Lability in Parent-Child Warmth and Hostility and Adolescent Externalizing Behaviors

Abstract

Both longer-term developmental changes (increases in hostility, decreases in warmth) and lability (year-to-year fluctuations) in parent-child relationship quality across childhood and adolescence have been linked to adolescent externalizing behaviors. Using a prospective longitudinal study of 561 children who were adopted into non-relative families at birth (57% male, 56% White, 19% multiracial, 13% Black, 11% Hispanic) where parental warmth and hostility reflect environmental influences or child-evoked reactions, we examined associations between parent-child relationship measures and externalizing behaviors at age 11 and across adolescence (i.e., from age 11 to 13-15 years). Because studies considering gene-environment interplay especially in associations between lability and child externalizing behaviors is sparse and parent-child relationship measures support the intergenerational transmission of psychopathology, we also tested whether parent psychopathology of both adoptive (AP; environmental intergenerational transmission) and birth parents (genetic intergenerational transmission) moderated these associations in multivariate regression models. Findings generally supported more effects of fathers’ than mothers’ warmth and hostility. Although there were some linear associations of increased lability with externalizing behaviors, these did not persist in the context of a multivariate model. Associations between both parents’ increasing hostility across childhood on age 11 externalizing behaviors, and for fathers increasing hostility and decreasing warmth on increases in externalizing behaviors across adolescence more likely reflect a combination of bidirectional evocative and parenting environmental associations than purely parenting environmental transmission. Moderation by parent psychopathology was sparse, and sensitivity tests revealed no differences by child sex.

Introduction

Parent-child relationships shift across childhood and adolescence, as parents balance the needs to promote autonomy and protect youth from potentially harmful risky behavior (Marceau, 2023; Smetana & Rote, 2019). This renegotiation of roles, responsibilities, and rules manifests in changes in the levels of warmth and hostility in parent-adolescent dyads (Oropesa Ruiz, 2022). From childhood through mid-adolescence there tend to be decreases in parent-child warmth and closeness, and increases in hostility and conflict (e.g., 5-10 years old: Zheng & McMahon, 2022; 8 to 16 years old: Shanahan et al., 2007; Marceau et al., 2015; 11 to 13 years old: Lippold et al., 2018), which typically re-balance later during emerging adulthood as new family relationship patterns solidify (Oliveira et al., 2020). Although some amount of longer-term developmental changes (i.e., increases or decreases over years) in parent-child relationship quality is normative and adaptive, larger declines in warmth and increases in conflict are associated with adolescents’ externalizing problems concurrently and increase the risk for problems longitudinally across adolescence (e.g., Burt et al., 2005; Lippold et al., 2018). A nascent body of work explores the unique role of lability, typically operationalized as year-to-year fluctuations, in parent-child relationship quality in relation to child outcomes. We extend this literature by disentangling whether lability is a potential environmental influence on externalizing behaviors, or whether lability operates via gene-environment interplay. Using a genetically-informed adopted-at-birth design, the goals of the present study were to examine 1) associations of developmental change and lability in parent-child warmth and hostility across childhood with adolescent externalizing behaviors at age 11 years and changes in externalizing behaviors from age 11 to 13-15 years, and 2) examine the interplay between genetic and environmental risk for psychopathology with developmental change and lability in parent-child warmth and hostility in relation to the development of adolescent externalizing behaviors.

Lability in Parent-Child Warmth and Hostility

Year-to-year lability typically explains about 75-90% of the variance (though these estimates also contain measurement error) in warmth and hostility within-families over childhood and adolescence (e.g., Lippold et al., 2018; Marceau et al., 2015; Zheng & McMahon, 2022). The importance of lability as a parent-child relationship construct is predicted by dynamic systems theory, which highlights the essential role of variability in dyadic processes for supporting change in family interaction patterns that are needed for the successful renegotiation of the parent-child relationship across adolescence (Witherington, 2007). Year-to-year lability captures the fluctuations in relationship quality that occurs across life stage transitions (Lippold et al., 2018), for example, as youth transition between schools, begin to spend more time in friend groups, and family members adapt to new roles. Thus, lability in parent-child relationship quality is expected, and to a certain extent is the product of successful family development (Lippold et al., 2019). However, very high lability over the course of childhood could indicate an unstable family environment and/or reflect inconsistent parenting, which has been shown to be a risk factor for externalizing behaviors (e.g., Marceau et al., 2015; Villarreal et al., 2022; Van Lissa & Keizer, 2020).

Lability in Parent-Child Relationship Quality and Externalizing Outcomes

In the literature, associations of parent-child relationship quality lability and child externalizing outcomes are somewhat mixed. Lippold et al. (2018) examined parent and youth report of mothers’ and fathers’ warmth and hostility lability from 6^th to 8^th grade in relation to several externalizing phenotypes in grade 9: delinquency, tobacco use, and polysubstance initiation, in boys and girls. The pattern of findings from this study were complex. The most prevalent finding was linear effects such that more lability was associated with more problems, although in one instance the linear association was inverse (less lability was associated with more problems). For fathers, these effects were all for youth-reported phenotypes – there were no associations with lability of father-reported warmth or hostility. For mothers, effects for warmth lability and polysubstance initiation were opposite when reported by youth (positive association) vs. mothers (negative association) but were consistent (positive association) for delinquency. A couple of nonlinear associations were found, whereby moderate lability predicted externalizing phenotypes, whereas high and very low parental lability predicted fewer problems – it is important to note that these effects are in the opposite direction than hypothesized. Zheng and McMahon (2022) investigated warmth lability across childhood (kindergarten to 5^th grade) in relation to 7^th grade behavior problems, finding no evidence of associations with externalizing behaviors. Although this small literature is quite mixed, across phenotypes, the most common finding is that more lability is linearly related to more externalizing behaviors (Lippold et al., 2021). This expectation of more lability being linked to externalizing behaviors in children is largely corroborated by findings that inconsistency in parenting (a different but related phenotype) is associated with child and adolescent externalizing behaviors (Berg-Nielsen et al., 2002; Stanger et al., 2004).

This mixed literature base underscores the importance of examining moderators in the association between parenting lability and child externalizing behaviors. In past studies of heterosexual two-parent families, researchers have considered differences between mothers and fathers and boys and girls. There was evidence of sex differences in associations between lability and delinquency in 50% of associations tested, often stronger for girls than boys (Lippold et al., 2018; Lippold et al., 2016), though this pattern is not always found (e.g., no moderation by child gender for substance use phenotypes; nor for lability in parental knowledge and externalizing phenotypes; Lippold et al., 2016). It has been theorized that girls’ adjustment problems would be more linked to relationship measures in general than boys in part because girls tend to be more relationship-oriented (Leaper, 2002). In general, similar effects were found for mothers and fathers, especially when reported by youth (Lippold et al., 2018). Thus, although sex differences are sometimes found, systematic differences based on the sex composition of the dyad remain unclear.

Parent-Child Relationship Quality and Intergenerational Transmission of Psychopathology

One way that parent-child relationships are hypothesized to influence the development of externalizing problems is by supporting the intergenerational transmission of psychopathology. Robust evidence across decades of work shows that parent psychopathology is associated with youth externalizing problems (e.g., intergenerational transmission; Connel & Goodman, 2002; Branje et al., 2020; Jami et al., 2021). There is also robust evidence that parents experiencing mental health problems tend to exhibit more harsh and lax parenting and less positive or warm parenting (e.g., Berg-Nielsen et al., 2002; Park et al., 2017), and both offspring and father (but not mother) externalizing problems have been related to more negativity in parent-adolescent interactions (Kullberg et al., 2023). Parent-child warmth and hostility are key theorized indirect mechanisms of intergenerational transmission of psychopathology (among several other indirect mechanisms; Branje et al., 2020; Jami et al., 2021). However, it is rare for parent psychopathology to be included in studies examining associations of lability or longer-term changes in parent-child relationship quality with externalizing problems (e.g., in only two studies that we are aware of: Lippold et al., 2019 and Zheng & McMahon, 2022). We fill this gap, exploring whether lability plays a unique role in the development of externalizing behaviors, or whether it operates in conjunction with parent psychopathology in line with models of intergenerational transmission of externalizing behaviors.

