Predictors of Fathers’ Participation in a Longitudinal Psychological Research Study on Child and Adolescent Psychopathology

When compared with mothers, fathers continue to be considerably underrepresented in developmental research on child and adolescent psychopathology. The present study examined the factors contributing to fathers’ participation in such studies in which both mothers and fathers were asked to participate. The sample consisted of 477 families which were examined four times over the course of ten years (Pre to Follow-up after ten years [FU10]). The average age of the children at Pre was 4 years, and that of the adolescents ten years later was 14 years (FU10). On average, 70.4% of fathers participated in the assessments. The average transition probability for participation over four assessment points was 93.1%. Fathers from two-parent families participated significantly more often than fathers from single-parent families. Household income, a good father-adolescent relationship, and joint custody, if applicable, were related to paternal participation. For fathers from two-parent families, participation at previous assessment points was the decisive predictor. For fathers from single-parent families, the relationship between the adolescent and the father was the decisive predictor. Fathers who had participated in previous assessments remained involved in the study over the long run. Therefore, the primary goal should be to encourage as many fathers as possible to participate when starting clinical empirical studies. Monetary incentives could be used to recruit families with low household incomes. This longitudinal study examined the frequency of fathers’ participation and factors leading to lower father participation. 70.4% of fathers participated. Fathers from two-parent families participated significantly more often than fathers from single-parent families. For fathers from two-parent families, participation at previous assessment points was the decisive predictor for paternal participation. For fathers from single-parent families, the relationship between the adolescent and the father was the decisive predictor. The primary goal should be to encourage as many fathers as possible to participate in empirical studies at an early stage (e.g., by offering monetary incentives). This longitudinal study examined the frequency of fathers’ participation and factors leading to lower father participation. 70.4% of fathers participated. Fathers from two-parent families participated significantly more often than fathers from single-parent families. For fathers from two-parent families, participation at previous assessment points was the decisive predictor for paternal participation. For fathers from single-parent families, the relationship between the adolescent and the father was the decisive predictor. The primary goal should be to encourage as many fathers as possible to participate in empirical studies at an early stage (e.g., by offering monetary incentives).

• This longitudinal study examined the frequency of fathers' participation and factors leading to lower father participation. 70.4% of fathers participated.
• Fathers from two-parent families participated significantly more often than fathers from single-parent families.
• For fathers from two-parent families, participation at previous assessment points was the decisive predictor for paternal participation.
• For fathers from single-parent families, the relationship between the adolescent and the father was the decisive predictor.

•
The primary goal should be to encourage as many fathers as possible to participate in empirical studies at an early stage (e.g., by offering monetary incentives).
This study addresses the recruitment and participation of fathers in a ten-year longitudinal study. The purpose of this study is to identify the characteristics that led to increased or decreased paternal participation.
Although research of fathers has experienced significant growth over the past 20 years (Cabrera & Tamis-LeMonda, 2013;Schoppe-Sullivan & Fagan, 2020), and there are now a variety of studies examining the role of fathers in different contexts (Ahnert & Schoppe-Sullivan, 2020;Cabrera, & Tamis-LeMonda, 2013;Cowan & Cowan, 2019;Lamb, 2010), it is still important to note that fathers are underrepresented in longitudinal psychological research compared to mothers. It is still seen as a challenge to recruit fathers and to maintain their participation, especially in long-term studies. Even when explicitly asked to participate, many fathers tend to refuse or drop out during the course of a study. This is especially the case for developmental psychopathology research involving children, adolescents, and their families (Parent et al., 2017).
To investigate the question whether researchers ignore fathers, Phares and Compas (1992) conducted a comprehensive literature review spanning the period from 1984 to 1991. The authors examined eight prominent journals of clinical and developmental psychology. Phares et al. (2005) conducted a subsequent review of studies in the same eight journals from 1992 to 2004. The results were comparable: Only 1% of the 577 studies reviewed from 1984 to 1991 included fathers only (2% in 1992 to 2004), while 24% (28%) of the studies included mothers as well as fathers and analyzed them separately. Parent et al. (2017) replicated the Phares-studies covering a timeframe from 2005 to 2015. During this period, 1048 studies were published: 1% included fathers only, while 24% involved mothers as well as fathers and analyzed them separately. Chi-square analyses showed that there were no significant changes from 1984 to 2015 in fathers' participation in child psychopathology research.
An important differentiation should be made between 1. fathers' participation in family-based interventions in clinical practice (e.g., parenting trainings), where a large number of studies and reviews are available (Cowan & Cowan, 2014;Fagan & Pearson, 2021;Lechowicz et al. 2019;McKee et al. 2021;Panter-Brick et al., 2014), and 2. fathers' participation in empirical studies that do not focus specifically on fathers, such as studies evaluating prevention and treatment interventions or studies with developmental psychopathology research questions (Costigan & Cox, 2001;Edwards, 2012;Mathiesen et al., 2018). Fathers are underrepresented in both clinical practice and empirical studies. This study is exclusively about empirical studies, although the reasons and barriers for non-participation in empirical studies may be similar to those for nonparticipation in family-based interventions.
An inspection of a large number of studies with developmental psychopathology issues has demonstrated that the proportion of fathers analyzed in such studies is smaller compared to mothers, and the number of fathers examined, even when they were explicitly asked to participate, was also small. To a large extent, findings were based on the assessment of mothers. Moreover, there were only a few studies, especially in German-speaking countries, that have collected data from mothers and fathers simultaneously (Laucht, 2003). To our knowledge, there is no review that has provided detailed figures on this issue. This study explored factors that contribute to this discrepancy in participation. If such factors could be identified, they could be considered in future studies and efforts could be made to increase fathers' participation rates.

