Understanding Fathers’ Involvement Relative to the Other Parent After Parental Separation

ABSTRACT Following parental separation, fathers’ greater or lesser parental involvement relative to the other parent may be differently accounted for by father, child, and coparental factors. A representative sample of 671 separated fathers completed questionnaires two and four years after separation. For fathers less involved than the other parent, a better coparenting relationship accounts for greater T1 involvement, but predicts a decrease in involvement by T2. For fathers more involved than the other parent, a better coparenting relationship accounts for more balanced involvement of both parents at T1 and T2. For all fathers, more custody time accounts for greater T1 and T2 involvement and greater psychological well-being accounts for greater T1 involvement. Implications for intervention and research are discussed.

In the Canadian province of Quebec, it is estimated that more than 30% of children will experience a parental breakup by the age of 15 (Desrosiers et al., 2018).Similar estimates have been reported for the United States and France (Andersson et al., 2017).Following parental separation, sole custody to mothers is the most common child custody arrangement, but the awarding of shared or sole custody to fathers is increasing in prevalence (Biland & Schütz, 2015;Sodermans et al., 2013).Compared to fathers with sole or shared custody of their child, fathers whose child is primarily in the mother's custody (i.e., noncustodial fathers) are less involved in providing daily care to their child, as they have less opportunities to do so, but are also less involved in decision-making, in parenting tasks that do not occur on a daily basis, and in leisure activities with their children (Koster et al., 2021).This suggests that noncustodial fathers are generally less involved in parenting than the child's other parent, whereas sole custody fathers are more involved than the other parent.However, as previous research has shown that separated fathers' involvement (its absolute level or relative to the child's other parent) is not fully accounted for by custody time (Koster et al., 2021;Larouche et al., 2022), other factors must be considered to explain father involvement after separation.Furthermore, as the contexts in which separated fathers are either more involved or less involved than the mother after separation may be different (Cohen et al., 2014;Troilo & Coleman, 2012), the relative importance of factors which help understand parental involvement in each of these two groups of separated fathers may also differ.
As separated parents' involvement in parenting activities tied to daily routines within the home are more strongly determined by custody time than other aspects of parenting (Koster et al., 2021), it may be useful to consider parenting activities that can be shared to varying degree across two households to understand father involvement which is less determined by custody (e.g., decision-making).This is specifically what the Father's Relative Involvement Post-Separation Scale (FRIPS;Larouche et al., 2022) was designed to do.Specifically developed for separated fathers and validated for noncustodial as well as shared and sole custody fathers, it can help better understand what favors or poses an obstacle to fathers equally sharing parental responsibilities with the other parent, beyond the aspects of parenting most logistically constrained by custody time.Greater equality in parental involvement between separated parents lessen their respective parental burden, is beneficial for their psychological adjustment (Sodermans et al., 2015;van der Heijden et al., 2016) and is conducive to the child having access to both parents' psychological, social and economic resources (Steinbach, 2019).
Research on father involvement post-separation has focused on noncustodial or nonresident fathers, concerned with what contributes to greater father involvement, implicitly assuming this leads to shared responsibilities and equal involvement of both parents.Research has paid little attention to departure from equality in the other direction, essentially neglecting the other half of the continuum in which fathers assume more parental responsibilities than the other parent after a separation.To our knowledge, no study has attempted to distinguish what accounts for fathers' greater or lesser involvement in parenting relative to the other parent.Using the FRIPS, the aim of the present study is to examine what accounts for departure from equal parental involvement, toward either greater or lesser parental involvement of fathers relative to the other parent in the years following parental separation, and beyond what might be explained by the amount of time fathers have custody of their child.To do so, this study relies on the Longitudinal Survey of Separated Parents and Stepfamilies in Quebec (Saint-Jacques et al., 2018), which, to this day, surveyed parents in the first two years following separation (T1) and about two years later (T2).It first considers the extent to which variables previously associated with greater father involvement post-separation differentially account for greater or lesser father involvement relative to the other parent in the first few years following separation (T1), which are considered a key period in the redefining of family relationship (Emery, 2012) and for setting precedence for father involvement in the subsequent years (Cheadle et al., 2010).The present study also takes advantage of the longitudinal data available to examine the stability of father involvement over the two subsequent years and what might account for more equal parenting involvement of both parents or, conversely, greater departure from equality in the form of either lesser or greater father involvement over time.The longitudinal data is also used to test reciprocal associations considering to what extent, over time, father involvement may both shape and be shaped by other aspects of the family system.Overall, this study could help in identifying specific intervention targets for each of these two groups of separated fathers to favor equal involvement of each of the child's parents.Doherty et al. (1998) proposed a systemic and ecological model of father involvement according to which father involvement is influenced by aspects pertaining to the various subsystems within the family, including individual family members (i.e., each parent, child) and the relationships between them (parent-child and between parents), but is also influenced by contextual factors external to the family.Psychological well-being is an influential father factor, whereas behavioral difficulties, age and gender are important child factors according to Doherty et al. (1998) model.Their model also highlights the coparenting relationship and the child custody arrangement (e.g., how much custody time the father has) as two key factors pertaining to the coparental subsystem.The model also postulated that institutional practices and gender role beliefs within society are contextual factors that exert an overall influence on all these subsystems.As such, after parental separation, social norms pertaining to custody arrangements and beliefs in Western societies regarding gender equality, but also the primacy of the mother-child bond, may influence father involvement.Finally, Doherty et al. (1998) postulate that individual, relational and contextual factors are also likely to have additive and interactive effects on father involvement.Moreover, family system theory (Cox & Paley, 1997), on which Doherty et al. (1998) model is based, postulates that the different members and relationships in a family influence and are influenced by each other.Thus, this entails the possibility that father involvement also influences other individual and relational factors within the family.

