The association between paternal depression and adolescent internalising problems: A test of parenting style as a mediating pathway

Whilst there is a large evidence base demonstrating the impact of maternal depression on the development of adolescent internalising problems, less is known about the association between paternal depression and adolescent internalising problems, and the mechanisms through which risk is conferred. This study examined the association between paternal depression and adolescent internalising problems, investigating parenting style as a pathway through which this association may be mediated. Participants included 4048 families taking part in the Growing Up in Ireland child cohort study. Self-report measures of paternal depression were completed when the study child was aged 9. Adolescents assessed paternal demandingness, responsiveness and autonomy granting at the age of 13. Adolescent internalising symptoms were measured at the age of 17/18 by the primary caregiver. A parallel multiple mediator model was used to test the total and specific indirect effects of the three parenting styles, whilst controlling for covariates and other mediators in the model. A direct effect of paternal depression on adolescent internalising problems was found (B = .051, 95% CI: 0.020, 0.083). However, no support for mediation via any of the paternal parenting styles (i.e., responsiveness, demandingness, or autonomy-granting) were found. These findings build on an emerging evidence-base demonstrating a specific direct association between paternal depression and adolescent internalising problems, and suggest that interventions ought to also target fathers suffering from depression to help reduce the risk of adolescent internalising problems.


Introduction
Behavioural and psychosocial difficulties that children and adolescents face are often categorised into two broad groupings of internalising and externalising problems (Cicchetti, 1984). Internalising problems in particular, have been suggested to be characterised by an effort to control or suppress the expression of emotions, which may in part result in over internalisation of complex emotions such as anger and guilt, along with prolonged periods of low mood and anxiety (Graber et al., 2004;Zahn-Waxler et al., 2000). Adolescents are particularly prone to internalising problems (Green et al., 2004), and there is a marked increase in prevalence of disorders such as depression and anxiety in the teenage years (Kessler et al., 2007). In addition to the immediate distress these difficulties cause, adolescents who experience anxiety and depression are at increased risk of poorer physical health, family relationships, adjustment at work, and less life satisfaction in adulthood, as well as being more likely to be diagnosed with adult anxiety disorders, major depressive disorders and substance misuse problems (e.g., Essau et al., 2014;McLeod et al., 2016;Pine et al., 1998). Various risk factors have been associated with the development of internalising problems, such as genetic vulnerability, environmental stressors, temperament, socialisation experiences and gender (Zahn-Waxler et al., 2000). One specific environmental factor that has been linked to child and adolescent internalising problems is parental psychopathology, and depression in particular (Goodman & Gotlib, 1999;Kane & Garber, 2009;Lieb, 2002;McLaughlin et al., 2012;Natsuaki et al., 2014).