The Need to Include the Fathers' Perspective
Previous findings from paternal research suggest that including the father's perspective can contribute significantly to a better understanding of the onset and course of child's psychopathology. Fathers seem to interact with their children differently. They perceive them differently, and their relationships with their children differ from the relationships children have with their mothers (Cabrera & Tamis-LeMonda, 2013;Lamb, 2010;Schoppe-Sullivan & Fagan, 2020).
Mother-child relationships are considered to be supportive "attachment relationships", because mothers show more nurturing behavior, and they seem to talk to their children more often about emotional and intimate topics. In contrast, fathers and their children are said to have "activation relationships". They challenge their children to regulate their emotions autonomously by offering them less explicit structures (Van Lissa et al. (2019)). Children and adolescents describe their relationships with their mothers as more loving, closer, and less distant than their relationships with their fathers (Huber & Walter, 2015). However, at the same time, the adolescents also report that conflicts are more often carried out with their mothers than with their fathers (Branje, 2018;Huber & Walter, 2015;Laursen et al., 1998). Furthermore, mothers seem to be more overprotective compared to fathers (Titze & Lehmkuhl, 2010).
Other paternal characteristics that demonstrate the need to include the father's perspective are gender ideology and sex role attitudes. Several studies have demonstrated an impact of these factors on fathers' involvement in their children's upbringing (Parke & Cookston, 2019). For example, Bonney, Kelley, and Levant (1999) found that fathers' gender role ideology and attitudes about the fathers' role appear to be important for fathers' involvement in child care. In a cross-sectional study with a sample of 2,233 children aged 6 to 12 years, Hofferth et al. (2013) concluded that positive attitudes toward fatherhood have a very strong influence on fathers' involvement in child care.
Parke and Cookston (2019) proposed a comprehensive model of paternal involvement that lists a variety of predictors of fathers' involvement. They distinguish between biological (hormonal, neurological, temperament) and social (individual, co-parental, contextual) characteristics as well as specific characteristics of the father (e.g., self-identity, mental and physical health) and the child (e.g., cognitive, emotional, and social development). Furthermore, they identify three mechanisms responsible for paternal engagement: cognitive and emotional processes, and attention regulation. Parke and Cookston (2019) emphasize that first, these characteristics interact; second, paternal involvement is crucially shaped by culture (ethnicity); and third, it is subject to historical change. Since our study examined fathers' participation in empirical studies, the question arises to what extent the model can be applied to our research question or whether participation in empirical studies is an expression of paternal involvement. However, in the absence of empirical studies, caution is warranted here.
Particularly important for the need to include the father's perspective are studies that examine possible differences in the way mothers and fathers perceive the development and course of their child's mental health problems. For example, Felnhofer et al. (2020) asked 42 parents about the suspected causes of their child's mental health problems. They then compared the mothers' and fathers' assessments. The children suffered from a "neurodevelopmental disorder" or a "psychosomatic disorder." The authors concluded that fathers assumed more external causes (medical and environmental stressors) for their child's condition in psychosomatic disorders than mothers. As a result, fathers were more likely to view the causes as uncontrollable, which led them to not take full responsibility for the child's condition and its treatment. Grebe, Mire, Kim, and Keller-Margulis (2022) compared fathers' and mothers' views of their child's autism spectrum disorder. The sample consisted of 27 coparents (biological parents of the same child). Results showed significant differences between mothers and fathers: mothers had significantly higher self-reported stress scores in the difficult child domain, but also higher positive coping scores and better social support. The authors recommend that treatment interventions should be tailored to the individual needs of mothers and fathers.
The state of research on the transmission of mental health problems also points to the importance of the fathers' perspective. It is important to include fathers in studies because of their non-negligible contribution to offspring development. Psychological distress in fathers also negatively affects their offspring independently of maternal pathology (Kane & Garber, 2009). In a meta-analysis with 174 included studies, Connell and Goodman (2002) found that maternal psychopathology was more strongly associated with internalizing child mental health problems than paternal psychopathology. This difference was particularly evident in younger children. No differences were found between maternal and paternal influence on externalizing problems in children. Some more recent studies also suggest that maternal symptoms are more strongly related to child mental health problems overall than paternal symptoms (Flouri, Sarmadi & Francesconi, 2019;Narayanan & Naerde, 2016;Tyrell, Yates, Reynolds, Fabricius & Braver, 2019). However, this is often not the case for children's externalizing behavior problems (Ramchandani & Psychogiou, 2009;Roetman et al., 2019). In contrast, other studies found no differences (Amrock & Weitzman, 2014;Lewis et al. 2017).