Fathers' psychological well-being
The multiple changes fathers experience as a result of parental separation (e.g., material reorganization, mourning of conjugal and family life) can negatively impact their well-being (Bottom, 2013;Mercadante et al., 2014), especially in the first months following separation (Halford & Sweeper, 2013), which is associated with father involvement (Wilson & Durbin, 2010).For noncustodial fathers, not being involved with their child as much as they would like can have a negative impact on their psychological well-being whereas low psychological well-being can also make it difficult for them to be involved as parents (Deslauriers & Dubeau, 2019).Sole custody fathers' psychological well-being may be less decisive to their parental involvement compared to noncustodial fathers, yet assuming most parental responsibilities can be psychologically exhausting over time (Shorey & Pereira, 2022).Thus, the association between psychological well-being and parental involvement may be bidirectional for both separated fathers who are less involved and more involved than the other parent.However, the association might be positive for fathers who are less involved than the other parent whereas for fathers who are more involved than the other parent it might be initially positive (well-being to involvement) but become negative over time (involvement to well-being).

Child's behavioral difficulties
Compared to children whose parents form a couple, children whose parents have separated are more likely to display internalizing (e.g., anxiety, depression) and externalizing (e.g., antisocial conduct) behavior problems (Amato, 2014) that can be particularly prevalent in the first few years post-separation (Trottier et al., 2022).Much research has demonstrated positive consequences for many aspects of child development and well-being of father involvement, not only in quantity, but also better quality of parenting (e.g., Cabrera et al., 2018;Lamb, 2010;Rollè et al., 2019).It is thus tempting to conclude that maintaining father involvement would prevent child behavior problems postseparation.Yet, some studies have suggested that difficult child temperament or behavior may be more challenging and hinder father involvement (e.g., Santos et al., 2022).A meta-analysis by Adamsons and Johnson (2013) of research examining nonresident father involvement and child behavioral and psychological problems published prior to 2007 reports an overall negative yet weak association and heterogeneous effect sizes, ranging from negative to positive associations.Weaker associations with behavioral outcomes are also noted in representative compared to convenience samples.It is important to note that nearly research on child outcomes and father involvement postseparation has been cross-sectional, as were the studies analyzed in Adamsons and Johnson's (2013) meta-analysis, which precludes causal interpretations.
Research has also focused on noncustodial fathers who have less contact with the child than the other parent, neglecting situations of shared custody and sole custody to fathers.We found a single longitudinal study, by Hawkins et al. (2007), that tested a cross-lagged model of father involvement and child behavioral problems in a representative sample of nonresidential biological American fathers and their adolescent child (ages 12-19 years) with two waves of data collected 12 months apart.No significant effects of nonresident father involvement on subsequent adolescent externalizing or internalizing problems were found, but both adolescent internalizing and externalizing problems predicted less subsequent father involvement.Thus, adolescent/child behavioral problems predicted a greater absolute level of nonresident father involvement after separation rather than the reverse.However, when considering father involvement relative to the other parent, the association may be more complex.As research on fathers who are more involved than the other parent post-separation is scarce, there is little basis upon which to formulate a hypothesis about how child behavioral difficulties might account for their involvement.Greater child behavior problems may predict less involvement for fathers who are less involved than the other parent, but potentially not for those who are more involved than the other parent.

Coparenting relationship quality
Although separation ends the couple relationship, ex-partners remain the parents of their children and, if they both want to take care of the children and be involved in their lives, they need to work together, which can be a particularly challenging task shortly following separation (Emery, 2012).This includes agreeing on how to educate their child, divide parental tasks and responsibilities, supporting (or not) the other parent in his/her parenting, and jointly managing child and family-related issues (Feinberg et al., 2012).To develop a good postseparation coparental relationship, parents must put aside negative feelings toward the other parent and adjust their behaviors to fit the new demands of their relationship (Jamison et al., 2014).Dissatisfaction with separation-related decisions (e.g., child custody) and questioning the other parent's parental fitness can also make it difficult for parents to establish a high-quality coparenting relationship (Russell et al., 2016).
Research also suggests a better coparenting relationship facilitates nonresident fathers' involvement.Carlson et al. (2008) followed a cohort of American mothers (mostly African American) of 1-year-olds born out of wedlock.Using a cross-lagged model, they found that mothers' greater perception of coparenting cooperation predicted nonresident fathers spending more time and engaging more in leisure and educational activities with their child 3 years later, and that coparenting more strongly predicts subsequent nonresident fathers' involvement than the reverse.Moreover, Sobolewski and King's (2005) of American mothers of older children (aged 10-18 years) also found that cooperative coparenting was associated with more frequent noncustodial father-child contact as well as higher father-child relationship quality and more responsive fathering.In a study of divorced Israeli fathers of minors (<18 years of age), Finzi-Dottan and Cohen (2016) showed that both noncustodial and sole custody fathers were less involved as coparenting coordination with the other parent was poorer, but that, compared to noncustodial fathers, sole custody fathers' involvement was more weakly associated with coparenting coordination.In contrast, using cross-lagged analyses of longitudinal data for 184 American separated parents (including fathers with various child custody arrangements, children on average 8 years old), Petren et al. (2021) reported a non-reciprocal positive effect from frequency of father involvement in activities with the child about 3 months following divorce to parental cooperation 3 to 6 months later.However, analyses did not distinguish results for different custody arrangements nor according to fathers' level of involvement relative to the other parent.
Thus, prior research suggests that a better coparenting relationship may contribute positively to and be positively influenced by the parental involvement of both separated fathers less involved and those more involved than the other parent.However, given that fathers more involved than the other parent already assume most parental responsibilities, their coparenting relationship might be less important for their parental involvement that it is for fathers less involved.Given the scarcity and conflicting results of relevant research, further longitudinal research is needed to determine if the association between the quality of the coparenting relationship and father involvement is reciprocal over time.

