactions between work-to-family conflict and family structure, which revealed that the slope of work-to-family conflict did not differ between lone and partnered mothers (Table  A2). Next, we introduced two-way interactions between work-to-family conflict and working from home to the models (Table A3). Analyses revealed no differences in the relationship between work-to-family conflict and parenting outcomes by the use and type of working from home (i.e., whether it was used during contract hours or for supplemental work). Finally, we tested three-way interactions between work-to-family conflict, working from home, and family structure for each of the parenting outcomes (Table A4). Again, the moderation analyses indicated no significant group differences by family structure. All interaction effects were nonsignificant; most of them were small in magnitude and some had comparatively large confidence intervals. Additional analyses of predictive margins and average marginal effects, which we used to further inspect and contrast differences in the slopes of work-to-family conflict, did not yield any significant results. In sum, based on the results of the two-way and three-way interaction analyses, we rejected the moderation hypotheses concerning the use and type of working from home and differences in the relationship between work-to-family conflict and parenting practices by family structure for all parenting dimensions.

Sensitivity analyses
We conducted several alternative model specifications in order to test the robustness of the results. One important restriction of our analyses pertained to the age of children: We only included schoolchildren to have comparable results across the different parenting outcomes (see Method section). For younger children (starting at age 3), parents rated three of the four parenting outcomes: responsive communication, responsive decision-making, and hostile communication. The results (see Table A5 in the online appendix) remained largely unchanged in a sample including these younger children and none of the interaction terms were significant. Because the correlation between the two items for hostile communication was only moderate, we investigated the robustness of the composite score. Separate regression models for these two items showed highly consistent results and therefore confirmed the findings for the composite score (see Table A6 in the online appendix).
Another area of concern was whether the data had sufficient statistical power to correctly detect (even small) effects (i.e., to minimize the risk of falsely rejecting the hypotheses concerning the moderation effects). Specifically, our sample size might have been too small to provide enough power for three-way interactions. To answer this question, we performed R-squared tests (Cohen, 1988) to calculate the minimum detectable difference in R 2 between a reduced model without interaction terms and a full model that included the seven interaction terms for each of the parenting variables. The parameters of the power analysis were set at conventional levels, assuming a power of 0.9 and an alpha level of 0.007 (which corresponded to an alpha of 0.05 after a Bonferroni correction for multiple comparisons of the seven interaction terms). The results of this power analysis shown in Table A7 (A-D) in the online appendix indicate that the minimum detectable R 2 difference between the full and reduced models (including 26 control variables and 7 interaction terms) ranged between 0.009 for school involvement at home and 0.014 for hostile communication for a sample size of 1,723 mothers. This is a conservative estimate given that the effective sample size was considerably larger and Bonferroni is rather conservative because it assumes that the interaction terms are not correlated, which was not the case. In a more realistic setting, where the effective sample size ranged between 2,820 for school involvement at home and 2,511 for hostile communication, 4 we could have expected to correctly detect an even smaller increase in R 2 of 0.006 to 0.01. Thus, the sample size allowed us to correctly detect even very small associations with high power, and the risk of falsely concluding that there was no moderation was low.
Another reason for the greater standard error of the interaction terms could be multicollinearity, which is why we calculated variance inflation factors (vif). The mean vif was about 2.65 and no single variable reached the critical value of 10 (tolerance threshold of 0.1), which would have indicated collinearity issues (see Table A9 in the online appendix). However, two interaction terms came close to the tolerance threshold of 0.1, namely the two-way interaction between work-to-family conflict and lone mother status and the threeway interaction between work-to-family conflict, lone-mother status, and not working from home. This could be the case because the slopes of work-to-family conflict were highly similar for lone compared to partnered mothers.
In sum, the results of the sensitivity analyses substantiated the initial set of findings. This meant that we had to reject all moderation hypotheses concerning the use and type of working from home, as well as concerning differences related to family structure, for all parenting dimensions.