Agreement Between Maternal and Paternal Reports
When data from mothers and fathers are available, the findings are often inconsistent. Duhig et al. (2000) reported in their meta-analysis of 60 studies a mean correlation of r = 0.61 for the maternal and paternal correspondence for child behavior problems. Van der Valk et al. (2001) examined a sample of 3501 Dutch three-year-old twin pairs whose parents completed the Child Behavior Checklist (CBCL; Achenbach & Rescorla, 2001) separately. The authors analyzed the data by using two models. The "rater bias model" assumed that both parents were assessing exactly the same behaviors in their child. This indicated that only the assessment of one parent might be necessary to fully assess the child's psychopathology. In contrast, the "psychometric model" assumed that each parent also assessed a unique aspect of the child's behavior. The "psychometric model" provided a significantly better fit to the data from the internalizing and externalizing CBCL scales than the "rater bias model". Based on these results, it can be concluded that each parent provided unique information from their own perspective in addition to the shared views.

Reasons for the Low Participation of Fathers in Empiric Research Studies
Several reasons for the low participation of fathers are discussed in the literature. First, it is important to emphasize that the paternal participation rate is directly related to the recruitment strategy and the recruitment efforts. Unless targeted efforts are made to ensure that fathers are recruited, paternal participation will remain low (Sherr et al., 2006).
Second, fathers are often less willing to participate in research projects compared to mothers. In case of parental separation, in most cases, the children stay with the biological mother. If this happens, the fathers are often no longer interested in participating further in the research project (O 'Connell & Goodman, 2002).
Third, sociocultural norms represent another barrier. Mothers are considered to have greater responsibility for child development, which is the reason why the research interest in this area is focused on the mothers' perspective (Cabrera et al., 2000).
Fourth, another common reason for the low participation rate of fathers is that researchers often are not concerned about the perspective from which the information about the child is given. From an economic point of view, it is usually too expensive to interview both parents. Therefore, in many studies, the parents themselves can decide who will be interviewed or who will fill out the questionnaires (Parent et al., 2017). Typically, this is the mother. A large German cohort study about the health of children and adolescents, such as the KiGGS baseline survey from 2003 to 2006 (N = 17,641), speaks only of parents who were interviewed. The study does not report in detail how many fathers and mothers participated (Ravens-Sieberer et al., 2008).
In the past, this approach often led to the conclusion that mothers were primarily responsible for the development of mental health problems in their children ("blame the mother"). This assumption was frequently criticized (Caplan, 1989;Phares, 1992). Systematic bias also occurred when the characteristics of the father and the child were not collected directly but indirectly by interviewing the mother. Valid assessments require different perspectives due to the different points of view (Laucht, 2003).

Characteristics for Paternal Participation
The contact with the father plays a significant role regarding paternal participation. Single mothers who have little or no contact with the father and who have sole custody may have trouble encouraging the father to participate in a study. Separated fathers who have contact with their children may also take less responsibility for their upbringing. Furthermore, those fathers are rarely involved in the daily care and provision of their shared children. For this reason, they cannot make statements about these aspects in the research studies (Bjarnason & Amarsson, 2011;Tazi-Preve et al., 2008).
Furthermore, it can be assumed that sociodemographic characteristics of the parents, such as the socioeconomic status, play a significant role for fathers' participation. Families with a lower social status as well as families with a migration background are less likely to participate in studies. This is also likely to be true for fathers. The higher the level of education and income of the family, the more fathers are involved in the upbringing and the care of their children. Additionally, parental coparenting is also higher in these families (Frantz et al. 2015;Teubert & Pinquart 2010). Fathers from these families are more likely to participate. Costigan and Cox (2001) analyzed 661 parents from two-parent families. In their study, mothers and fathers were both asked to participate. Two-thirds of the fathers (64.6%) participated. Characteristics of participating and nonparticipating fathers, that were reported by the mothers, were compared. Among participating fathers, there was an underrepresention of fathers with less education, later-born children, distressed marriages, partners with more traditional parenting beliefs, families with unplanned children, and ethnic minority families. However, no differences were found in child's gender, family income, mothers' psychosocial functioning, either parent's work experiences or child-care arrangements.
Willingness to participate appears to be greater among fathers whose partnership is better and whose coparenting behavior is more coordinated. When parents make decisions together and share concerns about issues affecting their child, the father is also more likely to be informed about such a study. Successful cooperation between parents, which also includes mutual support, is important in order to agree on tasks and to handle them together. If both parents are equally involved in raising the child, it is likely that both will also participate in a research study. The quality of the partnership has a particularly positive effect on the parents' cooperation. Both factors in turn lead to positive parenting behavior (Barnett et al. 2011;Bronte-Tinkew et al. 2010;Teubert & Pinquart 2010).
In addition, the presence of children's mental health problems is likely to influence fathers' participation rates. We are not aware of any studies on this influential factor. In general, mothers seem to care for their mentally ill child more often. This is supported by the higher participation rates of mothers in accompanying child and adolescent psychotherapy (Heinz, 2001) and parenting counseling (Lohmeier, 2004). In another study, Flouri and Buchanan (2003) found for children at age 7 that fathers' involvement with their children was negatively related to child behavior problems. In another study, Grych and Clark (1999) found that when children have a difficult temperament, fathers care less about their children. In this context, it can be assumed that fathers with a child with mental health problems are less likely to participate in parenting. There may also be a possible link to participation in empirical studies.
Last but not least, the participation of fathers might depend on whether parents are only asked for information or whether they are offered some kind of service as part of the study. The current study brings with it the unique feature that parents were offered participation in the Positive Parenting Program (Triple P; Sanders et al., 2014). This aspect could also have influenced later participation in the survey. By participating in the Triple P, the parents, and thus the fathers, could on the one hand be motivated to continue participating in the research project, but on the other hand they could also feel obliged to do so.