Intergenerational transmission need not occur only from parents to children, but also includes child evocative effects. One study has examined child evocative effects and parent psychopathology associations with parent-child relationship lability. Higher youth delinquency in 6^th grade predicted more lability in fathers’ warmth across adolescence (Lippold et al., 2019). Further, parenting phenotypes are unlikely to only have a mediating role in the intergenerational transmission of psychopathology. Parenting phenotypes have also been shown to serve as moderators (e.g., warmth as a buffer and hostility exacerbating) of developmental trajectories of risk, including intergenerational transmission (e.g., Burt et al., 2003; Burt & Klump, 2014; Marceau et al., 2019). For example, the child evocative effects differed based on parent psychopathology: youth behavior problems predicted more warmth lability specifically for mothers who had high internalizing problems but predicted less warmth lability for mothers low in internalizing problems (Lippold et al., 2019). Zheng and McMahon (2022) found no evidence of evocative effects of kindergarten externalizing problems on lability in warmth from kindergarten to 5^th grade. Together, there is a need for additional studies to clarify these effects, especially studies that examine caregivers separately, include prior risk for psychopathology in parents and youth, test for nonlinear associations of lability with adolescent outcomes, and consider sex differences.

Genetic and Environmental Mechanisms of Association

A key limitation of research on parent-child relationship lability and youth externalizing behavior to date is that this work has thus far been conducted exclusively in families where parents and youth are biologically related and without a study design capable of disentangling genetic from putatively environmental influences. Intergenerational transmission of externalizing problems occurs via both genetic and environmental mechanisms (Jami et al., 2021; Marceau et al., 2022), and parent-child relationship quality is influenced by both parents’ and children’s genetic and environmental influences (Kretschmer, 2023; Marceau et al., 2016; McAdams et al., 2014). However, it remains unclear whether gene-environment interplay is involved in associations of lability and externalizing problems. It is important to use genetically informed designs in order to understand whether lability and parent psychopathology actually exert environmental influences on the child or the extent to which gene-environment interplay explains these associations. If lability is a unique environmental influence, this makes lability a potentially more malleable target of interventions focused solely on the parent. However, evidence of lability operating via gene-environment interplay could potentially point to different intervention strategies (e.g., targeting child behaviors instead of or in addition to parents’).

Associations between parent-child warmth and hostility with child externalizing behaviors can arise because of direct environmental effects, passive gene-environment correlation (rGE), evocative rGE, or a combination of these mechanisms. Passive rGE is a non-causal explanation whereby parents’ warmth or hostility is influenced by the parents’ genes, and the parents’ genes are passed to the child, and in the child, those genes (and not the warmth or hostility) also influence the child’s externalizing behavior. Evocative rGE occurs when the child’s externalizing behavior is genetically influenced, and the (lower) warmth or (higher) hostility is a response to that child’s genetically influenced externalizing behavior. Generally, there is evidence that each of these mechanisms plays a role in associations between parenting and externalizing behaviors (e.g., Jami et al., 2021).

The adopted-at-birth design is a useful tool for examining mechanisms by which parent-child relationship quality is associated with child behavior. In the case of the adopted-at-birth design, because adoptive parents (APs) do not share genes with the child, associations between parent-child relationship quality and child behaviors either operate as environmental influences on the child (which could be informed in part by genetic nurture, but not by genes parents and youth share), or as evocative effects (which can be tested in mediation models). Associations between birth parent (BP) characteristics and child behaviors, on the other hand, reflect genetic influences because BPs and children share genetic material but not the postnatal environment. Passive rGE is effectively controlled for because the adoptive parents share no genes with the adopted child. This design has been used to show, for example, that dimensions of children’s temperament (e.g., negative reactivity, Liu et al., 2020; anger, Shewark et al., 2021), which were each genetically influenced in the child, predicted adoptive parents’ hostility, both consistent with evocative rGE.

Consistent with the idea that parent psychopathology and/or genetic risk can affect parenting phenotypes and their associations with child outcomes, a final key mechanism of gene-environment interplay is gene-environment interaction (Samek et al., 2015). In the adopted-at-birth sample used here, the Early Growth and Development Study (EGDS; Leve et al., 2019), there has been general support for a goodness-of-fit interaction model across a wide array of parenting phenotypes and child outcomes. In the goodness-of-fit interaction pattern, the same parenting behavior is beneficial for some children but less beneficial for others based on their heritable characteristics (e.g., the child’s genetic predisposition or potential moderate the influence of their environment; Reiss et al., 2023). That is, the goodness-of-fit pattern allows for the observation that the same environment can have a positive or a negative effect for different children, in part based on their genetic predisposition or potential.

Although no studies to date have examined gene-environment interplay for lability in parent-child relationships, evidence of gene-environment interplay for parenting and externalizing behavior more generally (Reiss et al., 2023), and evidence of moderation in studies examining lability in parent-child relationships including child sex (Lippold et al., 2018) and parent psychopathology (Lippold et al., 2019) suggest that biological predisposition and/or environmental context may modify optimal parent-child relationship quality lability across middle childhood and adolescence. That is, lability, if an environmental influence on behavior, may be an additional intervention target that could be leveraged to reduce the intergenerational transmission of psychopathology. The EGDS sample affords a unique opportunity to examine the role of both heritable psychopathology risk and exposure to parental psychopathology in the postnatal period for associations between longer-term developmental changes and lability of parental warmth and hostility and adolescent externalizing behaviors to disentangle whether associations of parent-child relationship quality measures with youth externalizing (and potential moderation effects of parent psychopathology) in the prior literature reflect gene-environment interplay or environmental influences.

Present Study

Evidence is building that lability (fluctuations/inconsistency) of warmth and hostility in parent-child relationships across childhood is linked to adolescent externalizing behaviors, in addition to levels and developmental changes. Following prior studies (Marceau et al., 2015), we will quantify the amount of within-family variance into a lability score for each family, as well as examine levels and longer-term developmental changes in parent-child warmth and hostility across childhood. Studies examining lability have used samples of biologically related families, so the mechanisms by which lability in warmth and hostility may be associated with externalizing behaviors remains unclear. In the EGDS sample, where children were adopted into non-relative families at birth, genetic confounding is controlled by design, and adoptive parent warmth and hostility reflect environmental influences or evoked reactions to the child.

Aim 1: associations with externalizing in multivariate models.

We included two measures of externalizing behaviors, the first at age 11 (a proximal outcome co-occurring with the end of the developmental period captured in our models of parent-child relationship quality), and the second at the latest adolescent assessment available, which was age 13-15 (see measures section) to assess how earlier relationship development is associated with changes in externalizing behaviors across adolescence. We expected: H1: higher levels of hostility and lower levels of warmth would be associated with youth externalizing behaviors. H2: Increasing hostility and decreasing warmth would be associated with youth externalizing behaviors. H3: We expected mainly linear associations whereby higher lability in hostility and warmth will be related to more youth externalizing behaviors.

Aim 2: gene-environment interplay.

We included measures of BP psychopathology (indexing genetic risk for externalizing behaviors) and AP psychopathology (indicating environmental risk for externalizing behaviors) in the multivariate models for aim 1. In aim 2, we include interactions between genetic and postnatal risk. These interactions are exploratory since no other study has included separate indicators of genetic and environmental risk for psychopathology when examining associations of lability with externalizing behaviors. Based on previous findings in EGDS, we expected that genetic influences (BP psychopathology) would moderate the association between parent-child relationship quality and externalizing, consistent with the goodness-of-fit model.

Sensitivity analyses.

EGDS includes two adoptive parents per family, designated as adoptive parent 1 (AP1) and adoptive parent 2 (AP2). About 7% of the sample include same-sex parents. AP1 is typically a mother (96.4%) and AP2 is typically a father (94%). Given the arbitrary labels of AP1 and AP2, we instead use more meaningful conceptual labels of mothers and fathers in our analyses.¹ Finally, given that the prior literature has examined sex differences of not only parents but also youth, but are sufficiently mixed to prevent strong hypotheses, we have also included a series of sensitivity analyses exploring interactions with child sex. These analyses are conceptualized as exploratory, included for completeness, and are intended to aid in future hypothesis generation.