Father's custody time
Separated fathers who have more face-to-face time with their child have more opportunities to be involved with them and to do so in several ways.Koster et al. (2021) observed that the more custody time divorced or separated Dutch parents (fathers and mothers) had with their children (aged 2-18 years), the more they provided direct and indirect care, took part in leisure activities, and had an influence on child-related decisions.Conversely, Bakker and Mulder (2013)'s results suggest that fathers who were more involved in parenting prior to separation (i.e., symmetrical rather than nonsymmetrical task division) are likely to have more custody time after separation.Yet neither of these studies examined potential reciprocal associations, over time, between father involvement and custody time after separation.In short, custody time may positively contribute to separated fathers' involvement, whether they are less involved or more involved than the other parent.However, it cannot be excluded that initial father involvement predicts subsequent changes in their custody time.

Father's psychological well-being, child's behavioral difficulties, coparenting relationship quality and custody time
Several studies have shown that fathers' psychological well-being is associated with their child's behavioral difficulties, coparenting relationship quality and separated fathers' custody time.In their systematic review of 21 studies, Sweeney and MacBeth (2016) reported that depressive symptoms in fathers are associated with an increased risk of internalizing and externalizing behaviors in their children (aged 2 months − 21 years).In their study including families in which parents form a couple, Price-Robertson et al. (2017) reported a negative association between fathers' psychological distress and coparental relationship quality.Finally, Bottom (2013) reported that sole custody fathers have a higher well-being than shared custody fathers who themselves have a higher well-being than noncustodial fathers.
Several studies have also found associations between coparenting relationship quality, child's behavioral difficulties and fathers' custody time.Teubert and Pinquart's (2010) meta-analysis, based on 59 studies of families of children 7 months to 16 years of age whose parents still formed a couple or had separated, revealed fewer behavioral difficulties and better social functioning in children of parents with a positive coparenting relationship (high cooperation and agreement and low conflict).Leclair et al. (2019) meta-analysis of 13 samples suggests that separated parents report a more cooperative coparenting relationship, but not necessarily a less conflictual one, if they have a joint custody arrangement rather than sole custody to one parent (i.e., to mothers in 90% of the families sampled).Yet this association was significant only in studies which included only mothers as informants, not those that included parents of both genders.Baude et al. (2016) meta-analysis of 19 studies of children (<18 years) of separated parents revealed fewer behavioral problems and better social competency in children in shared custody compared to children in sole custody to one of the parents, generally the mother.Thus, it would be important to control for correlations between these variables, that may reflect shared variance between factors explaining father involvement.Yet little research has simultaneously considered father, child, coparental and custody variables to account for post-separation father involvement, either in cross-sectional or longitudinal research.None considered father involvement relative to the other parent and possible differences in the associations as a function of whether fathers' involvement is either greater or lesser than the other parent's.

The present study
The present study uses data from the first two waves of a longitudinal, populational survey representative of separated parents in Quebec, Canada (Saint-Jacques et al., 2018), which includes a first assessment within the first two years after parental separation and a second assessment two years later.As the first few two years following a separation represent a key transition period for family members with respect to the renegotiation of parental roles, decisions about custody and contact arrangements (Ahrons & Miller, 1993;Baude et al., 2023;Cox & Paley, 1997), which sets the tone for the father-child relationship (Doherty et al., 1998), a first objective of the present study is to evaluate if fathers' psychological well-being, child's behavioral difficulties, coparenting relationship quality and fathers' custody time distinctively help account for separated fathers' involvement relative to the child's other parent within the first two years after separation.Building on prior longitudinal research of father involvement and family system theory (Cox & Paley, 1997), a second objective of this study is to test reciprocal associations between factors and father involvement over the first two waves of the survey with a cross-lagged model.Drawing on previous research, greater psychological well-being (hypothesis 1) is expected to account for greater father involvement, albeit potentially less clearly for fathers more involved than the other parent than those less involved.Indeed, for fathers who are more involved than the other parent, prior research suggests greater initial involvement may also predict poorer subsequent well-being (hypothesis 2).Also, although little to no research has isolated how the quality of the coparenting relationship relates to father involvement when fathers are more involved than other parent, based on previous research we can hypothesize that a better coparenting relationship may accounts for and predicts greater shared parenting between parents, that is greater involvement of fathers who are less involved than the other parent but less involvement of fathers who are more involved that the other parent (hypothesis 3).Greater child behavioral difficulties are expected to account for less relative involvement of fathers (hypothesis 4), at least for fathers less involved than the other parent.Finally, greater custody time is expected to account for greater involvement of all fathers (hypothesis 5).