Mediation analyses: Associations between working from home and parenting practices mediated by work-to-family conflict
In the next step, we conducted mediation analyses to test the second model, which hypothesized that working from home may affect parenting practices indirectly by increasing or decreasing work-to-family conflict. Figure 2 shows the standardized coefficients of the direct associations between working from home, work-tofamily conflict, and parenting practices. In addition, Table 3 reports the (unstandardized) direct, indirect, and total effects of not working from home and working from home for supplemental work compared to working from home during contract hours for each parenting outcome together with the bootstrap confidence intervals. Confidence intervals (CIs) that do not include zero indicate a significant positive or negative association (highlighted in bold). Although we did not expect to find direct effects of working from home on parenting practices, by comparing the indirect with the direct and total effects, we hoped to gain additional information about the process of interest (MacKinnon et al., 2007). As hypothesized in the mediation model, the CIs for the indirect effects showed that working from home was indirectly associated with three of the four parenting indicators mediated by work-to-family conflict. More specifically, compared to working from home during contract hours (as the reference category), not working from home and working from home for supplemental work were both negatively associated with responsive communication and responsive decision-making and positively associated with hostile communication. This meant that mothers who did not work from home or who did so at least partly for supplemental work reported higher levels of work-to-family conflict than those who worked from home mostly during contract hours (see Figure 2). This, in turn, was associated with lower levels of responsive communication and decision-making and higher levels of hostile communication. In contrast, the bootstrap CIs indicated no indirect effect of working from home on school involvement at home. The CIs for the direct effects confirmed the regression results by indicating that working from home was not directly related to any of the four parenting dimensions. In sum, the results support the mediation hypothesis for responsive communication and decision-making, as well as for hostile communication, but they require its rejection for parental school involvement at home.
With regard to the size of the indirect effects, informative effect size measures have yet to be established; particularly in the case of inconsistent mediation, research has argued against using the often-reported ratios of the indirect to the total (or direct) effect (Hayes, 2018). 5 As a proxy, we calculated the partially standardized effects of working from home by dividing the point estimates of its indirect effects by the SD of each parenting variable. The size of the indirect effect of not working from home transmitted through higher levels of workto-family conflict corresponded to about 0.01 SD of responsive communication and decision-making, respectively, and to about 0.02 SD of hostile communication. The size of the indirect effect of working from home for supplemental work during overtime hours corresponded to about 0.02 SD of responsive decisionmaking and to about 0.03 SD of responsive and hostile communication, respectively. Although comparable evidence is still lacking, the overall size of these indirect effects of working from home was quite small. 5 It should be noted that the direction of the indirect effects, particularly of working from home for supplemental work, differed from those of the direct effects, which has been referred to as inconsistent mediation (MacKinnon et al., 2007). In such cases, there may be opposing processes at work, which offset each other and result in small and nonsignificant total effects. Here, this could mean that there could be another underlying process, through which working from home for supplemental work actually had a positive impact on responsive parenting and a negative impact on hostile parenting. This will be further discussed below.

Figure 2:
Associations between working from home and parenting practices mediated by work-to-family conflict Note: Standardized coefficients; standard errors (not shown) are adjusted for clustering at the level of mothers (N = 1,723); N (children) = 2,820; weighted data; * p < 0.05, ** p < 0.01, *** p < 0.001; WFC = work-to-family conflict; Not WFH = not working from home; WFH OH = working from home to do supplemental work during overtime hours; reference category: working from home mostly during contract hours (WFH CH). All models control for: family structure; mothers' occupation, employment status, commuting time, age, education, migration status, residence in Eastern Germany, no. of children; children's age, gender, younger siblings, older siblings, enrolment in formal childcare during afternoons.
In the next step, we tested whether the indirect effects of working from home on parenting practices mediated by work-to-family conflict differed between lone and partnered mothers. Because the moderation analyses reported above did not indicate any differences in the relationship between work-to-family conflict and parenting practices by family structure, we only tested whether the association between working from home and work-to-family conflict was moderated by lone-parent status. Because lone mothers face higher demands than partnered mothers with regard to managing work and care responsibilities, not working from home, as well as supplemental work from home, may both be associated with higher levels of work-to-family conflict than among partnered mothers. In turn, these higher levels of work-to-family conflict may result in less responsive and more hostile parenting practices among lone compared to partnered mothers. However, the results for this conditional process model did not show any group differences in the direct or indirect effects of working from home between lone and partnered mothers (see Table A10 for the direct, indirect, and total interaction effects, as well as bootstrap CIs). In sum, the results prompted us to reject all hypotheses related to family structure.

Sensitive analysis
Because the results of the mediation model with a multi-categorical predictor variable were sensitive to the specification of the reference category, we reran our models using Helmert coding (see, e.g., Hayes, 2018). The Helmert transformation of the three categories of working from home allowed us to test the direct and indirect effects of (a) working from home (irrespective of the type) vs. not doing so, and (b) supplemental work from home during overtime hours vs. working from home during contract hours simultaneously in the same model. Results (see Table A11 in the online appendix) showed that using work-from-home arrangements (vs. not doing so) was not indirectly related to any of the four parenting outcomes through work-to-family conflict. Yet again, compared to working from home during contract hours, doing supplemental work from home during overtime hours was indirectly related to lower levels of responsive communication and decision-making, as well as to higher levels of hostile communication. Thus, only supplemental work from home was associated with a lower frequency of supportive parenting practices through higher levels of work-to-family conflict. Again, the analyses did not reveal any indirect effects of working from home on parental school involvement at home. In addition, results did also not reveal any direct relationships between working from home and the four parenting outcomes, except for a positive direct relationship between using work-from-home arrangements (vs. not doing so) and responsive decisionmaking. Altogether, the models using Helmert coding were in line with the results presented above.