Paternal Depression
Children of parents with depression have been found to be at greater risk for internalising problems, as well as experiencing academic and peer difficulties, poorer physical health and increased likelihood of receiving a mental health diagnosis in adulthood (Downey & Coyne, 1990;Goodman & Gotlib, 1999;Havinga et al., 2017;Natsuaki et al., 2014;Weissman et al., 2006). Whilst claims have been made about the association with parental psychopathology, research into the association with parental depression has tended to focus on mothers only, with insufficient consideration given to the role of fathers (Connell & Goodman, 2002;Phares & Compas, 1992). Historically, this under-representation may have been a reflection of a cultural assumption that, due to being the main breadwinners and spending most of their time outside of the home, fathers have little influence on child development (Cabrera et al., 2000). With the increase in numbers of mothers working outside the home and increased father involvement over the last few decades in particular, these perceptions are being challenged (Cabrera et al., 2018).
A growing body of research over the past two decades has been redressing this imbalance and exploring the varied roles that father's play in their children's development (e.g., Lamb, 2004). This shift has been reflected in a significant increase in empirical research into the role of paternal mental health in child and adolescent development (Gentile & Fusco, 2017;Sweeney & Macbeth, 2016;Wickersham et al., 2020;Orri et al., 2019), with a recent focus on paternal depression in particular. For example, in a meta-analysis including 31 studies, Connell and Goodman (2002) found a positive association between fathers depression and children's internalising problems, albeit with a small effect size (weighted means r = .14). Kane and Garber (2004), likewise found a positive association between paternal depression and children's internalizing problems in a meta-analysis of 17 studies (n = 1157; mean effect size r = .24). These effects are broadly comparable with the effect size found in a metaanalysis of 121 studies investigating the risk of maternal depression on children's internalising problems (n = 65,619, weighted mean r = .23, Goodman et al., 2011), suggesting that the association with paternal depression may in fact be similar to that of maternal depression.
Various mechanisms explaining the ways in which paternal depression may be associated with child and adolescent development have been proposed. For example, Ramchandani and Psychogiou (2009) have proposed that impaired parenting could be one potential environmental pathway through which paternal depression confers risk from father to child. Other potential pathways include the impact of paternal depression on maternal psychological wellbeing and transmission through genetic liability (Ramchandani & Psychogiou, 2009). Whilst paternal depression could impact parenting indirectly in a practical sense through socio-economic factors such as loss of income or unemployment, or relationally by adversely affecting the couple relationship (Keller et al., 2009), it could also have a direct impact by affecting both the quality and quantity of time fathers spend with their children. This is consistent with theories such as attachment theory (Ainsworth et al., 1974), which highlights the importance of the parent-child relationship in forming the relational context in which children learn to regulate their emotions and develop a sense of personal control. Moreover, as children progress into and through adolescence, the support that they require from their parents and the nature of the parent-child relationships changes. Therefore, factors such as depression, which might interfere with a parent's ability and flexibility to provide sensitive and appropriate supervision and support, may have implications for children's emotional wellbeing.

Parenting Style
One factor that may play a mediating role between paternal depression and adolescent internalising problems is parenting style. Parenting style refers to a pattern of attitudes and ways of relating to the child across multiple situations, that shape the emotional climate of the parent-child relationship (Darling & Steinberg, 1993). The literature has taken two approaches to describing parenting style. One has taken a typological approach whereby parental approaches to regulating their children's behaviour, and being sensitive to and accepting of their children's behaviour and needs, are measured across a dimension and combined into four distinct types: authoritative, authoritarian, indulgent and neglectful (Maccoby & Martin, 1983). This approach has been critiqued for its lack of specificity, for example in distinguishing between positive forms of behavioural control and negative forms of coercive control (Smetana, 2017). Thus, current research tends to focus on an alternative approach (i.e., a dimensional approach), that investigates specific aspects of parental style such as autonomy granting and responsiveness. In terms of these parenting styles, parental responsiveness denotes warmth, acceptance, nurturance and supportiveness (Maccoby & Martin, 1983), and communicates parental responsiveness towards the adolescent, not the adolescent's given behaviour (Darling & Steinberg, 1993). Parental demandingness can be delineated as varying forms of behavioural control whereby parents set clear expectations for behaviour and monitor their children's compliance holistically. This is distinct from harsh control, where physical or verbal punishment is used, and psychological control where parents attempt to control their children's inner life (Barber, 1996). The parental style of autonomy granting can be described as parents' promotion of the child's individuality, input into decision making, and increasing of independence (Silk et al., 2003).
From an attachment perspective, the salience of these parenting styles will change throughout development. For example, in the early years when the goal of attachment is to enable the development of a sense of self and of internal working models of relationships, responsiveness and demandingness would need to be high. By middle childhood, as the social world of the child expands through school and they display an increased preference for peers (Seibert & Kerns, 2009), there is an increasing need to foster autonomy. Here the focus of the parent-child emotional relationship shifts to one of availability, thereby enabling the maturing child to improve their self-regulation skills (Kerns & Brumariu, 2016). This trajectory of increasing emotional and behavioural autonomy from parents continues into adolescence, where the parent remains an important attachment figure amongst others such as peers and romantic partners (Allen & Tan, 2016). Within this framework, healthy development occurs within the context of close and warm relationships that foster increasing levels of autonomy as the child matures through childhood into adolescence (Steinberg, 2001), whilst parent-child relationships characterised by over-control, rejection and hostility are thought to lead to problems with children's adjustment (Collins & Steinberg, 2008). Thus, in theory, paternal depression could be associated with changes in parenting style, for example by limiting father's responsiveness, warmth, and appropriate behavioural monitoring, which may be a risk factor for internalising problems in adolescence.