Aims and Hypotheses
Mothers' and fathers' perspectives are essential in developmental psychopathology studies to avoid biased and onesided results and conclusions. Therefore, it is necessary that both parents are included in the studies. Since fathers are rarely recruited, the question arises as to what factors are responsible for this circumstance and what opportunities exist to encourage fathers to become more involved. The basic assumption is that fathers from at-risk families, who are less involved in raising and caring for their children, are less likely to participate in empirical research studies.
First, the participation rates of fathers were examined descriptively at the four assessment points (Pre [children aged 3 to 6 years], Follow-ups after 1 year [FU1], after 2 years [FU2], and after 10 years [FU10]). Second, the transition probabilities of participation between the different assessment points were calculated.
Several hypotheses were tested. When selecting predictors, we were driven by the limited literature that exists on fathers' participation in empirical studies (see the chapter "Characteristics for Paternal Participation"). Second, the selection of variables was limited by the surveys that were conducted. Linear relationships were assumed in the formulation of the hypotheses and the choice of statistical procedures.
Hypothesis 1: The participation rate of fathers from twoparent families should be significantly higher than the participation rate of fathers from single-parent families (at Pre and at FU10).
Hypothesis 2a: In early childhood (at Pre), the participation of fathers from two-parent families should be significantly predicted by parents' social characteristics (mother's school graduation, household income), children's mental health problems, and parents' parenting style (predictors assessed at pre).
Hypothesis 2b: In early childhood (at Pre), the participation of fathers from single-parent families should be significantly predicted by parents' social characteristics (mother's school graduation, household income), children's mental health problems, and parents' parenting style (predictors assessed at pre).

Hypothesis 3a:
In adolescence (at FU10), the participation of fathers from two-parent families should be significantly predicted by parents' social characteristics (mother's school graduation, household income), adolescents' mental health problems, adolescents' relationships with their fathers, parents' parenting style, parental coparenting, parental partnership quality (predictors assessed at FU10), the participation in the Triple P, and the participation in previous surveys (at Pre, FU1, and FU2).
Hypothesis 3b: In adolescence (at FU10), the participation of fathers from single-parent families should be significantly predicted by parents' social characteristics (mother's school graduation, household income), adolescents' mental health problems, adolescents' relationships with their fathers, parents' parenting style, custody arrangements (predictors assessed at FU10), the participation in the Triple P, and the participation in previous surveys (at Pre, FU1, and FU2).
In this study, single-parent families are single mothers at Pre. Single-parent families and two-parent families were analyzed separately in our study, because the living situation of the two family types differs significantly (e.g., in the type and frequency of contact with the father; single-parent families often have no contact with the father at all). Furthermore, single-parent families may have other reasons for non-participation (e.g., custody arrangements). Possible reasons for non-participation among two-parent families may also be a lack of parental coparenting or a low partnership quality; however, such characteristics are not available for single-parent families.
In this study, no distinction was made between the biological father and the social father. The reference person who had the most contact with the child or adolescent at the time of the survey completed the questionnaires.

Methods
The surveys were conducted as part of the Future Family (FF) research projects funded by the German Research Foundation (DFG) from 2001 to 2013. The FF I-study (Heinrichs et al., 2005) was a randomized controlled trial, while the FF II-study (Heinrichs, Krüger & Guse, 2006) was a non-controlled trial. Both studies examined the effectiveness of the Triple P (Sanders et al., 2014). The FF III-study (FU10; Hahlweg & Schulz, 2019) was based on a longitudinal design examining the effectiveness of the Triple P and the prediction of mental health problems in adolescence, considering risk and protective factors in kindergarten age.