Discussion
Our study contributes to the emerging literature on links between work-to-family conflict and parenting (Cooklin et al., 2015;Hess & Pollmann-Schult, 2020;Matias et al., 2017;van den Eynde et al., 2020) and on the role of working from home as a potential resource gain or drain for supportive parenting practices (Kim, 2020;Kim et al., 2020). These issues are particularly relevant, because, while the vast majority of mothers are gainfully employed in most Western nations (del Mar Alonso-Almeida, 2014), they still shoulder a larger share of childcare-related duties than fathers (Schoppe-Sullivan & Fagan, 2020). Consequently, mothers tend to face higher levels of role strain (Perry-Jenkins & Gerstel, 2020). At the same time, working from home is gaining in importance. This is not just due to the COVID-19 pandemic (Arntz et al., 2020), although it certainly has triggered new research on the increase in working from home and its links to parental wellbeing during the pandemic (Huebener et al., 2021;Li et al., 2020). Yet the implications of this flexible work arrangement for parenting practices have still received little attention in family research.
In line with prior findings on the detrimental spillover effects of work-to-family conflict (Cooklin et al., 2015;Danner-Vlaardingerbroek et al., 2013;Haines et al., 2020;Hess & Pollmann-Schult, 2020), our results revealed that mothers' experiences of higher levels of work-to-family conflict were significantly associated with the less frequent use of responsive communication and responsive decision-making as well as more frequent use of hostile communication. These findings support our first hypothesis and suggest that, despite higher rates of maternal part-time employment in Germany compared to other countries (Kelle et al., 2017), the time pressure and role strain faced by mothers with higher levels of work-to-family conflict may spill over to the family domain. In turn, this seems to reduce mothers' capacity to apply more supportive, attentive, and child-centered parenting practices in daily interactions with their children. Although the strength of this relationship was meaningful for all three dimensions of parenting practices (standardized effect sizes for large differences in work-to-family conflict between 0.21-0.31), it was not very strong. The most substantial link was found for hostile communication. The strength of this relationship is not directly comparable to that found in previous work because this literature is still emerging and characterized by a great variety of parenting dimensions and/or measurements. Nevertheless, other studies based on German data have found either a stronger link or no direct link for harsh parenting practices (Hess & Pollmann-Schult, 2020;van den Eynde et al., 2020). In addition, there was no link between mothers' levels of work-to-family conflict and the frequency of school involvement at home. This could indicate that, regardless of the perceived level of workto-family conflict, mothers may prioritize school involvement at home because of the increased value of education and the societal emphasis on supporting academic achievement to foster children's later career prospects (Blossfeld et al., 2019).
We further analyzed the role of working from home in the relationship between work-to-family conflict and parenting practices by developing and testing two competing arguments based on the job demandsresources model (A. B. Bakker & Demerouti, 2007;Demerouti et al., 2001;Demerouti et al., 2017), the workhome resources model (Brummelhuis & A. B. Bakker, 2012), and the work-family boundary literature (Allen et al., 2014): (a) Working from home during contract working hours could dampen the deleterious impact of work-to-family conflict on supportive and harsh parenting practices as a result of resource-enrichment processes. More specifically, working from home as a contextual resource may save, or even increase, mothers' energy and emotional resources, which can help them to engage in supportive parenting practices even in high-work-demand situations. In contrast, working from home for supplemental work is likely to deplete mothers' personal resources even further, and to reinforce the detrimental impact of work-to-family conflict on their parenting practices. (b) Alternatively, because prior studies showed that having more control over working hours can reduce work-to-family conflict (Chung & van der Lippe, 2020;Perry-Jenkins & Gerstel, 2020), working from home during contract hours could also directly reduce some work demands and, thus, diminish work-to-family conflict. This, in turn, may increase opportunities for (supportive) parent-child interactions. In contrast, working from home for supplemental work may directly increase mothers' work demands and, thus, their experience of work-to-family conflict, and thereby diminish mothers' capacity for supportive parent-child interactions. The results prompted us to reject the first argument but were largely in support of the second argument. The moderation analyses revealed no differences in the relationship between work-to-family conflict and parenting practices depending on the use and type of work from home. Our mediation models, however, suggest that mothers' parenting practices were indirectly affected by whether and how they used work from home. Compared to mothers who worked from home during their contract hours, those who never worked from home or who only performed supplemental work from home tended to experience higher levels of work-to-family conflict which, in turn, were related to less frequent responsive communication and decision-making and to more frequent hostile communication.