Methods

Participants

Participants were drawn from the Early Growth and Development Study (Leve et al., 2019), a prospective longitudinal study of children adopted at birth (mean age = 6 days, SD = 12.45, maximum = 91 days). We leveraged data from 561 adopted children (57% male, 55.6% White non-Hispanic, 19.3% multiracial, 13% Black, 10.9%, Hispanic, 1.2% other) and their birth parents (BPs) and adoptive parents (APs), collected in two cohorts recruited in 2003-2006 (cohort 1) and 2008-2010 (cohort 2). Most adoptive families included an adoptive mother and father (90.8% at the start of the study, 80% at the age 11 assessment), with some same-sex APs (7.0% at the start of the study, 7.2% at the age 11 assessment), single APs (1.8% at the start of the study, 1.9% at the age 11 assessment), or separated or divorced (none at the start of the study, 11.7% at the age 11 assessment). Compared to APs, BPs were more ethnically diverse (BP: ~70% White vs. AP: ~90% White) younger at the time of placement (mid-20s vs. the mid–late 30s), had a lower median education (BP: high school vs. AP: 4-year college), and had a lower median income (BP: below $40,000 vs. AP: between $100,000 –$150,000).

Procedures

The study was approved by the Institutional Review Board at the University of Oregon. Families were eligible if the adoption was domestic in the United States, placement occurred before 3 months of age, the child was adopted into a non-relative family, had no major medical issues, and both adopted and birth parents could understand English at the 8^th grade level. Families were recruited with the help of 45 adoption agencies in 15 states that were representative of the various types of domestic adoption agencies in the United States at the time. In a cohort sequential design, the families were followed every couple of years; at the time of the drafting of this manuscript, age 15 data collection is ongoing for cohort 2 and cohort 1 is completing a late adolescent assessment. Thus, the latest wave of completed data are for cohort 1 at approximately age 15 and cohort 2 at approximately age 13. Further, due to the timing of the funding and the differences in ages of the two cohorts, there are some differences in assessments across cohorts. Most importantly, for the parent-child relationship measures, cohort 1 was assessed at age 7 whereas most of cohort 2 was assessed at age 9 (see parent-child relationship section), and cohort 1 does not have an age 13 assessment on the outcome measures.

Measures.

Parent-child relationship quality was measured via parent self-report on the warmth and hostility scales of the Iowa Warmth and Hostility (Dunn et al., 2011; Melby & Conger, 2001), including all assessments available between (and including) age 2 and 11 years to capture childhood and adolescence. Cohort 2 did not systematically include a measurement occasion at age 7; only 50 youth in cohort 2 had age 7 data. Cohort 2 children were also assessed at age 9 (Cohort 1 does not have an age 9 assessment). Thus, if a child in cohort 2 was missing age 7 data, we supplemented their data with age 9 data instead. This yielded 5 assessments for all children that were used to derive the intercept, slope, and lability scores; the target age at the first assessment was 2y, second assessment: 4.5y, third assessment: 6y, fourth assessment: 7y (sometimes age 9 for Cohort 2), and fifth assessment: age 11y. See Supplemental File 1 “Warmth and Hostility Levels, Changes, Variability” for the distributions of age at each assessment and the data cleaning code. Across each rater and assessments, Cronbach’s alphas suggested good internal consistency for warmth and hostility measures (α > .70). Description of the creation of levels, slopes, and lability measures are provided in the analytic strategy and results section.

Adolescent externalizing behaviors were measured using the average of mothers and fathers report on the externalizing broadband scale of the Child Behavior Checklist (Achenbach & Rescorla, 2001) in order to reduce single-rater bias. We included two externalizing scores, one in early adolescence, at age 11 for both cohorts (M = 11.37, SD = 0.54, min = 10.48, max = 12.88). We also examined externalizing behaviors at the last available assessment for each cohort, which was age 13 for cohort 2 (M = 13.19, SD = 0.42, min = 12.60, max = 14.59) and age 15 for cohort 1 (M = 15.74, SD = 0.55, min = 14.92, max = 18.07 years). Cronbach’s alphas suggested good internal consistency for each rater at each assessment (α > .89). mothers and fathers-reported externalizing scores were correlated, r = .69, p = <.001, at each assessment.

The raw scores were used for data analysis. For descriptive purposes, at age 11, 71.4% of youth had both parents report symptoms in the normal range, 6.9% of youth had both parents report symptoms in the clinical range, and 21.6% had one or both parents report borderline clinical or clinical problems based on published T-scores. At the last available assessment (age 13-15), 72.9% of youth had both parents report symptoms in the normal range, 5.1% of youth had both parents report symptoms in the clinical range, and 22.0 % had one or both parents report borderline clinical or clinical problems.

Externalizing behaviors were skewed (see Supplemental File 1 “Outcome Var Prep” for histograms), with some outliers that were >3 SD above the sample mean. Thus, we first winsorized outliers to the 3SD value and then square root transformed the outcome data to better approximate a normal distribution in order to meet the assumption of hypothesis testing models that the residuals are normally distributed.

Heritable and Postnatal Risk for Externalizing.

The same strategy was used to measure the children’s heritable (BP psychopathology, because BPs and children share genetic material but not postnatal environments) and postnatal (AP psychopathology, because APs and children share postnatal environments but not genetic material) risk for externalizing behaviors. The heritable risk scores have been previously described and used in the EGDS sample (Marceau et al., 2019; Marceau et al., in press). Based on the literature showing that intergenerational transmission of psychopathology is more likely to be captured by a general factor than one-to-one associations of symptom type (e.g., parent internalizing predicting specifically child internalizing; Marceau et al., 2022), the risk scores reflect a general psychopathology (p-factor) like score based on measures of externalizing, internalizing and substance use problems. Principal Component Analysis (PCA) was used to create measures of externalizing, internalizing, and substance use based on four indicators each (see below). Then, an overall ‘p-score’ was conceptualized and calculated as a higher-order factor based on the factor scores for substance use, internalizing problems, and externalizing behaviors (see Marceau et al., in press). PCA’s were computed in r using the FactoMineR (Lê et al., 2008) and missMDA (Josse & Husson, 2016) packages in order to accommodate missing data on the indicators with single imputation (see Marceau et al., 2019). Results of the PCA analyses have been previously reported (Marceau et al., in press); they are also reproduced and available in the supplemental file “TECH REPORT EGDS Genetic Risk Scores” on OSF: https://osf.io/ta4fw/ (for BPs) and Supplemental File 1 “AP Psychopathology scores” for APs.

Externalizing, internalizing, and substance use indicators.

For BPs, externalizing, internalizing and substance use scores included eight indicators: (a) birth mother and birth father diagnoses of psychopathology (b) birth mother and birth father symptoms of psychopathology (c) birth mother and birth father onset age of disorder, and (d) birth mother and birth father’s proportion of first-degree relatives with that type of problem, as each of these phenotypes are expected to reflect greater genetic risk (see Marceau et al, 2019 for more details and specific items). For BPs, externalizing scores included data from conduct disorder and antisocial personality from the Diagnostic Interview Schedule (DIS; Robins et al., 1981). Internalizing scores included major depression, brief recurrent depression, dysthymia, separation anxiety, adult separation anxiety, social phobia, agoraphobia (with/ without panic), panic disorder, specific phobia, and generalized anxiety from the Composite International Diagnostic Interview (CIDI; Kessler & Üstün, 2004). Substance use scores included alcohol abuse and dependence, drug abuse and dependence, and tobacco dependence from the CIDI. Proportion of first-degree relative scores were asked via separate items.

Adoptive parent (AP) psychopathology scores were created to resemble BP (genetic risk) psychopathology scores, although there were some measurement differences. First, APs did not have data on agoraphobia or separation anxiety. Thus, the AP internalizing scores are from a reduced item set compared to the genetic risk scores. In addition, DIS data was not collected for APs. Instead, at child age 9 and 18 months, APs reported on their antisocial behavior on the Antisocial Action Questionnaire (Levenson et al., 1995), which includes items such as telling lies, cheating at work or other places, stealing, and driving recklessly (conceptually similar to antisocial personality problems). For AP’s, first degree relatives indicate a higher (extended) family shared environmental effect, as the child would potentially have more exposure to family members with psychopathology.