Recruitment and Sample Characteristics at Pre
At pre-assessment, families with children aged 3 to 6 years were recruited out of kindergartens in the city of Brunswick in Germany. The study sample consists of two subsamples, although no distinction is made between them in the further course of the study: (a) Subsample FF I: N = 280 families were recruited in 2001/2002 in 17 randomly selected municipal daycare centers, using a stratified randomization to assign treatments to the day care centers. The census bureau of the city provided the Social Structure Index, which served as a stratification variable. (b) Subsample FF II: Since children from the lower social class were underrepresented in the FF I sample, an additional N = 197 families were recruited in 2003 from 15 randomly selected municipal day care centers located in social hot spots of the city. After the day care centers had given an information letter to the parents (at Pre), further contact was made with families who agreed to participate in the research project.
The strategy used in the FF research project will now be described in more detail, since the participation rates of the families and thus also the participation rates of fathers are related to the recruitment strategy (see theoretical background). At all assessment points, the letters sent to the families addressed the parents rather than mothers or fathers specifically ("Dear Family…,"). In the case of single parents, the single parent was addressed.
At the subsequent assessment points, all families who had participated at Pre were contacted to inform them of the continuation of the project and to announce a call to schedule an interview. The parents themselves decided with whom the interview should be conducted. Both parents were then sent a questionnaire package in advance with the request to complete it by the interview date. The single parents, in 99% the mothers, were asked to hand over the questionnaire package to the other parent to complete. The single parents were asked to decide for themselves with which person the child had the most contact and to forward the questionnaire package accordingly: to the other biological parent or, if applicable, to the new life partner. If there was no contact at all with the father, it was not possible to fill out the questionnaires. No special efforts were made to motivate fathers to participate.
At FU10, adolescents were on average 14 years old (SD = 1), and 45% of the children were girls. Fifteen percent of the mothers had less than a secondary school diploma, 38% had a secondary school diploma, and 47% had a high school diploma as their highest level of education (fathers: 20%/24%/56%). Every fifth family (20%) had a migration background.
An analysis at FU10 revealed significant differences between participants and drop-outs. The drop-out families were more likely to be single parents (p < 0.001) and they were more likely to belong to the lower social class (mother's and father's school graduation, both p < 0.001). For details on the methodological procedure and the sample see Hahlweg and Schulz (2019).

Measures and Procedure
Data from the families were assessed with structured interviews and standardized questionnaires. Two project staff members visited each family for approximately 2 to 3 hours to interview one parent and, after FU1, the child/adolescent as well. The interviews were usually completed by the mothers (97%). Data collection in terms of parents who were interviewed, questionnaire completion, type, and scope was identical at all assessment points. Compensation was provided for the time and effort spent on the assessments ($70 at the pre-assessment, and $80 [$40 each for mother and adolescent] at FU10). Participants were informed in advance in an information letter about the aims of the research project and the survey procedure, as well as how their data would be handled. In a telephone call, they had the opportunity to ask questions about this. The informed consent was given in a written form. The Human Subjects Protection Board of the German Association of Psychology approved all procedures.
Sociodemographic characteristics (age, sex), social status (mothers' and fathers' school graduation, household income), migration background, adolescents' current school attendance, parenting status (two-parent family vs. singleparent family), and custody arrangements (with the categories: mother only, father and mother jointly) were collected in the interviews at Pre and at FU10. In the interview, questions were also asked about physical punishment at Pre. Household income was calculated in "Deutsche Mark" at pre and in Euros at FU10.

Dysfunctional Parenting-Parenting Scale (PS)
Dysfunctional parenting was assessed using the German version (Naumann et al., 2010) of the Parenting Scale (PS; Arnold et al., 1993). The 35 items of this self-report questionnaire were rated on a 7-point Likert scale by the parents to assess their dysfunctional parenting practices (e.g., "I am the kind of parent that… (1) …sets limits on what my child is allowed to do. (7) …let my child do whatever he/she wants."). The total score is based on three factors: Laxness (permissive discipline), Overreaction (authoritarian discipline), and Verbosity (overly long In this study, single-parent families are single mothers at Pre FU1 = one year after pre; FU2 = two years after pre; FU10 = 10 years after pre reprimands). The internal consistencies of the total score in the present sample were α = 0.81 for mothers and α = 0.75 for fathers. Higher total scores indicate more use of dysfunctional parenting practices.

Child Mental Health Problems-Child Behavior Checklist (CBCL)
We used the German versions of the Child Behavior Checklists (CBCL; Achenbach & Rescorla, 2001) for children aged 1.5 to 5 years and for children aged 4 to 18 years (Arbeitsgruppe Deutsche Child Behavior Checklist, 1998;. Parents were asked to rate the presence and frequency of their child's behavioral and emotional problems using 100 and 113 items, respectively (e.g., "Destroys things belonging to his/her family or other children"; 0 = not true, 1 = somewhat or sometimes true, 2 = very true or often true). The two subscales internalizing (e.g., anxiety symptoms) and externalizing mental health problems (e.g., ADHD symptoms) were combined to a total score. The internal consistencies for internalizing (α mothers/fathers = 0.86/0.89) and externalizing mental health problems (α mothers/fathers = 0.90/0.92) as well as for the total score were satisfactory (α mothers/fathers = 0.94/0.96). Higher scores indicate more child mental health problems.

Coparenting-Parent Problem Checklist (PPC)
The Parent Problem Checklist (PPC; Dadds & Powell 1991; German version: Kroeger et al. 2009) was used to assess parental coparenting. Sixteen items about parenting conflicts that arise due to a lack of cooperation between partners were rated on a 4-point Likert scale (e.g., "Disagreement over type of discipline, e. g. smacking children"; 1 = not true, 2 = rather not true, 3 = rather true, 4 = true). These areas of conflicts were assessed in terms of the extent to which they have posed a problem for the couple over the course of the last four weeks. The number of problem areas was summed up to a total score. The internal consistencies were satisfactory (α mothers/fathers = 0.84/0.85). Higher scores indicate more coparenting conflict areas.