Paternal Depression, Parenting Style and Internalising Problems
There is growing evidence to support the proposed pathways in this model of mediation. First, as previously discussed, meta-analytic studies support concurrent associations between paternal depression and children and adolescents' internalising problems (Connell & Goodman, 2002;Kane & Garber, 2004), although longitudinal studies have yielded mixed results (e.g., Cummings et al., 2013;Lewis et al., 2017;Tyrell et al., 2019;Reeb et al., 2015). Second, the literature suggests that depression can hinder a parent's capacity to provide behavioural monitoring, appropriate discipline, and emotional encouragement. For example, parents suffering from depression have been found to show lower warmth and responsiveness and greater emotional unavailability in interactions with their children (Lovejoy et al., 2000). However, most of this research focuses on maternal, rather than paternal depression (Conger et al., 1995;Lovejoy et al., 2000;Middleton et al., 2009;Phares et al., 2005).
Despite the larger focus on mothers, a meta-analysis of 28 studies investigating paternal depression and parenting style found that depression was linked with a significant increase in negative parenting (r = .16, p < .001), which included behaviours such as hostility, poor discipline and overactive parenting (Wilson & Durbin, 2010). No longitudinal studies were included in the meta-analysis, making it difficult to draw conclusions as to the contribution that paternal depression has on parenting style over time.
Third, there is a large body of evidence demonstrating associations between parenting style and internalising problems in children and adolescents. For example, in a metaanalysis of 1015 studies, Pinquart (2016) found both small negative concurrent and longitudinal associations between parental warmth (r = −.20 and − .12, respectively), behavioural control (r = −.09 and − .06, respectively), autonomy granting (r = −. 16 and − .07, respectively) and internalizing problems. Conversely, harsh parental control (r = .16 and .12, respectively) and psychological control (r = .24 and .19, respectively) were found to be associated with increased levels of internalising problems. Another metaanalysis examining parental style and adolescent anxiety, depression, and internalising problems found similar associations (Yap & Jorm, 2015). Negative concurrent and longitudinal associations were found between parental warmth (r = − .17 and r = −.08, respectively) and adolescent internalising problems. Although no studies were found exploring the longitudinal association, concurrent associations were found between autonomy granting and adolescent anxiety (r = −.29). Aversiveness, and overinvolvement were positively associated, both concurrently and longitudinally, with internalising problems (r = .17, .17 and r = .24, .13, respectively). Although neither meta-analysis specifically investigated the differential impact of paternal vs. maternal parenting style, Pinquart (2016) reported that most of the associations did not differ according to parental gender.
Finally, a small number of studies provide support for paternal parental behaviour mediating the association between paternal depression and adolescent internalising problems (Cummings et al., 2013;Elgar et al., 2007;Keller et al., 2009). For example, Cummings et al. (2013) found that paternal depression affected adolescent internalising problems longitudinally via negative expressivity and child insecurity, however no direct associations were found for paternal depression or negative expressivity on children's internalising problems (Cummings et al., 2013). Keller et al. (2009), also found that covert father negativity in conflict, meaning communication that is characterised by worry, helplessness and shame, mediated the longitudinal association between paternal depression and children's internalising symptoms. However, both studies utilised non-representative community samples, presenting potential issues of generalisability to other populations. Using a sample from a Canadian national cohort to explore the mediating role of parenting behaviour in the association between parental depression and adolescent adjustment, Elgar et al. (2007) found that high parental rejection and low monitoring mediated the association between parental depression and internalising problems more specifically. A combined assessment of parenting behaviours was utilised in this study, so specific inferences regarding the role of paternal practices cannot be inferred. To the best of our knowledge, only two studies have specifically explored the mediating role of fathers parenting style when examining paternal depression and adolescent internalising problems (i.e., Cummings et al., 2013;Keller et al., 2009), thus there is a strong need for further studies to build upon this emerging evidence base.