Linking to prior studies, the results of our mediation analyses suggest that work-to-family conflict is an important mechanism for explaining how working from home can be a resource gain or drain for mothers' parenting practices. Mothers could benefit from the opportunity to work from home during their contract hours with a view to balancing work and family demands more effectively (Abendroth/Reimann 2018); this could leave more time and physical or psychological capacity for responsive and supportive parenting practices (Kim, 2020). Being able to work from home during contract hours may also increase mothers' wellbeing by reducing commute times and increasing levels of autonomy when working from home , which could, in turn, diminish parenting stress and mothers' use of harsher parenting practices (Jackson & Choi, 2018). Thus, working from home during contract hours could indeed decrease role strain and parental stress (Grunau et al., 2019;Kim et al., 2020). In contrast, mothers who perform supplemental work from home during overtime hours may experience blurred boundaries, increased time pressure, and psychological distress (Duxbury et al., 1996;Ojala et al., 2014), which then depletes their resources for empathetic parenting. This finding is also consistent with previous research on the harmful impact of nonstandard work schedules on parenting quality through the mediating impact of work-to-family conflict and strain (Haines et al., 2020). The fact that we did not find an indirect effect of working from home on school involvement at home mediated by work-to-family conflict could indicate that this type of instrumental support for the child is likely implemented as a daily routine (see also Kim, 2020) and may therefore be less dependent on mothers' work-related demands. In addition, the indirect effects of working from home through work-to-family conflict were rather small. It is therefore likely that there is at least one other relevant process (MacKinnon et al., 2007) that is not captured in our model. For instance, the level of paternal involvement or the quality of the parental coparenting relationship has likewise been shown to shape parenting practices (Matias et al., 2017).
Because of long-standing disparities in levels of financial strain, unstable employment patterns, and maternal well-being by family structure (Bull & Mittelmark, 2009;Millar & Ridge, 2013;Pollmann-Schult, 2018), we also examined differences between lone and partnered mothers. Prior research has shown that lone mothers face more time pressure, role strain, and parental stress (C. E. Cooper et al., 2009;Kendig & Bianchi, 2008;Nomaguchi & Milkie, 2020). We therefore expected the links between work-to-family conflict and parenting practices to be more pronounced among lone mothers compared to partnered ones. This was not supported by the results of the moderation analyses and suggests that work-to-family conflict is similarly detrimental to the parenting practices of lone and partnered mothers. Comparative evidence is still lacking and more research is needed to probe this finding. Furthermore, we also tested the two competing models on the implications of working from home for differences by family structure. Neither the moderation analyses nor the mediation analyses revealed any differences between lone and partnered mothers. In other words, working from home did not seem to specifically dampen or amplify the detrimental impact of workto-family conflict on parenting among lone compared to partnered mothers. Likewise, neither the use of work from home nor the type of use seemed to directly diminish or magnify the level of work-to-family conflict more strongly among lone compared to partnered mothers. Hence, working from home seems to have no differential indirect impact on mothers' parenting practices mediated by work-to-family conflict. This could suggest that not being able to work from home during contract hours generally increases mothers' role strain (Kim, 2020;Ojala et al., 2014), irrespective of mothers' partnership status. Likewise, both lone and partnered mothers seemed to be able to utilize work-from-home arrangements during contract hours as a strategy to balance work and family demands (see Hwang & Jung, 2020 for related findings on nonstandard work schedules).

Limitations and future research
Our study has several limitations. First, our analyses relied on cross-sectional data, which do not allow researchers to infer any causal claims or undertake tests of reversed causation. Our data only provided one single snapshot of mothers' parenting practices, their levels of work-to-family conflict, and their use of workfrom-home arrangements at the time of data collection. However, contextual resources and demands may initiate spirals of resource gain or drain (Brummelhuis & A. B. Bakker, 2012). High levels of time-based workto-family conflict may, for example, urge mothers to perform supplemental work at home as a coping strategy, which can further exacerbate their levels of work-to-family conflict and subsequently affect their parenting practices adversely. Future research should therefore implement study designs with more fine-grained assessments, such as daily or at least monthly diary data, to track meaningful dynamics in these patterns over time.