Covariates included two adoption process variables: openness and knowledge of the other parent(s), two prenatal risk indicators: smoking during pregnancy and pregnancy complications, cohort (binary: 1 or 2), and exact age at the 11-year assessment (for the age 11 externalizing outcome only). The adoption openness variable is a standard covariate in the EGDS study as openness/contact is a threat to the validity of the study design, which separates genetic and postnatal environmental influences by ensuring that adoptive and birth parents are completely unrelated individuals. More open adoptions with more contact introduces the possibility that adoptive parents’ behaviors are influenced by the birth parents themselves, introducing a gene-environment correlation that operates outside of the child’s actual behavior. As described elsewhere (Ge et al., 2008; Marceau et al., 2019), at the first assessment birth mothers and both adoptive parents reported on the extent to which they perceived that the adoption was open on a 7-point scale (1 = very closed; 7 = very open). They also rated the extent to which the respondent knew about the other parents’ (e.g., AP’s knowledge of BP’s and BP’s knowledge of AP’s) physical and mental health, ethnic background, reasons for adoption and family health. The standardized mean of the three reports was used to measure adoption openness and knowledge, respectively.

Past work in the sample used here has identified smoking during pregnancy as an important predictor of conduct problems in middle childhood in models that include genetic risk and parental hostility (Marceau et al., 2019). Thus, we will include smoking during pregnancy as a key covariate here. Frequency of maternal smoking during pregnancy was measured via birth mother self-report on a pregnancy history calendar (adapted version of the life history calendar; Caspi et al., 1996) assessed at 4 months postpartum. Mothers reported the average number of cigarettes smoked per day in each trimester, which we averaged across trimesters (Marceau et al., 2019). Forty-three percent (43%) of mothers reported smoking during pregnancy. Pregnancy complications were also measured using a weighted risk index (PRI), including a wide variety of prenatal risks (e.g., infections, high blood pressure, excess weight gain, maternal age-related risk). Most mothers (75%) experienced 1-3 distinct types of pregnancy complications severe enough to be potentially harmful or relevant to the fetus (Marceau, De Arujo-Greecher, et al., 2016).

Missing Data

Missing data in the current study come primarily from attrition. Supplemental File 2 “Preliminary Analyses: Missing Data” includes a depiction of missing data patterns and percents. Overall, 86.7% of the data were present. The variables most systematically missing were parental warmth and hostility variables (between 12 and 19% missingness per variable), age 11 externalizing (27% missing) and age 13-15 externalizing (49% missing). We first conducted Little’s MCAR test on all of the variables included in the analysis, and found the data were missing completely at random (statistic = 818, df = 797, p = .30, number of missing patterns = 51). We nonetheless examined differences in study variables and sample demographics across groups where (a) any relationship quality measure was missing (25% missing any measure across variables) vs. was not missing, (b) age 11 externalizing data were missing vs. were not missing, and (c) age 13-15 externalizing data were missing vs. were not missing. Variables included covariates and earlier predictors (cohort, sex, adoption openness, BP and AP psychopathology, smoking during pregnancy; relationship measures for age 11 and age 13-15 externalizing behaviors; age 11 externalizing behaviors for age 13-15 externalizing behaviors), as well as demographic indicators (placement age, child race/ethnicity, Adoptive Parent 1 (mothers) and Adoptive Parent 2 (fathers) education, AP household income, birth mother, mothers and fathers ages at the birth of the adopted child). These analyses yielded a total of 76 t-tests, so we used a Benjamini-Hochberg adjustment to control multiple testing. Cohort 2 was more likely to be missing any age 11 externalizing data, t(254.66) = −4.85, p <.0001). This cohort effect is likely explained in part because the Cohort 2 age 11 assessment occurred during the COVID-19 pandemic, and we experienced some recruitment difficulties during that time; Cohort 1 completed the age 11 assessment pre-COVID19 pandemic. Youth who were younger at the age 11 assessment were more likely to be missing age 13-15 data, t(256.82) = −3.46, p = .00063. This age effect may reflect a difference in the timing of assessment between cohorts – Cohort 2 was a bit older at the age 11 assessment (11.7 on average) than Cohort 1 was (11.2 on average). There were no other significant predictors of missingness.

Analytic Strategy

All data were analyzed using R, version 4.3.0 (R Core Team, 2023).

Data Preparation.

Supplemental File 1 includes all data preparation code and results.²

Parent-child Relationship Measures.

We used multilevel models run via the lme4() (Bates et al., 2009) and lmerTest() (Kuznetsova et al., 2015) packages to quantify developmental trends and lability in parental warmth and hostility from age 2 to 11 years, constructed for mothers and fathers separately. Prior to fitting multilevel models, we selected only individuals who had at least 3 of the 5 assessments (excluding 66 participants for mothers’ warmth, 83 for mothers’ hostility, and 104 for fathers’ warmth and hostility). First, we ran an “empty” model to calculate intra-class correlations which yields information about the extent of between-family differences and within-family variation in mothers and fathers’ warmth and hostility over time. We then fit a series of multilevel models of change, using within-person centered age as the metric of time in order to account for differences in timing between assessments within and across individuals, and to assess a purer within-person developmental effect (without confounding between person differences in age at any assessment). The series of multilevel models included: 1. linear growth (with random slope), 2. quadratic growth (with random linear slope and acceleration terms), 2b. quadratic growth (with only random linear slope), and 3. Cubic growth (with random linear slope and acceleration terms). If the fixed effect was not statistically significant (defined as p < .05), we moved back one step to the simpler model. If there were convergence issues, we removed random effects until there were no problems with convergence. For mothers’ and fathers’ warmth, model 1, linear growth with a random intercept and a random linear slope provided the best, most parsimonious fit to the data, and were thus used to quantify levels, slopes, and lability measures for warmth. For mothers’ and fathers’ hostility, model 2, quadratic growth with a random intercept, random linear slope, and random acceleration term provided the best fit to the data, and were thus used to quantify levels, slopes, and lability measures for hostility. See Supplemental File 1 “ICCs and MLMs” sections for full results.

We saved each individual’s estimated intercept term to index the intercept level of warmth and hostility, which due to the within-person centering is interpreted as the level of warmth or hostility half-way through the study, or in middle childhood. We saved each individual’s estimated slope to index longer-term developmental changes across the study period (from approximately age 2 to 11 years). Finally, we quantified lability by taking the standard deviation of each person’s time-specific residuals (between 3 and 5 per person).

Preliminary Analyses.

Prior to any hypothesis testing models, we examined plots of the data to understand a) correlation patterns, b) multicollinearity amongst measures, and c) whether lability should be assessed linearly or with quadratic terms. Code and results for these preliminary analyses are located in Supplemental File 2.³

Hypothesis-testing models.

To test hypotheses, we built regression models stepwise, separately for mothers and fathers in lavaan() (Rosseel et al., 2017) in order to use full information maximum likelihood estimation to handle missing data and obtain bootstrapped standard errors. Model 1 included only covariates: smoking during pregnancy, pregnancy complications, adoption openness and knowledge, household income, cohort, and child sex (and child age at the 11-year assessment for the age 11 externalizing behaviors outcome). Model 2 added parent-child relationship measures so that we could understand the additional variance explained by only these measures. Model 3 added birth (BP) and adoptive parent (mothers or fathers) psychopathology. Model 4 added interactions of BP and AP psychopathology with relationship measures.

Transparency and Openness

Study results and materials are available on OSF [https://osf.io/ta4fw/]. EGDS data is available upon PI (last three authors) request, as is full documentation of assessment and measures via codebooks and measurement books. All analysis code is available using the OSF link above. This study’s design and its analysis were not pre-registered. However, as is standard practice for accessing and using data from the EGDS, an abstract was submitted prior to analysis (also available using the OSF link above), which serves as a record of the initial plan as well as an opportunity for co-authors to comment on and shape the study aims and framing, which includes the original analytic plan. A description of deviations from our original analytic plan is included in Supplemental File 1 “Changes to the Original Analytic Plan”. Finally, we added several post-hoc analyses to aid in interpretation, explained in the results section and located in Supplemental File 2.

Results

Data Preparation

Parent-child relationship measures from age 2 to 11 years:

Model estimated middle childhood levels (intercepts), slope, and lability descriptive statistics, as well as correlations, are available in Table 1. Longitudinal plots of the raw data, fitted curves, residuals, and histograms of the saved parent-child relationship measures are included in Supplemental File 1 at the end of each “ICCs and MLMs” section. Results from ICC’s showed that across phenotypes, about half of the variance was attributable to stable between-family differences, and the other about half of the variance was attributable to within-family variation (see Table 1). For both mothers and fathers, middle childhood levels of warmth were relatively high (25.5 for mothers, 24.8 for fathers, on a scale of 4 to 28), and declined slightly over time at an average rate of −.13 points on the scale per year (SE = .01) for mothers (fathers: β = −.15, SE = .02). For both mothers and fathers, middle childhood levels of hostility were relatively low (11.0 for mothers and 10.5 fathers, on a scale of 5 to 35), and increased slightly over time at an average rate of .27 points on the scale per year (SE = .02) for mothers (fathers: β = .26, SE = .02). The quadratic slope typically manifested as a deceleration of this increase, mothers: β = −.05, se = .005, p <.001; fathers, β = −.05, SE = .006, p <.001. Developmental change (linear growth for warmth and quadratic growth for hostility) explained 14-33% of the within-family variance across phenotypes, with the majority of the within-family variation explained by lability (see Table 1).