Partnership Quality-Abbreviated Dyadic Adjustment Scale (ADAS)
The ADAS (Sharpley & Rogers 1984) was used to assess the quality of parents' partnership quality. The ADAS is the 7-item version of the 32-item Dyadic Adjustment Scale from Spanier (1976). The items assessed the agreement about domains of the parental relationship (e.g., philosophy of life) and the occurrence of positive interactions between the parents (e.g., "Do you and your partner make future plans together?"). Finally, the overall relationship quality was rated by the parents (0 = very unhappy to 5 = very happy). The answers to these items were summed up to a total score, whereas scores of 22 and above indicate a high partnership quality. The internal consistencies were satisfying (α mothers/fathers = 0.80/0.81). Higher scores indicate a higher partnership quality.

Relationship With the Father-Parent Image Questionnaire (EBF)
At FU10, the relationship with the father was rated by the adolescents on a 6-point scale from "very poor" to "very good". This item was taken from the Parent Image Questionnaire (EBF; Titze & Lehmkuhl, 2010). The EBF assesses the quality of the parent-child relationship from the perspectives of the children and adolescents between the ages of 10 and 20 years. A higher score indicates a better relationship with the father.

Statistical Analyses
To test our hypotheses, fathers were initially divided into (a) participants and (b) non-participants at each assessment point. The participant group included fathers who had completed at least one of the following questionnaires: PS, CBCL, PPC, or ADAS. The participation rates of fathers at the four-time points were analyzed descriptively. The transition probabilities (moving from one state into another state) of fathers' participation were calculated between the different assessment points. Chi²-tests were computed to test hypotheses 1. Nonhierarchical and hierarchical binary logistic regressions were calculated to test hypotheses 2 and 3.

Transition Probabilities
The transition probabilities for participation ( Fig. 1) ranged from 86.7% to 95.6% with a mean of 93.1%; for non-participants, they ranged from 61.6% to 94.7% with a mean of 83.5%. Interestingly, of the n = 99 fathers who did not participate at FU2, n = 38 (38.4%) participated at FU10.

Hypothesis 2
Two stepwise binary logistic regressions, each separately for two-parent families and single-parent families, were Note. Fathers' participation rates from one assessment point to the next one.   used to examine whether the combination of different characteristics could predict fathers' participation in early childhood (Pre). The following independent variables were used for the prediction: mother's school graduation, household income, CBCL total score, PS total score, and the level of physical punishment. The results of the binary logistic regression for the twoparent families are shown in Table 4. The model was significant (Omnibus test: p = 0.021), but the model quality was only partially given, as the explained variance was only 3.6% (Nagelkerkes R²). The results demonstrated that only household income could significantly predict fathers' participation (p = 0.020, OR = 1.18): the higher the income, the more likely fathers were to participate. In contrast, the CBCL total score, the PS total score, and the level of physical punishment did not significantly predict fathers' participation.

Participators (fathers) or non-participators (fathers)
The binary logistic regression for single parent-families resulted only in non-significant results.

Hypothesis 3
To test hypothesis 3, two hierarchical binary logistic regression models were calculated, each separately for twoparent families and single-parent families. The following independent variables were used to predict fathers' participation in adolescence (FU10): mother's school graduation, household income, adolescent-father relationship (EFB), CBCL total score, and PS total score. For the two-parent families only, the PPC total score and the ADAS total score were additionally included in the models. For the singleparent families only, the custody arrangement (mother only or both parents) variable was included. In the first step, the variables were entered into the regression models stepwise. In the next step, we examined whether participation in the Triple P improved the prediction. In a final step, we analyzed, whether paternal participation in the surveys at Pre, FU1, and FU2 (included as the number of total participations) further improved the prediction. For each of these last two steps, the inclusion method was chosen to detect the additional effects.
The results for the two-parent families are presented in Table 5. The model was significant at all three levels (Omnibus tests: p = 0.001/0.003/0.001). Nagelkerke's R², the Hosmer-Lemeshow statistics, and the proportion of correctly classified fathers' participations were mostly indicative of a good model fit. At the first level, household income (p = 0.023, OR = 1.45) and adolescent relationship with the father (p = 0.011, OR = 1.67) significantly predicted fathers' participation at FU10. Fathers who had a high income and a good relationship with the adolescent were more likely to participate. However, these variables were no longer significant at the third level, when the prior paternal participation was also included in the models. Previous participation in the Triple P did not significantly predict paternal participation. The best predictor was the previous paternal participation (p < 0.001, OR = 2.13). In contrast, the CBCL, PS, PPC, and ADAS total scores were non-significant predictors in the regression models.
The results for single-parent families are shown in Table 6. The model was significant at all three levels (Omnibus tests: p < 0.001). Nagelkerke's R², the Hosmer-Lemeshow statistics, and the proportion of correctly classified fathers' participation indicated a good model fit. The results showed that the household income (p = 0.026, OR = 1.61), the adolescents' relationship with the father (p = 0.012, OR = 1.73), and the custody arrangement (p = 0.025, OR = 2.10) were significant predictors at the first level. The higher the household income and the better Only the results of the significant predictors are reported in the table. Non-significant predictors: mother's school graduation (Pre), CBCL total score (Pre), PS total score (Pre), and the level of physical punishment (Pre) the relationship with the father, the more often fathers participated. Furthermore, if both parents had custody, it was also more likely that fathers took part in the survey. However, these variables lost some of their effects at the second and third levels. Only the adolescent's relationship with the father consistently proved to be a significant predictor. Previous participation in the Triple P significantly predicted paternal participation (p = 0.038, OR = 4.39) indicating that participation in the Triple P had a favorable impact on fathers' participation at FU10. However, this variable was not significant in the final step. In contrast to the results of the model for the two-parent families, earlier participation was not a significant predictor in the models for single parent families (p = 0.183, OR = 1.47). Step 1  Omnibus χ² = 37.4, p < 0.001; Nagelkerke's R 2 = 0.503; Cox and Snell R 2 = 0.359; Hosmer -Lemeshow-Test χ 2 = 0.81, p = 0.421; correctly classified: 83.3% Step 3  Only the results of the significant predictors are reported in the table. Non-significant predictors: mother's school graduation (FU10), CBCL total score (FU10), PS total score (FU10) (Step 1). * In this study, singleparent families are single mothers at Pre Only the results of the significant predictors are reported in the table. Non-significant predictors: mother's school graduation (FU10), CBCL total score (FU10), PS total score (FU10), PPC total score (FU10), ADAS total score (FU10) (Step 1)