Aims and Hypotheses
In summary, paternal depression has been associated with increased levels of internalising problems in children and adolescents, with some evidence suggesting that parenting style may mediate this association. However, the existing evidence base is limited and conflicting, as discussed above. Thus, this study aims to contribute to the emerging literature by examining the association between paternal depression and adolescent internalising problems, and whether parenting style mediates this association. The first research question asks whether paternal depression is associated with adolescent internalizing behaviour. The second research question asks whether there is support for mediation of this association via parenting style. Drawing on the current literature, it was hypothesised that 1) higher levels of paternal depression would be positively associated with adolescent internalizing problems, 2) parental demandingness would positively mediate the association between higher levels of paternal depression and adolescent internalising problems, and 3) parental responsiveness and autonomy granting would negatively mediate the association between paternal depression and adolescent internalising problems.

Sample and Participants
The Growing up in Ireland (GUI) child cohort is a national longitudinal cohort study examining the experiences of children and adolescents living in the Republic of Ireland that started in 2006. Children were recruited via the national primary school system, which has been previously well documented (see Murray et al., 2010). Thus far, four waves of data have been collected in the child cohort, however at the start of this study only three waves were available for use (i.e., wave one when children were aged 9 (n = 8568), wave two when they were 13 years old (n = 7, 525) and wave three when they were 17-18 years old (n = 6216)). One adult in each family self-identified as the primary caregiver for who gives the most care to the study child and knows them the best. Where relevant, partners resident in the household were designated as the secondary caregiver, regardless of biological relatedness to the study child. The vast majority of primary caregivers were mothers (n = 8465, 99%), who were biological parents (n = 8358, 99%). Of families with a secondary caregiver (n = 7, 118), the majority of these were fathers (n = 7072, 99%), who were biological parents (n = 6, 775, 96%), stepparents (n = 216, 3%) or another parent or guardian (n = 81, 1%). The first inclusion criterion in the current study was two parent families. This was due, in part, to the majority of fathers in the sample being secondary caregivers, and also to permit for maternal depression, a known risk factor for adolescent internalising problems (Pearson et al., 2013), to be adjusted for in the analysis. Relatedly, a second inclusion criterion was that the secondary caregiver was the biological father of the study child. In some cases (i.e., close to 20%), the secondary caregiver changed from wave 1 to wave 2. At wave 2, when adolescents were 13 years of age, adolescents completed separate questionnaires related to parenting styles for their mothers, fathers, and where applicable the resident partners of either the mother or father. Thus, to ensure we were capturing within person (i.e., paternal) depression and parenting style across waves 1 and 2, this inclusion criterion was necessary. The study also adjusted for marital satisfaction, as rated by the biological father at wave 1, as it has been found to impact child wellbeing (Cummings et al., 2005). As such, another inclusion criterion was having complete data on paternal reports of relationship satisfaction and adjustment. Following all inclusion criteria, complete data were available for 4048 families in the GUI, who were included in the current study. Given the reduction in sample size, we examined the characteristics of the sample with missing data, as compared with the sample included in the present analysis, which can be found in Table 1. Ethical approval for the GUI cohort was obtained from the Department of Health and Children in Ireland and written informed consent was provided by all families prior to each wave of data collection. The present study further obtained ethical approval from the University of Edinburgh, School of Health in Social Sciences Ethics Research Panel.