Table 1.

Variance Explained from Multilevel Models of Change.

	Mothers’ Warmth	Mothers’ Hostility	Fathers’ Warmth	Fathers’ Hostility
	n = 495	n = 478	n = 457	n = 457
% Between-family variation (ICC)	56%	50%	51%	47%
% Within-family variation	44%	50%	49%	53%
% of within-family variation due to change	14%	24%	24%	33%
% of within-family variation due to lability	86%	76%	76%	67%

Note. Lability includes measurement error. To determine the % of total variation due to lability, multiply the proportion of within-family variation due to lability by the proportion of within-family variation (e.g., for mothers’ warmth, .86*.44 = .38, or 38% of the total variance in warmth is due to lability (+ measurement error), and .14*.44 = .06 or 6% of the variance in warmth is due to developmental change).

Table 2 shows that the measures of warmth and hostility middle childhood levels, slopes, and lability were generally correlated. For mothers’ warmth and hostility, a higher middle childhood level was associated with a steeper slope, r’s = .88 and .97, respectively, forecasting probable multicollinearity issues with including both in hypothesis testing models. These associations were moderately strong for fathers as well, r’s = .56 and .65, respectively. Within-parent, higher warmth during middle childhood and flatter slopes were associated with less lability in warmth (warmer parents were more consistently warm), r’s between −.23 and −.55. Within-parent, higher hostility middle childhood levels and steeper slopes were associated with more lability in hostility (more hostile parents fluctuated more in hostility), r’s between .18 and .42. Cross-parent within-phenotype associations were small to moderate, r’s between .08 and .39.

Table 2.

Correlations and Descriptive Statistics for Relationship Variables.

Note. N’s range from 455-495 per variable. Correlations ≥ |.09| have associated p values of < .05.

Preliminary Analyses

Correlations.

Findings from correlations among all study variables, including Pearson’s r, p-values, and n’s, and heatmaps are available in Supplemental File 2 – Main Analysis, “Correlations”, and bivariate associations of study variables with externalizing behaviors are also reported in Table 3. Sex was correlated with age 11 externalizing (boys > girls). Age 11 and 13-15 externalizing behaviors were correlated, r = .72. Adoption process variables, prenatal risk variables, and BP, mothers’, and fathers’ psychopathology were uncorrelated with externalizing behaviors at either age. Higher household income was related to fewer externalizing symptoms at age 13-15 (but not at age 11). Cohort was associated with age 13-15 (but not age 11) externalizing (cohort 2 > cohort 1). For mothers’ and fathers’ warmth, lower middle childhood levels and steeper declines were associated with more age 11 and 13-15 externalizing, r’s = −.19 to −.28. More mothers’ warmth lability was positively associated with age 11 (but not age 13-15) externalizing r’s = .16, .08, respectively; fathers’ warmth lability was not associated with externalizing at either assessment, r’s = .09, .03. For mothers’ and fathers’ hostility, higher middle childhood levels and steeper increases were associated with age 11 and 13-15 externalizing, r’s = .35 to .55. More mothers’ and fathers’ hostility lability were associated with age 11 but not age 13-15 externalizing, r’s = .24/.22 (age 11), .13/.02 (age 13-15), respectively.

Table 3.

Summary of Findings

	Mothers’ (AP1) Models						Fathers’ (AP2) Models
	Age 11 Externalizing			Age 13-15 Externalizing			Age 11 Externalizing			Age 13-15 Externalizing
Predictor	Biv. r	β	se	Biv. r	β	se	Biv. r	β	se	Biv. r	β	se
Genetic Risk for Psychopathology (G)	0.04	<0.01	(0.05)	0.01	0.03	(0.04)	0.04	0.04	(0.05)	0.01	0.07	(0.05)
Environmental Risk for Psychopathology (E)	0.10	−0.04	(0.05)	0.06	−0.07	(0.04)	0.10	−0.02	(0.05)	0.06	0.04	0.04
Smoking during pregnancy	0.07	0.02	(0.05)	0.01	−0.02	(0.05)	0.07	0.03	(0.05)	0.01	−0.05	(0.05)
Pregnancy Complications	0.02	0.01	(0.04)	0.02	<0.01	(0.04)	0.02	<0.01	(0.05)	0.02	−0.02	(0.04)
Cohort	−0.02	−0.01	(0.05)	0.10	0.11*	(0.04)	−0.02	−0.02	(0.05)	0.11	0.13*	(0.04)
Adoption Process: Openness	0.01	0.02	(0.05)	0.05	−0.05	(0.05)	0.01	0.01	(0.05)	0.05	0.05	(0.06)
Adoption Process: Knowledge	−0.04	0.01	(0.05)	−0.05	0.06	(0.05)	−0.04	−0.01	(0.06)	−0.05	−0.02	(0.04)
Child Sex (Female = 1)	−0.13*	−0.12 *	(0.04)	−0.05	0.03	(0.04)	−0.13*	−0.08	(0.04)	−0.05	0.05	(0.04)
Household Income	−0.10	−0.08	(0.04)	−0.12*	−0.08	(0.05)	−0.05	−0.05	(0.06)	−0.15*	−0.10	(0.05)
Age at 11-year assessment	−0.01	0.01	(0.05)				−0.01	0.01	(0.05)
Age 11 Externalizing				0.72*	0.71 *	(0.05)				0.72*	0.70 *	(0.04)
Warmth Intercept							−0.20*	−0.02	(0.06)	−0.21*	<0.01	(0.05)
Warmth Developmental Change	−0.27*	−0.06	(0.05)	−0.22*	−0.07	(0.05)	−0.19*	−0.05	(0.05)	−0.26*	−0.10 *	(0.05)
Warmth Lability	0.16*	0.01	(0.05)	0.08	−0.06	(0.04)	0.09	<0.01	(0.06)	0.03	−0.04	(0.04)
Hostility Intercept							0.46*	0.24 *	(0.07)	0.35*	0.01	(0.06)
Hostility Developmental Change	0.55*	0.51 *	(0.05)	0.40*	0.05	(0.06)	0.40*	0.19 *	(0.06)	0.40*	0.11 *	(0.05)
Hostility Lability	0.24*	0.01	(0.06)	0.13*	<0.01	(0.05)	0.22*	0.10	(0.06)	0.02	−0.10	(0.05)
G x Warmth Intercept								−0.12 *	(0.06)		<0.01	(0.06)
G x Warmth Developmental Change		−0.03	(0.05)		−0.05	(0.05)		0.06	(0.06)		0.01	(0.05)
G x Warmth Lability		0.07	(0.05)		−0.08	(0.05)		0.07	(0.05)		0.07	(0.04)
G x Hostility Intercept								−0.22 *	(0.07)		0.02	(0.06)
G x Hostility Developmental Change		−0.09	(0.05)		−0.03	(0.05)		0.11	(0.06)		0.04	(0.05)
G x Hostility Lability		0.04	(0.06)		0.14*	(0.05)		0.04	(0.06)		0.03	(0.05)
E x Warmth Intercept								−0.15 *	(0.07)		0.02	(0.06)
E x Warmth Developmental Change		−0.02	(0.05)		0.07	(0.05)		0.01	(0.09)		−0.02	(0.07)
E x Warmth Lability		−0.03	(0.05)		0.04	(0.04)		−0.03	(0.07)		−0.03	(0.06)
E x Hostility Intercept								0.04	(0.08)		0.01	(0.07)
E x Hostility Developmental Change		0.02	(0.06)		−0.06	(0.05)		−0.07	(0.07)		0.10	(0.06)
E x Hostility Lability		−0.06	(0.07)		0.03	(0.05)		0.02	(0.07)		−0.05	(0.06)

Table note. r is the bivariate correlation. β (se) refers to the standardized beta and associated standard error from the final model (model 4).