Second, the emphasis on more fine-grained assessments should also be extended to the measurement of parenting practices and work-to-family conflict. We considered only three dimensions of parenting practices because of data limitation issues related to the use of secondary data, but it is clear that there are several distinct aspects of the parental behaviors used in interactions with their children that were not covered by our study (Rhoades & O'Leary, 2007). In addition, our global measure of work-to-family conflict did not allow us to address the relevance of important subdimensions concerning time-based, strain-based, and behaviorbased conflicts (Carlson et al., 2000) for parenting. Studies conducting primary data collection could include full psychometric scales for these constructs to understand the manifold nuances in the relationship between work-to-family conflict and parenting practices.
Third and due to the limitations of survey data, our results may have been influenced by some degree of social desirability bias, because several key measures were based on mothers' self-reports. This could be particularly problematic with regard to the indicators for hostile communication toward the child because mothers may underreport or downplay the use of harsher parenting practices. In contrast, mothers may overestimate their use of positive and supportive parenting practices, such as on our indicators for responsive communication. Measuring the quality of parenting practices by using experimental designs or by implementing short intervals of mother-child interactions rated by trained observers could prove useful in future research to circumvent this bias.
Lastly, our models may have been underpowered to detect small interaction effects for lone mothers because of the low case numbers of lone compared to partnered mothers in our sample (about 20% of the sample). We showed that our total sample size allowed us to correctly detect even very small associations with a high degree of statistical power, but the ability to test three-way interactions including family structure could still be limited by the lack of power of the subsample of lone mothers. Although the small share of lone-parent families in our sample corresponded to the share of lone parents among German families with minors in 2019 (Bundesministerium für Familie, Senioren Frauen und Jugend, 2021), future studies on these issues could benefit from stratified data collection to recruit a larger sample of lone mothers.

Policy and practical implications
Despite the need for further research probing our results, the main finding concerning work-to-family conflict as a potential mechanism in explaining how working from home-during or outside contract hours-can help or hinder supportive mother-child interactions is particularly important for policymakers, family support services, and workplace representatives. Because the shortage of widely affordable childcare is one of the main barriers to maternal (full-time) employment in Germany (Boll & Lagemann, 2019;Zoch & Hondralis, 2017), mothers who perform supplemental work from home may simply lack sufficient childcare coverage to complete their work at their workplace. Alternatively, mothers may choose to complete supplemental work from home rather than at work in order to spend time with their children or save money for additional and often costly hours of childcare outside of their home. Thus, increasing mothers' access to work-from-home arrangements during regular hours, where possible, and fostering enriching workplace support and workfamily reconciliation policies that lower job stress and work-to-family conflict (Bull & Mittelmark, 2009) could facilitate the use of more supportive, attentive, and involved parenting practices (Cooklin et al., 2015). Family support services should be made aware of the potential problems arising from supplemental work from home as well and should assist working mothers with reaching agreements with their supervisors or employers for implementing flexible work-from-home options during contract hours. Our results further suggest that extending the access to work from home during contract hours could be equally important for lone and partnered mothers. However, because lone mothers tend to be overrepresented in more precarious and lowerpaying jobs (Hübgen, 2018;Millar & Ridge, 2013), the barriers to offering them work-from-home options may be higher. Strengthening the lone mothers' position in the workforce and their ability to access betterpaying and more qualified jobs with work-from-home options could be a fruitful area for policy intervention.

Conclusion
Our study is among the first of a still small but growing body of research that examines the detrimental impact of work-to-family conflict on parenting practices and the role of flexible work practices, such as working from home, in this relationship. Our results suggest that mother-child interactions can benefit or suffer as a result of mothers' opportunities to work from home, among both lone and partnered mothers.
However, research on whether working mothers themselves enjoy improved mental health when blending work and parenting demands at home is still scarce. This is a particularly timely issue because the demand for and use of work-from-home arrangements increased substantially in response to stay-at-home orders during the COVID-19 pandemic (Arntz et al., 2020). It is possible that in light of pandemic-related closures of schools and childcare facilities, working from home-even within contract hours-may have reinforced work-to-family conflict and its spillover on parenting practices because of the intensified time pressures and psychological demands on parents, especially mothers. Recent evidence for Germany suggests that parental well-being decreased during the pandemic, particularly among parents of young children and mothers (Huebener et al., 2021). Placing a broader focus on the consequences of flexible work routines-in combination with intensified parenting demands-for maternal well-being and health will therefore be a vital avenue for future research.