Measures
The data for GUI was gathered by an interviewer in the study child's home using computer assisted interviewing for the main questionnaire. Self-completed questionnaires were also used for more sensitive topics, such as the measures of parental depression and parenting styles detailed below.
Paternal Depression: At wave one, primary and secondary caregivers completed an eight item version of the Centre for Epidemiological Studies Depression Scale (CESD-8) (Melchior et al., 1993a). The CES-D is a self-report scale that is used as a screening tool for depression in the general population. With reference to their symptoms over the last week, example items including "I thought my life had been a failure" and "I had crying spells" were rated on a four-point scale, from 0 = 0-less than 1 day (rarely) up to 3 = 5-7 days (most or all of the time). Total scores can range from 0 to 24 with higher scores indicative of greater depressive symptoms. Scores were dichotomised using a previously identified cutoff of ≥7, as indicating clinically-significant depression (Melchior et al., 1993b). However, as the CES-D is a screening rather than diagnostic tool, these classifications only indicate the presence of psychological distress and do not represent a formal clinical diagnosis of depression. This short version has been found to correlate highly with the original measure 20-item version (r = .93) and has demonstrated good internal consistency in validating studies (α = .86, Melchior et al., 1993). Reliability in the current sample at wave one of the GUI study was good (α = .88 for mothers and α = .80 for fathers).
Parenting style: Parenting style was assessed at wave two with the Parenting Style Inventory II (PSI-II) (Darling & Toyokawa, 1997). The 13-year-old study child completed the measure with regard to both their primary and secondary caregivers. The measure is comprised of three subscales  (Darling & Toyokawa, 1997).
Internalising problems: Internalising problems were measured at wave three when the study child was 17/18 years old, using the emotional symptoms subscale of the parentreported Strengths and Difficulties Questionnaire (SDQ; Goodman, 1997). The SDQ is a brief screening tool widely used to assess socioemotional and behavioural problems in children and adolescents. The emotional subscale is comprised of five items assessing worries, fear, somatic complaints, clinginess, and unhappiness. Responses to statements about the adolescent are recorded on a scale ranging from 0 "not true" to 2 "certainly true", with higher scores indicating more problems. The full scale contains four additional subscales including conduct problems, hyperactivity/ inattention, peer problems and prosocial behaviour. The SDQ has exhibited adequate Cronbach's alpha (α = 0.73), moderate test-retest reliability (r = .71) and concurrent validity (r = .70) in large samples of British adolescents (Goodman, 2001). Cronbach's alpha in the GUI sample for the emotional symptoms subscale was also adequate (α = 0.73). Whilst authors of the scale suggest an upper age limit of 16 years for its use, previous work has demonstrated its validity as a measure of psychological adjustment in populations up to 19 years of age (Van Roy, Veenstra & Clench-AAS, 2008).
Covariates: Factors previously associated with parental depression and adolescent internalising problems that were included in the current study were as follows: sex, maternal depression, medical card status as a proxy for income, social class, maternal education, sibling status and marital satisfaction, all of which were measured at wave 1. Child sex was collected as male or female. Maternal depression was measured using the CES-D as detailed above, using the cut-off of ≥7, no/yes). Medical card status refers to family entitlement for assistance with medical costs. Two types of cards are available, one which entitles the holder to full coverage including GP visits, hospitalisation, and prescription medication costs, and the other entitles the holder to free GP visits only. Eligibility to receive a medical card is means tested, taking into consideration weekly income, marital status, age, number of dependents, and costs such as housing payments, childcare costs, and the cost of traveling to work. As such, medical card status was used a proxy variable for family income. The social class variable was derived from the occupation of the primary caregiver, and these were categorised into professional managers, other non-manual/ skilled manual workers, and semi-skilled/unskilled workers. Maternal education was categorised into primary/no education, secondary and third level education. Primary level/ no education is roughly equivalent to elementary or middle school education, secondary level is roughly equivalent to having graduated high school or having a technical trade/ vocational diploma, and third level is equivalent to higher education including having a college or bachelor's degree, graduate degree, or doctorate degree. Sibling status asked whether the study child had any siblings (yes/no). Marital satisfaction was based on paternal self-reports on the sevenitem version of the Dyadic Adjustment Scale (Hunsley et al., 2001).

Data Analytic Approach
Preliminary analysis included investigation of associations at the bivariate level using Pearson's correlation coefficient and Spearman's rho. Interpretation of the strength of association was small r = .10, medium r = .30, and large r = .50 (Cohen, 1988). Next, mediation analysis to explore the association between paternal depression at wave 1, parenting style as measured by the subscales of demandingness, responsiveness and autonomy granting at wave 2 and adolescent internalising problems at wave 3 was conducted using the PROCESS tool for SPSS 24 (Hayes, 2014). Using a parallel multiple mediator model (see fig. 1) enabled the investigation of specific indirect effects of each of the individual parenting dimensions, whilst controlling for the other mediators in the model. The HC 3 heteroskedasticity-consistent estimator of the regression coefficient standard errors was used (Davidson & Mackinnon, 1993). The statistical significance of the indirect effects of paternal depression via parenting style were explored using percentile bootstrapped confidence intervals (Hayes, 2018). The indirect effect of parenting style is positive if the pathways a 1-3 and b 1-3 are either positive or negative and is negative if only one of these pathways are negative.
In order to conduct the mediation analysis, categorical covariates were first converted into sets of contrasts. Medical card status was transformed into two contrasts comparing full medical card and GP only card, with no medical assistance as the baseline. For the social class covariate, the professional and managerial category was used as the baseline against which the non-manual/skilled category, and the semi-skilled/unskilled manual category were compared in a set of two contrasts. Maternal education was turned into two contrasts by comparing primary and secondary education with third level education as the baseline. The term significant is used thereafter to denote statistical significance.