^*p < .05.

Bolded estimates are effects that survive the multivariate model. G = genetic risk for psychopathology (birth parent psychopathology p-score). E = environmental risk for psychopathology (adoptive parent psychopathology p-score). Full correlation results including p-values and bivariate n’s and among all predictors and outcomes are located in Supplemental File 2, “Preliminary Analyses: Correlations”. Full regression results including standardized and unstandardized solutions and R² values for each step are located in Supplemental 2, “Main Model Building”.

Multicollinearity.

Findings from linear regression models predicting age 11 and age 13-15 externalizing including different combinations of parenting variables are available in Supplemental File 2 “Check for multicollinearity”. For mothers’ hostility and warmth, middle childhood levels and slopes were multicollinear. There was no multicollinearity for fathers’ hostility or warmth. We thus needed to exclude either the middle childhood levels or slopes from models including mothers. We excluded the middle childhood levels term, as developmental processes were of greater interest in this study.

Nonlinearity of Lability.

Scatterplots with loess smoothing lines and results from regression models predicting each outcome (age 11 and 13-15) with a) lability and b) lability² terms separately for each measure of lability (mothers’ and fathers’ warmth and hostility) are available in Supplemental File 2 “Check for nonlinear associations of lability.” There was no evidence of nonlinear effects. Thus, only linear terms were included in hypothesis testing models.

Hypothesis testing.

Full results of model-fitting steps are available in Supplemental File 2 “Main Model Building”. We focus on effect sizes here.

Age 11 Externalizing.

Model 1 (covariates only) explained 3% of the variance and only sex predicted age 11 externalizing (girls had less externalizing than boys). Model 2 added relationship measures. The model including mothers’ measures explained 32% of the variance in age 11 externalizing (ΔR²: 29%), driven by one finding: Steeper mothers’ hostility increases were associated with higher age 11 externalizing. The model including fathers’ measures explained 25% of the variance in age 11 externalizing (ΔR²: 23%), driven by two findings: Higher intercept levels and increases in fathers’ hostility over childhood were each related to higher age 11 externalizing.

Model 3 added birth and adoptive parent psychopathology (e.g., genetic and environmental influences on psychopathology). Neither predicted externalizing behaviors.

Model 4 added interactions between BP psychopathology and relationship measures (GxE) and AP psychopathology with relationship measures (ExE). None were present in the model for mothers.

In the model for fathers, there were three interactions that were probed by first running a linear regression model using the stats() package which listwise deletes data (as opposed to using FIML as in our main analysis) but affords a test of regions of significance using the interactions() package (Long & Long, 2019). See main analysis tech report; “Follow-up tests” for all plots. First, a nominal interaction between BP psychopathology and fathers’ intercept levels of warmth, β = −.06, SE = .03, p = .04, 95% CI = −.11 to .003, although the confidence interval included zero. This interaction did not replicate in the listwise deleted linear regression and thus is not probed. Second, there was an interaction between BP psychopathology and fathers’ intercept levels of hostility, β = −.10, SE = .03, p = .003, 95% CI = −.17 to −.03, such that higher fathers’ hostility in childhood predicts more age 11 externalizing among children with lower-than-average BP psychopathology (e.g., low genetic risk), but not among youth with high genetic risk. Finally, there was an interaction between fathers’ psychopathology and fathers’ intercept levels of warmth, β = −.07, SE = .03, p = .03, 95% CI = −.14 to −.02, such that lower fathers’ warmth in childhood predicts more age 11 externalizing among children who also experience higher-than-average father psychopathology, but fathers’ warmth is unrelated to age 11 externalizing when fathers have average or low psychopathology.

Age 13-15 Externalizing.

In Model 1, age 11 externalizing strongly predicted age 13-15 externalizing. Additionally, Cohort 2 (assessed at age 13 on average) had higher externalizing behaviors than Cohort 1 (assessed at age 15 on average), likely reflecting a normative decline in externalizing behaviors over adolescence. This covariates-only model explained 57% of the variance in age 13-15 externalizing. Model 2, including mothers’ measures explained no additional variance in age 13-15 externalizing (ΔR²: −1%), and none of the relationship measures predicted age 13-15 externalizing. The Model 2 including fathers’ measures explained 61% of the variance in age 13-15 externalizing (ΔR²: 4%), driven by two findings: Increases in fathers’ hostility over childhood was related to residualized gains in externalizing behaviors from age 11 to 13-15 externalizing (e.g., predicted age 13-15 externalizing after controlling for age 11 externalizing), whereas increased hostility lability was related to declines in externalizing behaviors from age 11 to 13-15 years.

In Model 3, neither birth nor adoptive parent psychopathology predicted externalizing.

In Model 4, one interaction was found in the mothers’ model: BP psychopathology x mothers Hostility lability predicting residualized gains in externalizing from age 11 to 13-15 years, β = .13, SE = .04, p = .002, 95% CI = .03-.20. Using listwise deleted data, this interaction was no longer significant (p = .06), and there was no evidence that genetic risk for psychopathology moderated the effect of mothers’ hostility lability on residualized gains in externalizing behaviors from age 11 to 13-15. There were no interactions in the fathers’ model. Further, the negative association between increased hostility lability was related to declines in externalizing behaviors from age 11 to 13-15 years was no longer statistically significant.

Planned sensitivity analyses revealed only one interaction with child sex (of 20 tested), between mothers’ hostility slopes and age 13-15 externalizing behaviors. This interaction was not robust to listwise deletion but indicated that the effect of increases in mothers’ hostility on residualized gains in externalizing behaviors from age 11 to 13-15 may be somewhat stronger for boys than girls.

Post-hoc follow-up tests.

Although residualized change is a more powerful approach than using difference scores as the outcome, residualized change can inflate parameter estimates when the “baseline” (in this case age 11 externalizing) measure is correlated with the predictors (Castro-Schilo & Grimm, 2018). Thus, we also used a difference score approach to verify the robustness of findings for age 13-15 externalizing from Model 4. In the mothers’ model, results were replicated. In the fathers’ model, the effects of increasing hostility and decreasing warmth were not present.

In order to aid in interpretation of findings with regard to evocative child effects and potentially direct environmental influences, we also explored the influence of age 2 externalizing behaviors (measured and treated identically to how age 11 and 13-15 are described in the measures section). Results did not substantially change when including age 2 externalizing behaviors as an additional predictor for Model 4 (full code and results are available in Supplemental File 2 “Follow-up tests”). Correlations and multivariate models revealed some associations (summarized at the end of the supplemental materials) between AP psychopathology and age 2 externalizing with relationship quality measures. Taken together, follow-up analyses including age 2 externalizing lend credibility that our findings are not actually attributable to a combination of reverse causation and stability in externalizing and indicate that findings are likely a combination of some evocative child and subsequent direct environmental influences.

Summary of Findings.

There were several bivariate associations between measures of parent-child relationship quality and externalizing behaviors that did not survive in the context of the multivariate model (see Table 3). For early adolescent (age 11) externalizing, these included the effects of developmental declines in mothers’ and fathers’ warmth, middle childhood intercept levels of fathers’ warmth, lability in mothers’ warmth and hostility, and fathers’ hostility lability. In contrast, increases in mothers’ and fathers’ hostility and higher intercept levels of fathers’ hostility were associated with early adolescent externalizing behaviors even in the context of the multivariate model.

Regarding change in externalizing from early- to mid-adolescence, effects for fathers’ increases in hostility and declines in warmth were present but smaller than bivariate correlations, suggesting that much of that influence operates via earlier associations with externalizing, but also that increasing hostility and decreases in warmth from fathers is associated with increases (or less of the normative decline) in externalizing from early- to mid-adolescence. This is in contrast to intercept levels of fathers’ warmth and hostility (present in bivariate associations but not models of residualized change), and findings for mothers, wherein the effects for declines in warmth, increases in hostility, and higher hostility lability were not present in the multivariate model. This suggests that for most of the findings, the vast majority of the influence of these relationship measures operates via earlier associations with externalizing and is not likely influential for change in externalizing during adolescence.