Discussion
Because studies of developmental psychopathology among children and adolescents often collect data only from mothers (Parent et al., 2017), there is a risk of one-sided and biased findings and conclusions. The literature repeatedly pointed out that the perspective of other caregivers must also be considered, especially the perspective of the father. It is precisely the explanation and discussion of divergent results that contributes to a better understanding of the respective findings and that prevents one-sided conclusions (Laucht, 2003). The aim of this study was to contribute to answering the research question of which fathers are more likely to participate in empirical studies using the example of a ten-year longitudinal study with four assessment points. The study was explicitly designed to collect questionnaire data from both the mothers and the fathers (and also from single parents).
Overall, on average, more than 70% of the fathers participated in the surveys over the four time points. This participation rate of fathers who were specifically asked to participate is comparable to the rate of other longitudinal studies reporting such data. A longitudinal study by Edwards (2012;"The Longitudinal Study of Australia Children (LSAC)") spoke of parent 1 and parent 2 rather than mothers and fathers, with parent 1 being the mother in most cases. Fathers' participation rates ranged from 84.3% to 90.7%, spread across four assessment points in this study. Mathiesen et al. (2018; "Tracking Opportunities and Problems From Infancy to Adulthood (TOPP)") obtained participation rates of fathers ranging from 70.6% to 77.4% for the last three of eight assessment points in their Norwegian longitudinal study (own calculations). Costigan and Cox (2001) reported a participation rate of 64.6% for fathers in the American study "NICHD Study of Early Child Care", in which N = 661 two-parent families were analyzed.
The probability of participation from one assessment point to the next one was 93%, while the probability of non-participation was 84%. We are not aware of comparable data from other studies. Over 60% of the fathers participated in all four surveys and only 15% participated in none. This result is encouraging, because 25% of fathers participated in at least one survey. It should be possible to motivate these fathers to continue their participation. One noteworthy result is the increase in the participation rate of the fathers from single-parent families from 10.1% at Pre to 58.9% at FU10. On the one hand, this increase was due to the drop-out rate at FU10. On the other hand, many of the single parents had a new partner at FU10 who participated in the survey.
The main objective of this study was to identify the characteristics that promoted fathers' participation in our longitudinal study. First, the results showed that the family type (two-parent family vs. single-parent family) was significantly associated with paternal participation. This result was expected, although to our knowledge this has never been explicitly examined, since in single-parent families (single mothers) there is often no contact at all, or if there is contact, it is very bad with the father (Bjarnason & Amarsson, 2011;Tazi-Preve et al., 2008). Separate analyses of two-parent families and single parents revealed consistent predictive factors, but also specific factors for each family type. However, it should be noted that based on the variables examined, fathers' participation at Pre could only be predicted to a very limited extent and only for the twoparent families, since the model for single-parent families showed only non-significant results. This stands in contrast to the prediction for FU10, where good predictive models were found for both family types.
First, the results showed that different factors played a role for paternal participation in two-parent families and singleparent families. Therefore, it was useful to distinguish between the two groups. The only predictor that showed significant associations with fathers' participation in both groups was the family's household income. This finding is congruent with studies that have found a positive relationship between income, educational resources, and father-child contact (Tazi-Preve et al., 2008). Fathers from a higher social class and with a higher level of education might be more receptive to scientific research. For this reason, they are also more likely to participate in empiric research studies.
Another important predictor was the adolescent's relationship with the father. In contrast, psychological variables such as parenting style, parental coparenting, partnership quality, and adolescents' mental health problems were non-significant predictors, contrary to our expectation. These results are not entirely congruent with those of other studies (see above, e.g., Costigan & Cox, 2001). Finally, for fathers from single-parent families, joint custody proved to be a significant predictor at the first level of the regression model. Surprisingly, participation in the Triple P played only a minor role among single-parent families. The predictor lost its effect when the fathers' previous participation in the surveys was included. This refutes the assumption that families who were helped by the intervention had a higher motivation than the families who were not affected by the intervention. For two-parent families, previous participation was the decisive predictor, which made all other characteristics recede into the background. This was not the case for fathers from singleparent families. Here, the relationship between the adolescent and the father was the decisive predictor.
Based on these results and the transition probabilities, it can be summarized that fathers who had participated in previous assessments remained involved in the study over the long run. Therefore, the primary goal should be to encourage as many fathers as possible to participate in empirical studies at an early stage. Increased monetary incentives could be of particular importance here, as they could increase the motivation of fathers with low household incomes to participate. Heinrichs (2006) concluded based on the basis of their literature review and own findings that monetary incentives increase the willingness of socially disadvantaged families to participate in prevention and treatment programs. It can be assumed that this also applies to participation in scientific studies. The aim of future research is to investigate this in detail and to determine the amount of money involved.