Participants
This study uses data from the two first time point of the Longitudinal Survey of Separated Parents and Stepfamilies in Quebec, which surveys separated parents from the province of Quebec in Canada at three-time points, that is, in 2019, 2021and 2023(Saint-Jacques et al., 2018).Data for the third time point was not yet available at the time analysis were conducted.Separated parents were identified through a target child's file in the provincial public health insurance databases.Children under the age of 14 whose parents did not have the same address for less than 24 months in 2018 were sampled.One of the target child's parents was randomly selected as the potential participant.They were sent a letter and leaflet explaining the study and inviting them to participate.To be eligible for the study, parents had to: 1) have lived with the target child's other parent at least during the pregnancy, 2) have stopped living with the target child's other parent for less than 24 months prior to June 1, 2018.It took several weeks to reach some parents and certain parents took several weeks to answer the questionnaire, explaining why some report being separated for more than 2 years at the first time point.Parents that met the inclusion criteria were invited to complete an online questionnaire.The survey was approved (#2016-154) by the Research Ethics Committee of the principal investigators' university.
The first wave of data (T1) was collected between September 2018 and September 2019 and the second wave (T2) was collected between January 2021 and June 2021.A final sample of 1,551 parents completed the questionnaire at T1, including 753 fathers.Some were excluded because their children were over 13 (n = 20) or under 3 years of age (n = 60) and thus did not complete the measure of the child's behavioral difficulties.Two participants were excluded due to invalid or missing data on all father involvement items, which resulted in a final sample of 671 fathers.At T2, 435 of the fathers who had participated at T1 completed the second questionnaire.Note that although fathers may have other children, the study focused only on the target child through which participants were identified.Table 1 contains descriptive statistics for the sample.

Father involvement
The Father's Relative Involvement Post-Separation scale (FRIPS; Larouche et al., 2022) assesses separated fathers' involvement in various activities and tasks compared to the other parent.On a scale ranging from 1 = always my expartner to 5 = always me, with 3 = both me and my ex-partner (fairly equally), fathers rated their involvement on the basis of 4 items reflecting positive involvement activities (e.g., celebrating significant events (e.g., birthdays) or holidays with our children), 4 indirect care items (e.g., running errands, shopping for our children) and 5 decision-making items (e.g., decisions related to daycare or school) for a total of 13 items.Higher scores (mean scores for each dimension measured) indicate greater father involvement with the child compared to the other parent.Cronbach's alphas are .82for positive involvement activities, .83for indirect care and .87 for decision-making in the present study.Fathers less involved were distinguished from those more involved than the other parent at T1 by first calculating the mean of items reflecting dimensions of father involvement (i.e., positive involvement activities, indirect care, decision-making).A general mean was then calculated by averaging the means for the three dimensions.Fathers were then identified as either less (<3 on the measurement scale) or more involved than the other parent (>3 on the measurement scale).Those whose general mean was 3.00 were randomly and equally distributed between the two subgroups, reflecting the most or the least involved fathers in each subgroup.This results in 373 fathers in the less involved than the other parent group at T1, 247 of which completed T2 (66,2%), and in 298 fathers in the more involved than the other parent group at T1, of which 188 completed T2 (63,1%).

Father's psychological well-being
Father's psychological well-being was measured by the 6-item Kessler Psychological Distress Scale (K6) (Arnaud et al., 2010) and fathers' general satisfaction with life.For each of the K6 items, fathers rated their mental health and internalizing and externalizing behaviors on a scale of 1 = none of the time to 5 = all the time (e.g., during the past 30 days, about how often have you felt nervous).Fathers rated their general satisfaction with life on a scale of 0 = completely unsatisfied to 10 = completely satisfied.The global measure of psychological well-being, combining these 7 Note.Percentages (%) are provided for discrete variables, whereas means (M) and standard deviations (SD) are given for continuous variables.Child information pertains to the target child.

Child's behavioral difficulties
Internalizing and externalizing behaviors were measured with the Behavior Problem Index (Peterson & Zill, 1986).Fathers rated their child's internalizing and externalizing behaviors over the past three months on a scale of 1 = not true to 3 = often true.Five items assessed internalizing behaviors (i.e., anxiety and depression; e.g., has sudden changes in mood or feelings, is overly fearful or anxious) and four to six items assessed externalizing behaviors (i.e., antisocial behaviors; e.g., cheats or tells lies, is disobedient at school) according to the child's age.Mean scores were used, higher ones reflecting more internalizing or externalizing behaviors.Cronbach's alphas were .75 for internalizing and .76 for externalizing behaviors.