Discussion

The present study adds to a growing body of literature suggesting that fluctuations in parent-child warmth and hostility are common across childhood, but in some cases are associated with child behavior problems. Strengths of this study include use of a genetically informed longitudinal adoption design that separates genetic from environmental influences by virtue of the study design. Because we found lability in parent-child relationships where parents were not genetically related to their children, our findings about associations between parent-child relationship measures and child externalizing behaviors can be interpreted as some combination of environmental effects of the parent on the child or evocative child effects (particularly for warmth lability), but they are not confounded by shared genetic influences or passive rGE due to our adopted-at-birth study design. We also focused on associations of lability in parent-child relationship quality in the context of a larger multifactorial model of development that included other key predictors of externalizing behaviors that may covary with parent-child relationship measures to more effectively isolate associations of lability with child externalizing behaviors, and found that lability was generally not a powerful predictor after accounting for these other developmental influences.

We characterized warmth and hostility in adoptive parents from age 2 to 11 years, finding support for between-family differences, developmental trends of a decline in warmth and an attenuating increase of hostility across childhood, and that more of the within-family variance was attributed to lability than developmental change. We also examined associations with externalizing outcomes, but with more mixed support of hypotheses. As hypothesized, (H2) increasing hostility was associated with externalizing in early adolescence and, for fathers, increasing hostility and decreasing warmth were associated with residualized gains in externalizing from early to mid-adolescence. We found some support (H3) for linear associations with lability, although these associations did not persist in the context of our broader model of the development of externalizing. Finally, we found limited evidence of interactions of parent-child relationship quality measures with heritable and postnatal risk for externalizing, and very little evidence of sex differences in the effects of lability. Follow-up tests revealed that fathers’ hostility lability and declining warmth effects may be environmental whereas both parents’ increasing hostility effects likely reflect bidirectional evocative and environmental associations.

Lability in Parent-Child Relationships and Externalizing Outcomes

Consistent with prior studies, we found that more of the variation in warmth and hostility was attributable to lability than developmental change, with proportions of variance highly consistent with prior reports (Lippold et al., 2018; Marceau et al., 2015; Zheng & McMahon, 2022). Also in line with recent conclusions from studies examining lability, our results add further weight to the idea that higher levels of lability in relationship quality is problematic, and that the associations between lability and child behavior are most frequently linear (Lippold et al., 2021). However, our findings temper this somewhat, as these associations with lability did not survive multivariate models. It was interesting that in both parents, warmth and hostility were correlated but only modestly, consistent with the idea that these phenotypes are not flip-sides of the same coin. Further, when considered together, hostility proved far more powerful for predicting externalizing than warmth for both parents, consistent with theory and findings on the differentiation and unique outcomes of warmth and hostility (e.g., Vaughan et al., 2021).

As noted by correlations between intercept levels and developmental slopes with lability measures, we found that warmer parents were more consistently warm, but hostile parents fluctuated more in hostility (less hostile parents were more consistent in levels of hostility), which is largely consistent with other measures warmth and hostility from 6^th grad to 8^th grade (Lippold et al., 2018). However, this pattern differs from (Zheng & McMahon, 2022), which found no evidence of associations of lability with levels or developmental trends in warmth from kindergarten to 5^th grade. Our assessment window aligns better with the latter study, as we examined youth from age 2 to 11 (typically 5^th or 6^th grade), however Zheng and McMahon (2022) had a more diverse sample that also included a high-risk sample selected for elevated conduct problems. Given the evidence in follow-up tests here and in the literature (Neiderhiser et al., 1999; Neiderhiser et al., 2007; Neiderhiser et al., 2004) on the evocative effects of child psychopathology on parent-child relationship quality, future research exploring family processes in samples at risk for child psychopathology and longer-term consequences for continuity and escalation of child mental health problems is warranted.

Caregiver differences.

Associations between levels, developmental change, and lability in warmth and hostility differed somewhat for mothers and fathers, and these differences may reflect differences in the functions of parents’ roles. Intercept levels and slopes were so highly correlated among mothers (r = .88 and .95 for warmth and hostility) that we could not include both in hypothesis testing models. However, for fathers, correlations were more modest (r = .56, and .65 for warmth and hostility). Further, associations of lability with intercepts and developmental slopes were somewhat higher (|r| about .1 to .2 stronger for mothers as compared to fathers). Further, fathers’ hostility was a more salient predictor of increases in externalizing from age 11 to 13-15 than mothers’ hostility was (though not for age 11 externalizing for which we found similar effect sizes for mothers and fathers).

These findings generally corroborate the idea that different parents provide different experiences to the child. A systematic review found that across 15 countries, for example, mothers tended to be more authoritative (e.g., behavioral control and warmth) whereas fathers were more authoritarian (e.g., psychological control and low warmth) (Yaffe, 2023). And, there is evidence that warmth is more salient than demandingness from mothers, whereas demandingness is more salient than warmth for youth emotional adjustment in adolescence (Van Lissa et al., 2019). Although discipline may be more common from mothers than fathers (Hallers-Haalboom et al., 2016), the less-frequent discipline coming from fathers may be more impactful for youth externalizing (Chang et al., 2003; Karreman et al., 2010).

Genetic and Environmental Mechanisms of Association

We found no evidence of genetic mechanisms, and no evidence of evocative rGE, though we did find some evidence of evocative child effects which could be influenced by unmeasured genetic influences. Although we specifically chose to examine birth parent general psychopathology to capture genetic intergenerational transmission, it may be that this multi-layered factor analytic approach was overly broad and did not best capture heritable risk. However, our measures of warmth/hostility are most likely characterizing the quality of the environment free from genetic confounds. That we found perhaps fewer associations than other studies or than we expected may show that those past estimates of the importance of warmth and hostility for adolescent externalizing could be inflated by gene-environment mechanisms, particularly passive correlations. Because the main findings of associations of relationship quality measures with externalizing did not diminish after controlling for earlier externalizing behaviors in post-hoc follow-up analyses, we believe our main findings are best understood as evidence for a combination of direct environmental effects of relationship quality on externalizing behaviors and bidirectional evocative and environmental effects. Specifically, the effects of increasing hostility across childhood are mostly likely reflective of bidirectional evocative and then subsequently environmental associations, whereas the effects of fathers’ hostility lability and declining warmth effects may have unique environmental associations with adolescent externalizing behaviors.

It was interesting that for mothers’ but not fathers’ own psychopathology predicted increased warmth and hostility lability in post-hoc follow-up tests. This is consistent with a spillover effect by which parents with elevated psychopathology symptoms experience more stress and are less able to provide consistent parenting over time. Because of the nature of psychopathology symptoms which wax and wane over years depending on the context of the parents’ life (e.g., more or less support or stress) and treatment, AP psychopathology could be expected to predict lability in relationship quality. This finding is in need of replication, especially in light of highly mixed findings in the prior literature: Lippold and colleagues (2019) found that higher maternal but not paternal internalizing was linked to parent-reported hostility lability (but not warmth or youth-reported lability), and higher paternal but not maternal internalizing symptoms were linked to parent-reported warmth lability (but not hostility or youth-reported lability), and Zheng & McMahon (2022) found no evidence that maternal depressive symptoms or earlier child behavior problems predicted lability in warmth. Thus, it remains unclear the extent to which and mechanisms by which parent psychopathology may be related to parent-child relationship quality lability. It is important to note, however, that Lippold et al., (2021) found some mixed evidence of moderated associations between parents’ internalizing symptoms and youth maladjustment that we did not test for here. It is possible, therefore, that child evocative effects are particularly context-dependent and may be more important under conditions of parent stress, emotion regulation challenges, and mental health.

Implications

Our findings have implications for our understanding of the intergenerational transmission of psychopathology. Studies of the intergenerational transmission of psychopathology have highlighted that the transmission of an underlying predisposition to psychopathology, akin to the p-factor used here, is linked to youth externalizing and internalizing symptoms via both genetic and environmental mechanisms (Jami et al., 2021). These findings are often found in twin studies that can explain all of the variance in youth psychopathology (Marceau & Neiderhiser, 2022; Marceau et al., 2022). Here, the predictive power of parents’ psychopathology was limited by what could be measured in birth and adoptive parents. At age 2, externalizing behaviors were modestly linked to both birth parent (r = .12) and adoptive parent (r = .26) psychopathology scores, but these correlations were no longer present by adolescence. The most predominant indirect mechanism of intergenerational transmission of psychopathology is through parenting practices (Jami et al., 2021). Our findings suggest that this may be in part the case for mothers’ increases in hostility across childhood, but that more of the measures of parent-child warmth and hostility were informed by earlier child externalizing behaviors than by birth or adoptive parent psychopathology. That is, evocative child effects likely explain some of the intergenerational “transmission” of psychopathology in adolescence if the adolescent previously had evoked at least some of the parents’ psychopathology. Of course, these conclusions come with the caveat that we were unable to capture all genetic and environmental risk for psychopathology, and that we chose to focus on the general liability instead of homotypic or heterotypic transmission of more specific forms of psychopathology.