Limitations
The generalizability of the results is limited due to the characteristics of the sample. First, families from the middle and upper social classes were overrepresented. Second, the sample was recruited in the context of an intervention study, with the majority of families participating in the Triple P (Sanders et al., 2014). Further, no distinction was made between the biological and the social father. It can be assumed that some two-parent families separated, and the mothers started living with new partners during the ten-year period; single mothers in particular can be expected to have found a new partner again. This was not examined and controlled for in our study. The single parents were asked to decide for themselves with which person the child had the most contact. This person completed the questionnaires for the fathers. In the sample of single-parent families, the proportion of fathers participating at Pre was very small, therefore the results should be interpreted with caution. Larger samples would increase the power, making it more likely to show significant effects.
While the fact that this study is a ten-year longitudinal study is on the one hand positive, on the other hand, the question arises to what extent these results can be transferred to today's situation, in which fathers are increasingly taking on responsibility in the upbringing of their children (Juncke et al., 2018). Another limitation of this study is that possible important predictors could not be assessed. There are several reasons for this: 1. Fathers who did not participate in the study could not be interviewed. Therefore, a comparison with participating fathers is not possible (e.g., regarding the gender ideology of fathers). 2. Because we focused on the social father, who may have changed across the assessment points, characteristics related only to the biological father could not be assessed (e.g., father's prenatal participation behavior). 3. Changing relationship dynamics are an important predictor to consider. However, on the one hand, in this study, we were predominantly dealing with stable two-parent families, and on the other hand, there were very different dynamics (e.g., multiple changing partnerships after separation from the biological father or after a new partnership return to the biological father). These dynamics are difficult to classify.
Methodological weaknesses also include the fact that the comparison of participating and non-participating fathers was based primarily on mothers' assessments in questionnaires and not on fathers' assessments, because they did not participate. No special recruitment efforts were made for fathers. Mothers and fathers were equally encouraged to participate in the study or to complete the questionnaires. As desirable as the participation of fathers and the separate analysis of mothers' and fathers' data may be, it must also be kept in mind that additional recruitment efforts are also associated with costs. Costs must be positively related to benefits, especially when there is no clear difference in outcomes between mothers and fathers (Pleck, 2010). Careful consideration must be given to whether the additional effort is really worthwhile (Teitler et al., 2003). This study only examined the factors that predict fathers' involvement in empirical studies; another interesting question would be to examine how fathers' involvement affects children's development.

Implications
It can be assumed that the division of gender roles has an influence on the distribution of tasks and thus on the fathers' participation. In our society, an increasing pluralization of lifestyles can be observed with a simultaneous decline in the classic intra-family division of labor, i.e., the decline of the image of the father earning the sole income and the mother being solely responsible for the household and children. This change is occurring more rapidly in higher social classes. Future studies should take into account the increasing diversity of lifestyles and family forms. A differentiated look at the exact structure of family life (parents' occupation, distribution of household tasks, etc.) could lead to interesting new findings.
In order to increase the participation rate of fathers, it is recommended to explicitly contact the father, especially for families with a single mother and for families from lower social classes. The fact that social class is related to repeated participation, at least among cohabiting families, demonstrates how difficult it is to approach families with higher social stress factors and to encourage them to participate. Once a father participates in the study, it can be assumed that he will remain involved in the study for a longer period of time.

Compliance with Ethical Standards
Conflict of Interest Kurt Hahlweg is member of the Triple P International Scientific Advisory Committee. The authors have no relevant financial or non-financial interests to disclose.
Consent to Participate Informed consent was obtained from all individual participants included in the study. We thank the families for their participation and Lina Vetter (BSc Psychology) for her pilot work.
Ethics Approval This study was performed in line with the principles of the Declaration of Helsinki. The Human Subjects Protection Board of the German Association of Psychology (DGPs) approved all procedures (WS 12_2010).
Publisher's note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons. org/licenses/by/4.0/.