Bivariate Analysis
Descriptive statistics (means and standard deviations) and bivariate correlations between paternal depression at age 9, parenting styles at age 13, adolescent internalising problems at age 17, and all covariates collected at age 9 are presented in Table 2. Small but significant positive associations were found between paternal depression and adolescent internalising problems. Conversely, small negative associations between paternal depression and paternal demandingness, responsiveness, and autonomy granting were observed, however only paternal responsiveness reached significance. All three parenting styles were negatively associated with adolescent internalising problems and were significant. Higher levels of internalising problems were associated with lower levels of maternal education, parent marital satisfaction, and social class, along with higher levels of assistance with medical costs. Child sex also demonstrated a small significant association with adolescent internalising symptoms.

Mediation Model
Results of the mediation model are presented in Fig. 2 (i.e., main results) and Table 3 (i.e., full results including all covariates), with unstandardised coefficients presented. After controlling for covariates, paternal depression was found to be directly associated with adolescent internalising problems, independent of its association with parenting style (direct effect B = .051, 95% CI: .020, .083, p = .001). With respect to specific indirect paths of the models, the results did not support paternal demandingness as significantly mediating the association between paternal depression and adolescent internalising symptoms (i.e., b = .000, 95% CI: −.001 to .001), contrary to the study hypothesis. Additionally, no support was found for the study hypotheses that paternal responsiveness or autonomy granting negatively mediated the association between paternal depression and adolescent internalising symptoms (i.e., b = .001, 95% CI: .000 to.003, and b = .000, 95% CI: .000 to.001, respectively; see Fig. 2 and Table 3). With respect to the total indirect path, after controlling for covariates, no support was found for mediation via any of the three parenting dimensions (i.e., b = .001, 95% BCa CI: .000 -.003). Bootstrapping (BCa) was based on 5000 samples.

Discussion
The present study aimed to investigate the association between paternal depression and adolescent internalising problems, and test whether parenting style mediates the association. Partial support of the study hypotheses was found, in that the presence of paternal depression when the study child was 9 years of age was found to be associated with their later adolescent internalising problems, almost a decade later. However, none of the paternal parenting styles examined were found to mediate this association, within the current modelling approach. This study makes an important contribution to the current evidence base that has traditionally tended to focus on the role of maternal mental health, by examining the specific role of paternal depression, helping to further develop our understanding of its association with adolescent internalising outcomes.
The association found in the current study between paternal depression and adolescent internalising problems is consistent with evidence from the small but growing body of existing studies that have found similar associations in younger children and adolescents (Connell  Fig. 1 Proposed Mediation Model. Note: the proposed mediation model testing whether paternal parenting style, rated by the study child at 13 years old, is a pathway through which paternal depression (when the study child is 9 years old) is associated with adolescent internalising symptoms at 17/18 years of age  & Goodman, 2002;Kane & Garber, 2004;Lewis et al., 2017), and in samples of young adults (Reeb et al., 2015). Of interest, Lewis et al. (2017) also used the GUI child cohort to investigate the association between paternal depression when the cohort child was 9 years old and internalising outcomes, however internalising outcomes were only examined up until the age of 13, whereby a larger magnitude of effect was found (i.e., r = .25). Thus, the current findings build upon this earlier work by suggesting that whilst the association with historic paternal symptoms appear to have lessened over time as compared to when the cohort child was 13 years of age, paternal depression was still associated with internalising outcomes in later adolescence, at 17/18 years of age. This is important as it suggests that fathers' mental health may be an enduring associated risk factor for adolescents' mental health. It should however be noted that the association found in the current study does not account for possible change in paternal depression across waves. For example, chronic paternal depression may contribute to a larger association or greater risk for internalising outcomes in later adolescence, whereas episodic or reduced paternal depression across time may result in smaller associations. Thus, future studies that model this process of change in levels of paternal depression over time when examining the association with adolescent internalising outcomes are needed. Nevertheless, these results contribute to the growing knowledge base that would suggest that paternal depression is indeed an associated risk factor for offspring internalising problems in adolescence.