Coparenting relationship quality
A modified version of the brief measure of the Multi-Domain Self-Report Coparenting Relationship Scale (Feinberg et al., 2012) was used.Six items were removed (sharing of parental responsibilities, which would have overlapped with the father involvement measure, as well as those measuring closeness between parents and child's exposure to interparental conflict) and all coparenting support items from the full scale were included.On a scale of 1 =not true of us" to 7 = very true of us, fathers rated the degree of coparenting support (6 items; e.g., my ex-partner asks my opinion on issues related to parenting), coparenting undermining (2 items; e.g., my ex-partner undermines my parenting), endorsement of the other parent's parenting (2 items; e.g., I believe my expartner is a good parent) and coparenting agreement (2 items; e.g., my expartner and I have the same goals for our child) with the child's other parent, for a total of 12 items.Higher scores (mean scores for each dimension measured, after reversing undermining items) reflect fathers' assessment of a better coparenting relationship.Cronbach's alphas were .93 for support, .84 for undermining, .84 for endorsement of ex-partner's parenting and .64 for agreement.

Father's custody time
Using a one-point percentage scale ranging from 100% of the time with the other parent (0% with them) to 100% of the time with them (0% with the other parent), fathers reported the amount of time the child lived with each parent in the last six months.Higher score indicates a higher proportion of custody time to fathers.

Analysis
Using SPSS 28 (IBM Corp, 2022), bivariate correlations were conducted to identify the relevant control variables to be included in the main analyses.The relatively large number or factors and relative complexity of the model for the available sample made it problematic to opt for latent factors in the model.Thus, at each time point, factor scores were calculated with Mplus 8.4 (Muthén & Muthén, 2017) using confirmatory factor analysis.Compared to mean or sum scores derived from items or subscales, factor scores better control for measurement error (Skrondal & Laake, 2001) and better preserve the nature of the construct (Millsap, 2011).Mean scores calculated for each dimension of father involvement (positive involvement activities, indirect care, decisionmaking) coparenting relationship quality (support, undermining, endorsement, agreement) and child's behavioral difficulties (internalizing and externalizing behaviors) were used as indicators of their respective factors.Individual K6 items and the satisfaction with life item were used as indicators of the father's psychological well-being factor.The resulting factor scores were used to fit a path model to the entire sample (full-sample model including associations between factors at T1 and T2, all paths to T1 father involvement, all paths from T1 to T2 factors and all paths from T1 involvement to T2 factors) using Mplus 8.4 (Muthén & Muthén, 2017).Second, a multigroup path model was conducted to test if associations between the different factors in the model differed depending on fathers being less involved or more involved than the other parent.The multigroup analysis ensured that significant differences in estimated associations between each group were not attributable to changes in covariance between other factors.Thus, conclusion about whether a factor similarly accounts for father involvement in each group can be more easily made.
To compare estimates between subgroups, a first multigroup model (i.e., using the one previously fitted to the entire sample) was tested.The most relevant constraints (i.e., associations suggested by Mplus to be different between subgroups) were then freed one at a time, each new model being compared to the previous one.A significant chi-square difference between the models indicated that the freed parameter estimate significantly differed across subgroups.The following fit indices allowed to determine the overall fit of the model to the data for both subgroups: Comparative Fit Index (CFI), the Tucker-Lewis Index (TLI), the Root Mean Square Error of Approximation (RMSEA) and the Standardized Root Mean Square Residual (SRMR).CFI and TLI values of .95 or higher and .90 or higher and RMSEA and SRMR values of .05 or lower and .08 or lower are deemed to reflect an excellent or acceptable model fit, respectively (Hu & Bentler, 1999;Little, 2013;Schermelleh-Engel et al., 2003).
It should be noted that all estimated models used a sample weight based on the probabilities of being eligible for the study, of being selected (based on age group, gender and geographical region), and of responding (based on age group, gender, language, geographical region, deprivation index) (Saint-Jacques et al., 2018).Depending on the known distribution of these characteristics in the population, greater weight was assigned to underrepresented parents in the sample and less weight to overrepresented parents so as to obtain a sample and estimates more representative of the population.Between 0.3% and 4.7% of data at T1 and between 0.4% and 5.2% of data for fathers who completed T2 were missing.Although the missing data pattern was not MCAR (x 2 (233) = 361.14,p < .001), the Full Information Maximum Likelihood Method (FIML;Muthén & Muthén, 2017) was used to retain cases with missing data and conduct analyses with the available data for the 671 fathers.The FIML relies on missing at random (MAR) assumptions and, even if the missing data pattern would have been missing not at random (MNAR; for which no method to detect is available), strategies to deal with MNAR rely on untestable assumptions (Enders, 2010).Thus, the FIML is a robust method to deal with missing data even if the missing data pattern is not MCAR (Enders, 2010).