More broadly, we showed that parent-child relationship quality is a dynamic, changing phenotype across childhood, consistent with prior studies and some predictions from family and dynamic systems theories. Changes and fluctuations, as noted by sample average levels, are normative, but exaggerated shifts in parent-child relationship quality can be problematic. That several associations of parent-child relationship quality, namely increases in hostility from both parents remained associated with externalizing behaviors during adolescence in the context of our multivariate model and genetically-informed study design highlights the important role, via environmental and/or evocative child effects, or these phenotypes for the development of externalizing behaviors. It also lends credibility to interpretations in non-genetically informed literature that parent-child relationship quality measures, including lability, can be thought of in terms of environmental influences and responses to children.

Reducing externalizing behaviors in adolescence is a critical developmental goal given the high associations with lifelong problems like substance use (Marceau et al., 2020; Marceau et al., 2021; Trucco & Hartmann, 2021). The evidence provided here adds to the growing number of studies suggesting that bounding the increase in hostility that is to some extent normative across adolescence is likely to be a critical intervention target for reducing externalizing behaviors in adolescence (Backhaus et al., 2023; Gershoff et al., 2017). There are a number of interventions (Backhaus et al., 2023) that include components to teach parenting skills to reduce parental violence and/or physical punishment (both phenotypes that would be expected to be correlated with hostile relationship quality). However, it is imperative to keep in mind that lability across years is a very different phenotype than studies using data on a shorter timescale that find rigidity in interaction patterns as a risk factor for externalizing (Hollenstein et al., 2004). The year-to-year fluctuations capture by lability may be more indicative of broader family patterns that are to some extent caused or bounded by structural influences such as changes in schools, extracurricular and work schedules, and relative importance of common topics that families may face that could lead to conflict and/or opportunities to express warmth (e.g., varying levels of needs/struggles to get places like school or work on time, time spent together, or shared or person-specific stressors that could spill over into relationship quality). Intervention trials targeting specific parenting skills for use over the course of interactions or days are expected to produce skills and interaction patterns that canalize into longer-term developmental patterns (Lougheed, 2020). In the future, the use of measurement burst designs that can map finer-grained and longer-term lability in parent-child relationship measures will clarify whether lability is a product to some extent of consolidation of interaction patterns on shorter timescales and/or a unique phenotype driven by the structural demands of the family.

Limitations

As noted previously, there were several measurement considerations. First, it is important to reiterate that lability measures include all measurement error. Second, we were only able to capture lability over years. Theoretically, there are more nuanced processes occurring at smaller timescales that canalize into the patterns we can observe here (Lougheed, 2020; Marceau, 2023), but we were unable to assess smaller timescales in this study. Third, the measure of genetic risk is also limited because the current study design can only infer genetic risk based on associations between birth parent characteristics and adopted child characteristics. We reasoned, based on prior studies, that a p-factor like score may best index genetic risk for externalizing given non-specific intergenerational transmission of psychopathology. That we failed to uncover genetic influence in this study design should not imply that genetic influences are less important, but rather likely indicate measurement error or a mis-match in birth parent and adopted child phenotypes. As in all behavioral genetic work, it is critical to conduct similar analyses testing similar questions in different types of study designs, as each genetically-informed design comes with its own sets of strengths and limitations.

Fourth, despite a similar measurement strategy and approach, there were some differences in measurement of parent psychopathology, specifically for externalizing phenotypes, which make the contrast between adoptive and birth parent psychopathology inexact. Finally, there were some measurement differences across cohorts. Age 13 data were not collected for Cohort I, and Cohort II age 15 data collection is ongoing (with insufficient sample size at present). This age difference introduces heterogeneity in the outcome variable, although it should be noted that a) there is also age heterogeneity within cohort, b) both cohorts were assessed within the same developmental period: mid-adolescence, and c) many other studies include wider age ranges than captured by both cohorts combined here. There were also some differences in the timing of lability assessments across cohorts – namely, for about 1/3 of the sample one of the measures of parent-child relationship quality occurred at age 9 instead of age 7. This difference may introduce heterogeneity in the estimates of lability, although we do not anticipate that this issue would introduce systematic bias between cohorts as the entire span captured was ages 2 to 11 for all youth in the sample.

Families change over time, and this is also true of EGDS families. Parents reported who was AP1 (referred to as mothers here) vs. AP2 (referred to as fathers here) at the beginning of the study, and this sometimes fluctuated over time. We re-aligned the reporters so whenever possible whoever was coded as the mother (and whoever was coded as the father) was consistent over time in this analysis. Our rationale was that youth will perceive changes in their relationship with their parent compared to that same parent over time rather than who is considered the “primary” caregiver (AP1) in any given year. At the same time, there were a handful of stepparents who were either mothers/AP1 or fathers/AP2 over time (range = 1 to 7 for fathers at the age 15 assessment). Thus, for a very small few children, lability could be driven by changes in who the parent was rather than the actual relationship with a single parent over time. Given the very small number of cases, we elected to keep these families in our analysis because the child is indeed experiencing warmth and hostility from them. The inclusion of these cases could inflate lability measures for those children. However, the sample size of children with stepparents were too small to test for differences in lability or externalizing behaviors.

Another key limitation in this study is missing data. As described above, missing data came primarily from attrition (in part due to assessment challenges during the COVID-19 pandemic) and from missing birth father data. Considering missing data, our sample is small compared to some other studies of lability. Our analysis of missingness revealed few predictors of missingness, and we chose to use FIML to accommodate missing data. Nonetheless, this missing data does limit our power to detect effects, particularly interactions predicting change in externalizing behaviors, and may limit generalizability of the findings.

There is also some concern about shared method variance. Adoptive parents reported on their own warmth and hostility, their own psychopathology symptoms, and child externalizing behaviors. We attempted to mitigate this shared method variance by examining mothers’ and fathers’ relationship measures separately, combining both parents to form psychopathology scores via principal components analysis, and using combined rater composites (averages) for externalizing behaviors. Shared method variance would inflate associations in the current study. Finally, we conducted a relatively large number of tests (e.g., 66 unique associations in the final models) and so multiple testing is a concern. It was for this reason that we chose not to interpret the findings from interactions in the discussion section: we view these as preliminary and believe it important to present the interactions that were and were not present but hesitate to over-interpret potentially false-positive findings prior to replication. Instead of correcting for multiple testing, we chose to focus on effect sizes and conducted a number of preliminary and post-hoc analyses to probe the robustness of results and weighed them accordingly in our discussion of findings.

Conclusion

The present study addressed gaps in the literature by using a genetically informed longitudinal adoption design that separates genetic from environmental influences by virtue of the study design and analyzing associations of parent-child relationship quality measures across child and adolescence in a longitudinal multivariate model. We corroborated studies of parents and biologically related children showing sample average increases in hostility and decreases in warmth from age 2 to 11, with most of the variance within-families over time attributable to year-to-year fluctuations, or lability. We add to the literature on lability by showing largely linear patterns of association when found, however, largely these associations do not persist in the context of a multivariate model. There were more effects for fathers than mothers, and fathers’ intercepts and slopes of change uniquely contributed to externalizing behaviors. Associations between both parents’ increasing hostility across adolescence with higher age 11 externalizing, and for fathers, increasing hostility and decreasing warmth with increases in externalizing across adolescence most likely reflect bidirectional evocative and environmental associations.

Public significance statement.

The present study used a longitudinal adopted-at-birth design to understand how longer-term developmental changes and year-to-year fluctuations in parent-child warmth and hostility are related to adolescent externalizing behaviors. Our findings corroborate the idea that supporting families, and especially fathers, to maintain warmth and decrease expressions of hostility across childhood, especially with their children who have externalizing behaviors, would help reduce adolescent externalizing behaviors.

Data, materials, and code availability statement.

Data supporting the findings of this study are available upon reasonable request to the study PIs (Ganiban, Leve, and/or Neiderhiser). All data prep and analytic code and results are available via the tech report available at https://osf.io/ta4fw/?view_only=d86cc35bd5354cddb45eb937bba4f999.