Mediating Role of Parenting Style
Many paths of transmission have been previously suggested between parental depression and offspring mental health outcomes, particularly in the literature examining early maternal depression and children's social-emotional development.
These have included poorer quality of parent-child interactions and increased genetic risks. Arguably, the former may likely have implications regarding parenting styles. Thus, we aimed to examine whether parenting style mediated the association between paternal depression and adolescent internalising symptoms. In contrast to our hypotheses, no support for either a total indirect path of parenting style or for specific indirect paths of the individual parenting styles examined were found in this cohort. More specifically, it was expected that fathers with higher levels of depression, would have lower levels of paternal responsiveness and autonomy granting, which in turn would confer higher risks for elevated adolescent internalising symptoms. These paths were expected within the theoretical framework of attachment theory and existing evidence that positive child and adolescent outcomes are associated with family environments that are characterised by warmth, connectedness and encouragement to express individuality (Collins & Steinberg, 2008;Gray & Steinberg, 1999;Steinberg, 2001). Whilst both the paths from paternal depression to paternal responsivity and autonomy granting operated as expected in terms of directionality, surprisingly neither path reached statistical significance. That is, no differences were found between families with fathers who had symptoms of depression as compared to those without regarding paternal responsivity or autonomy granting. This finding may reflect the fact that we were unable to capture either severity or chronicity of paternal depression between families, two factors which may contribute to the theoretically expected changes in parenting styles. For example, mild or episodic depression may not have any impact, or negligible impacts, on parenting style given that parenting style reflects an attitude towards the adolescent holistically. This heterogeneity with respect to paternal depression in our study (i.e., using a single threshold cut off) may have diluted any potential associations. Future studies would do well to examine both severity and chronicity of paternal depression when examining possible mediation of parenting styles with adolescent internalising problems. Thus, caution should be taken when interpreting this result until future studies are conducted. Support was however found for a direct statistically significant negative path between paternal responsiveness and internalising problems in adolescents, suggesting that warm and responsive  .537 .051 .016 .001 Paternal Demandingness  environments provided by fathers are important for adolescent emotional wellbeing. It was further expected that paternal demandingness would positively mediate the association between paternal depression and adolescent internalising problems, however no support for this mediating path was found, which is in contrast to findings from previous studies. For example, in a study investigating parental monitoring, a particular form of behavioural control within the broader construct of parental demandingness, Elgar et al. (2007) found that parental monitoring mediated the association between parental depressive symptoms and children's internalising symptoms. However, these results relate to the style of the parenting unit, rather than paternal monitoring specifically, which may suggest that maternal demandingness was driving the association. It is also possible that in the current study, paternal demandingness was found not to operate as a pathway due to measurement error and the inability to distinguish between the positive and negative aspects of parental control. The establishment of expectations for children's behaviour and parental monitoring have been linked with positive child outcomes, whereas harsh and psychological control have been associated with negative outcomes (Pinquart, 2016;Girard et al., 2016). Future research may benefit from clearly distinguishing between positive and negative forms of paternal control when examining demandingness and investigating both forms simultaneously in order to clarify whether harsh forms of paternal control mediates the association between paternal depressive symptoms and adolescent internalising problems.