Results
To identify potentially relevant control variables to retain in the path model, bivariate correlations between father involvement and sociodemographic variables were examined.Father involvement at T1 was significantly correlated with father's age (r = −.09,p = .02)and knowledge that the other parent was cohabitating with a new partner (r = .11,p = .003).Father involvement at T2 was significantly correlated with father's own current relationship status (r = −.11,p = .02).Correlations with none of the other sociodemographic variables reached the significance level (all rs ranged from −.10 to .08,ps ≥ .06).However, none of these associations remained significant once introduced into the path model and were thus excluded from the multigroup analysis.Factor scores were derived from CFA models for each concept which revealed items loadings ranging from .63 to .89,p < .001,except for slightly lower loadings for two of the K6-items (from .46 and .50., p < .001).
Pearson bivariate correlations between factor scores for all study variables, calculated separately for fathers less involved and those more involved than the other parent are presented in Table 2. Comparison of the correlation coefficients for each subgroup indicates a mean absolute difference of .21,ranging from .00 to .80.The largest differences are noted for correlations between father involvement (T1 and T2) and coparenting relationship (T1 and T2) (Zs ≥ 6.85, 2-tailed ps < .00001;Cohen & Cohen, 1983;Preacher, 2002) followed by correlations between coparenting relationship (T1 and T2) and custody time (T1 and T2) (Zs ≥ 3.73, ps ≤ .0002).However, absolute differences of .22 to .26 can be deemed significantly different at Z ≥ 3.40, p < .001,whereas those for which the absolute difference ranges from .16 to .21 can be deemed significantly different at Z ≥ 1.96, p < .05.In sum, 11 of the 45 correlations coefficients were significantly different between subgroups at p < .0002whereas 27 out of 45 attain a 2-tailed significance of p < .05.This support conducting multigroup analyses.

Multigroup path model
Factor scores were first used to fit the path model to the full sample.In addition to the associations and paths initially postulated, Mplus suggested to control for the path from both custody time and child's behavioral difficulties at T1 to father's psychological well-being at T2, as well as from coparenting relationship quality at T1 to child's behavioral difficulties at T2, which are consistent with previous studies reporting associations between these variables (Bottom, 2013;Sweeney & MacBeth, 2016;Teubert & Pinquart, 2010).This model showed an excellent fit to the data (x 2 (9) = 5.60, p = .78,CFI = 1.00,TLI = 1.00,RMSEA = .00,SRMR = .02).This model was thus used as the initial multigroup path model (see Table 3, Model 1).Fit indices of this initial multigroup path model suggest a poor fit, suggesting it may be best to allow certain estimates to differ between groups.Table 3 indicates the constraints subsequently released (i.e., parameters allowed to be freely estimated for each subgroup of the sample) one at a time, according to Mplus modification indices, the resulting model fit indices, model comparisons and improvements.The improved fit obtained by allowing estimates to differ between groups indicates that the path from coparenting relationship quality at T1 to father involvement at T1 differs significantly as a function of fathers' being less involved or more involved than the other parent.The same holds true for the correlation between father's custody time and coparenting relationship quality at T1, between father involvement and coparenting relationship at T2 as well as paths from custody time at T1 to father involvement at T2 and father's psychological well-being at T1 to father's psychological well-being at T2.The model showed acceptable fit for both groups when these paths were allowed to differ between groups.Modification indices do not suggest that any other associations should be allowed to differ between groups.Next, each path which did not attain significance (p ≥ .05)within both subgroups was removed by setting them at zero, one by one, and ensuring at each step that this did not significantly deteriorate the model fit (for technical explanations of path model fitting see Zyphur et al., 2023).The final multigroup path model is presented in Figure 1.The left portion of the model tests to what extent the different factors considered at T1 account for T1 father involvement.Controlling for the significant correlations between T1 factors, greater custody time and greater father's psychological well-being account for greater T1 involvement of all fathers.In addition, a better coparenting relationship at T1 accounts for greater involvement at T1 for fathers who are less involved than the other parent (see coefficients in parentheses) whereas a better coparenting relationship at T1 accounts for less involvement at T1 of fathers more involved than the other parent, that is, overall, a better coparenting relationship accounts for greater sharing of parental responsibilities between parents (see coefficients in brackets).Moreover, at T1, whereas custody time and coparenting relationship quality are significantly and positively correlated for fathers who are less involved than the other parent, the association between these factors does not significantly differ from zero when fathers are more involved than the other parent.Also, child's behavioral difficulties at T1 do not significantly contribute to explaining father involvement at T1, although they are negatively correlated with fathers' psychological well-being and coparenting relationship quality.
Results of the longitudinal cross-lagged analyses from T1 to T2 indicate that a better coparenting relationship at T1 is predictive of a lower father involvement at T2 for both groups, reflecting less sharing of parental responsibilities between parents for fathers less involved than the other parent, but greater sharing of parental responsibilities between parents for fathers more involved than the other parent.Greater custody time at T1 significantly predicts greater father involvement at T2, although the prediction is significantly stronger for fathers who are more involved than those who are less involved than the other parent.Results further suggest that father psychological well-being and child behavioral difficulties at T1 do not significantly predict father involvement at T2 (paths not significantly different from zero).Controlling for the temporal stability of the different measures (i.e., significant paths from T1 to T2 measures of the same variables) and significant correlations between factors at T2, results suggest that father involvement at T1 does not uniquely predict any factors at T2, fathers' psychological well-being just failing to attain significance (p < .10).As bivariate correlations between these variables were null or in a different direction (see Table 2), caution is recommended before interpreting what may result from a statistical suppressor effect (Krus & Wilkinson, 1986).

Discussion
Based on Doherty et al. (1998) model of father involvement, the present research evaluated the distinctive contribution of fathers' psychological wellbeing, child's behavioral difficulties, coparenting relationship quality and fathers' custody time to separated fathers' involvement in the first two years following separation, considering their reported involvement relatively to the other parent.Moreover, the current study took advantage of the longitudinal data available to test reciprocal associations between father involvement and each factor over time.
Whether fathers report being less involved or more involved than the other parent, results show that the more time they have custody of their child following parental separation, the more they are involved, both in the first two years following the separation and over the following two years.This supports hypothesis 5 and is consistent with findings of previous research using an absolute rather than a relative measure of father involvement (Koster et al., 2021).Moreover, results support a unidirectional association from custody time to subsequent father involvement relative to the other parent, which, to our knowledge, has never been examined in previous studies.Although increasing custody time to separated fathers as an intervention target may help those less involved than the other parent to be more involved with their child, when separated fathers are more involved than the other parent, more custody time to fathers entails less equal involvement of both parents within two years of separation and over the subsequent two years, the other parent thus having fewer opportunities to be involved with the child.As such, other intervention targets may need to be considered to help, if the context allows it, separated fathers initially less involved than the other parent to be more involved with their child as well as help separated fathers more involved than the other parent to more equally share tasks and responsibilities related to the child with the other parent.Results suggest that strategies to improve the quality of the coparenting relationship may be quite relevant in this regard.
Consistent with our third hypothesis, for fathers less involved than the other parent, a better coparenting relationship significantly and positively accounts for their sharing parental responsibilities with the other parent more equally within the first two years after separation by being more involved with their child, which is consistent with most of the previous studies regarding nonresident or noncustodial fathers that did not use a relative measure of father involvement (Carlson et al., 2008;Finzi-Dottan & Cohen, 2016;Sobolewski & King, 2005).For those fathers, the quality of their coparental relationship is particularly important for their parental involvement in the first years following separation, which may help them maintain their involvement over time.However, results show that for these fathers, the support to their parental involvement provided by a better coparenting relationship during the first two years after separation seems to fade in the following years.This emphasizes the importance of the first few years after a breakup in how changes in relationship between parents and between father and child are managed, which is consistent with what has been reported by a few authors regarding separated parents specifically (Ahrons & Miller, 1993;Emery, 2012).
For fathers more involved than the other parent, results suggest that a less collaborative coparenting relationship quality accounts for greater exclusion of the other parent from the child's life in favor of fathers taking in charge most of the parental responsibilities, both in the first years following separation and over time.Or conversely, consistent with what is found for fathers less involved than the other parent, that a better coparental relationship early on favors more equal involvement of both parents.To our knowledge, this is the first study to specifically consider fathers with such relatively high involvement and to report such results.It is possible that these fathers experience a distinctively different family situation compared to separated fathers who are less involved in parenting than the other parent.It has been noted that separated fathers sometimes assume primary care of a child because of the other parent's mental health problems (Cohen et al., 2014).Also, it has been observed that maternal distress makes it difficult to maintain a good coparenting relationship (Price-Robertson et al., 2017).The strong and negative association between the quality of the coparenting relationship and these fathers' involvement may therefore be explained by another variable that was not assessed in the dataset on which this study is based (e.g., other parent's mental health).This should be further explored in future research.
Contrary to Petren et al. (2021) findings, the present study reveals than the quality of the coparenting relationship within two years after separation is predictive of separated fathers' involvement overt the following two years, rather than the contrary.Yet beyond their analyses not distinguishing between fathers less and more involved than the other parent, this study differs for the present one in several important ways.Petren et al. (2021) study relied on a sample of only 184 recently divorced (3 to 6 months) parents (62% mothers) identified through court records.Most fathers were noncustodial (64.7% sole custody to mothers) and very few had sole custody (8.7%, i.e., n = 16).Thus, the differences in samples and in methods may render these studies less comparable.Furthermore, in Petren et al. (2021) study, father involvement was assessed through absolute frequencies (never to always) and primarily reported by mothers.Results of the present study suggest that the quality of their coparenting relationship is most predictive of the load that separated fathers assume and will assume in future years regarding various tasks and responsibility related to the child.However, it may not be the case for their absolute frequency of involvement in various activities.Fathers could not frequently engage in various activities with the child, but still be more involved overall compared to the other parent, for example.This suggests, as reported by Matte-Gagné et al. (2021), that different aspects of father involvement (such as relative versus frequency of involvement in this case) can be differently associated with the same correlates.This could be further explored in future research using various measure types of father involvement.That said, results of the present study suggest that interventions should seek to promote a good coparenting relationship soon after parental separation to help fathers assume a more equal share of parental responsibilities with the other parent early on and over subsequent years.
For both subgroups of separated fathers less involved and more involved than the other parent, results indicate that their psychological well-being is important for their parental involvement, at least in the first years following separation.This supports hypothesis 1 and is consistent with findings reported by Wilson and Durbin (2010) regarding father's involvement and well-being.However, results do not clearly suggest that father's psychological well-being predicts their subsequent level of involvement relative to the other parent, regardless of whether they were initially more or less involved than the other parent nor that fathers' relative level of involvement predicts their subsequent psychological well-being (hypothesis 2 not supported).Practitioners working with families should nonetheless monitor the psychological well-being of separated fathers, given the risk that low psychological well-being may represent for their parental involvement, in the first years post-separation, and for their child's well-being.