Limitations and Strengths
There are several limitations within the present study, which must be acknowledged. Firstly, whilst the study utilised multiple informants (i.e., self-and parent-reports, both maternal and paternal) to assess the key variables (i.e., parental depressive symptoms, parenting style and adolescent internalising symptoms), reducing the likelihood of shared method variance, all measures used were screening tools. Thus, these measures are less extensive as compared to clinical interviews and cannot be used to infer a clinical level of diagnosis.
Secondly, whilst the original study sample was designed to be representative of the general population in Ireland, attrition rates were high at each wave and the final sample of this study was less representative as a result. Demographically, the sample included in this study as compared to the entire cohort had higher levels of parental educational attainment and social status, along with having lower rates of family entitlement to financial support with medical fees. Moreover, all included families were two-parent households. On average, families included in this sample also exhibited lower levels of parental depression and adolescent internalising symptoms, higher levels of marital satisfaction and higher levels of paternal demandingness, responsiveness and autonomy granting. Thus, caution is warranted in the interpretation of generalisability of findings beyond the current sample, until additional research is conducted with a more socially diverse population. This would enable factors such as poverty, that are known to influence paternal depression and adolescent emotional problems, to be better accounted for.
Third, we do not examine all constructs of interest across all waves. Thus, we are not able to address potential processes of change across time within fathers. Instead, our results provide a comparison between families of fathers with and without depression at wave 1, differences in their parenting style at wave 2, and its association with adolescent internalising problems at wave 3. Future studies are needed to build upon the current work by capturing how changes in paternal depression across time may impact upon parenting style and whether a potential change in parenting style resulting from the depression acts as a mediating pathway between paternal depression and adolescent internalising problems.
Finally, whilst a number of key variables were controlled for in the study, it is possible that other factors not measured or controlled for might be responsible for the associations between paternal depression and adolescent internalising symptoms. These might include factors such as child temperament and personality (Goodyer et al., 1993;Kelvin et al., 1996;Masi et al., 2003), physical health problems, neurodevelopmental factors, and genetic liability (Gordon & Hen, 2004). Future research in this area might consider exploring ways to examine and account for these complex interactions between parent-child and the context in which those relationships unfold.
Despite these limitations, this study has a number of strengths. Previous research has been characterised by samples in which fathers are under-represented and have tended to focus on outcomes in younger children (Connell & Goodman, 2002;Thomas & Forehand, 1991). The large sample of fathers in this study and the extension of the age range to older adolescents enables this study to make a valuable contribution to the growing research examining the impact of paternal depression independent of maternal depression. Second, the data on paternal and child outcomes, as well as paternal parenting style were all provided by different informants, thus improving the reliability of these findings by limiting the impact of informant effects on the findings. Third, the longitudinal nature of the cohort study allowed for examining the association across almost a decade, where much of the previous research has examined the association concurrently or over a shorter time period.

Conclusions
The direct path of association between paternal depressive symptoms when children were nine years of age and adolescent internalising problems at 17/18 years of age are small, with an increase of 1 SD in paternal depressive symptoms leading to a 0.051 increase in adolescent internalising outcomes. Despite mediation of paternal parenting style not being found, the support found for paternal depression and paternal responsiveness as directly associated with adolescent internalising symptoms has important implications for moving research in this area forward. Our results suggests that paternal mental health and paternal responsiveness are risk and protective factors associated with adolescent internalising problems that ought not to be overlooked. Future research would do well to examine within person mediation models that capture changes in both paternal depression and paternal responsiveness across time, to better assess their potential impact on internalising problems. If support for paternal responsiveness as mediator of the association were found, this may suggest that interventions treating paternal depression should not only seek to target depressive symptoms in general, but also consider inclusion of resources that aim to support a father's development and maintenance of a warm and responsive parenting style with their children. Current evidence suggests that treatment of maternal depression can lead to improvements in children's outcomes (Gunlicks & Weissman, 2008). However, research is needed to test whether this would also be effective with fathers and to explore targeted interventions nurturing paternal responsiveness. Paternal depression and the corresponding association with parenting style are small pieces of a complex puzzle and further research is needed to understand how risk of mental health difficulties are transmitted from parent to child, what interventions might be best suited to help reduce this risk, and relatedly what mechanisms may be good targets for the development of effective interventions.

Data Availability
The data that support the findings of this study are available from the Irish Social Science Data Achieve (see for further information; https:// www. ucd. ie/ issda/ data/ guich ild/) but restrictions apply to the availability of these data, which were used under licence for the current study, and so are not publicly available. Data are however available from the authors upon reasonable request and with permission of Irish Social Science Data Achieve.

Conflicts of Interest/Competing Interests
The authors have no relevant financial or non-financial interests to disclose. The authors have no conflicts of interest to declare that are relevant to the content of this article. All authors certify that they have no affiliations with or involve-ment in any organization or entity with any financial interest or nonfinancial interest in the subject matter or materials discussed in this manuscript. The authors have no financial or proprietary interests in any material discussed in this article.
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