The child's behavioral difficulties were not directly and significantly associated with father involvement, nor did they predict subsequent father involvement, regardless of the relative level of fathers' involvement (hypothesis 4 not supported).This is inconsistent with the weak but negative association observed in Adamson and Johnson's meta-analysis (Adamsons & Johnson, 2013) and Hawkins et al. (2007) test of reciprocal effects.Yet these studies did not simultaneously consider the quality of the coparental relationship.The quality of the coparental relationship well-established predictor of child behavioral difficulties after parental separation (Teubert & Pinquart, 2010) is negatively correlated with child behavioral difficulties within both T1 and T2 and a better coparenting relationship at T1 also predicts less child behavioral difficulties two years later.This may account for the lack of a direct association between child behavior difficulties and father involvement.This discrepancy with previous findings may also be due to the use of a relative involvement measure in the present study rather than an absolute measure (Adamsons & Johnson, 2013;Hawkins et al., 2007), as well as the consideration of both direct (positive involvement activities) and indirect (indirect care, decision-making) forms of father involvement in the present study.Separated fathers could be less frequently involved with a child who presents more behavioral difficulties, but still assuming as much parental responsibility as the other parent.Furthermore, direct forms of father involvement might be more strongly associated with child behavioral difficulties than indirect forms of father involvement, as children experience that involvement firsthand.Future research should use both absolute and relative types of measures of father involvement and consider separately direct and indirect forms of father involvement when investigating child behavioral difficulties in relation to father involvement.
Importantly, results support that father involvement relative to the other parent early on following separation is strongly predictive of father involvement in subsequent years.This is consistent with Cheadle et al. (2010) findings based on an absolute measure of father involvement.It underscores the importance of interventions shortly after separation supporting a collaborative relationship and shared custody between separated parents (when possible) and parents' psychological well-being, to support balance between the respective parental roles and responsibilities fathers and their expartner assume in their child's life post-separation, which could benefit both parents as well as the child.
The current study nonetheless presents certain limitations.First, as father involvement is assessed through self-reports, perceptions may be somewhat inflated, reflecting a documented credit-taking bias in couples (Deutsch et al., 1993).Despite the advantages of the FRIPS, this measure can result in fathers reporting being more involved than the other parent, but still be less involved than another father.Moreover, if the other parent is little involved, fathers who reported being more involved can still be infrequently involved with the child.When possible, various measures of father involvement should be used to address this issue.Second, this study was conducted in the Province of Quebec.Generalizability of the results to other contexts may be limited, especially since this study includes a larger than expected proportion of fathers who have shared custody of their child, which departs from previous Quebec, albeit older, data (Desrosiers et al., 2018) as well as from post-separation custody statistics elsewhere in the world (e.g., Sodermans et al., 2013).Nonetheless, the substantially higher proportion of fathers with shared custody may reflect the Quebec values of fairness, equity and continuity of the parental couple and the parent-child relationship post-separation as well as Quebec's family policies, which are among the most supportive of early father involvement in the world (Côté & Gaborean, 2018).That said, fathers with shared custody may also be overrepresented in this sample.Thus, despite having recruited from a representative sample base and using a sample weight to correct estimates for many known factors, we cannot rule out the possibility that fathers who have little custody time and are the least involved with their child were less inclined to participate in the study and are thus underrepresented in the current sample.
Third, the COVID-19 pandemic began between the first and the second wave of the survey on which the present study is based.According to Goldberg et al. (2021), separated parents reported that the COVID-19 pandemic has led to legal (e.g., delays regarding custody arrangements or child support decisions), financial (e.g., job loss, not receiving child support as planned) and coparenting challenges (e.g., disagreements regarding health precautions, difficult transitions between households).Thus, in the present study, the COVID-19 pandemic could have had an impact on fathers' psychological wellbeing (through the stress caused by the challenges posed by the COVID-19 pandemic), coparenting relationship, and custody time, and their parental involvement.Unfortunately, this could not be controlled in analyses as the survey did not ask about the potential consequences of the COVID-19 pandemic on their family situation.
Noteworthy and important strengths of the present study are its reliance on a longitudinal survey in which a relatively large representative sample of separated fathers, which included noncustodial, shared and sole custody fathers, completed a validated multidimensional measure of post-separation father involvement relative to the other parent on two occasions, two years apart.This allows a better understanding of the temporal sequence of the associations between the various factors considered and father involvement as well as how these factors may account differently for separated fathers' relative involvement compared to the other parent.Thus, this study adds to the findings of the few studies of separated fathers we found that used longitudinal data to test opposing hypotheses about causal directions between variables with cross-lagged analyses (reciprocal associations), by considering such effects in a diverse populationally representative sample of separated fathers.
In conclusion, this study enhances the existing knowledge on separated fathers' involvement relative to the other parent.Consistent with Doherty et al. (1998) systemic and ecological model of father involvement, results suggest that individual, relational and contextual factors must be taken into account to understand what predicts father involvement.It highlights the importance of considering the heterogeneous reality of separated fathers, seeking to understand the experience of not only fathers who are less involved than the other parent, but also of fathers who are the most involved parent after separation.

Disclosure statement
No potential conflict of interest was reported by the author(s).

Table 2 .
Correlations between variables included in the multigroup path model for fathers less involved and those more involved than the other parent.Note.Below the diagonal = fathers less involved than the other parent.Above the diagonal = fathers more involved than the other parent.* p < .05** p < .01.

Table 3 .
Model fit indices allowing for differences in estimates for fathers less involved and more involved than the other parent.