University of Birmingham Understanding the terrible twos

Impairments in both executive function and parent–child interactions are associated with child externalizing behavior, but few studies have tested the uniqueness of these associations in the first years of life. Addressing these gaps, the current study involved an international sample ( N = 438; 218 boys) who, at 14 and 24 months, completed an innovative battery of executive function tasks and were filmed at home in dyadic interaction with their mothers, enabling detailed observational ratings of maternal support. In addition, parents rated infant temperament at 4 months and externalizing behavior at 14 and 24 months. Cross-lagged longitudinal analysis showed a unidirectional developmental association between executive function at 14 months and externalizing behavior at 24 months. In addition, infant negative affect moderated the inverse association between maternal support at 14 months and externalizing behavior at 24 months. The benefits of maternal support were only evident for children with low levels of negative affect in infancy. We discuss this finding in relation to theoretical models that highlight child effects (e.g. models of vantage sensitivity).

that underpin the control of thought and action) (e.g., Hughes, Dunn, & White, 1998) or (b) adverse early parent-child interactions (e.g., Pinquart, 2017). Despite progress within each of these strands of research, the first two years of life remain relatively unexplored. To address this developmental gap and provide a bridge between research on neurocognitive and family factors, we examine the unique roles of children's EF and the quality of early parent-child interactions in predicting individual differences in externalizing behavior in 2-year-old children.

| Executive function and externalizing behavior
More than two decades ago, Moffitt (1993) proposed that executive dysfunction might explain the characteristic difficulties of inhibiting emotions and controlling behavior associated with externalizing problems. Hughes et al. (1998) extended this 'executive account' of externalizing behavior to a community sample of 'hard-to-manage' preschoolers, who were shown to perform poorly on measures of planning, inhibition, and flexibility, when compared with typically-developing peers. Subsequently, a meta-analysis of 22 studies of 3-to 6-year-old children reported a moderate but significant association between EF and externalizing behaviors, r = .22 (Schoemaker, Mulder, Dekovic, & Matthys, 2013). While the association between EF and externalizing was stronger among clinical/ referred samples, r = .29, it was also significant among communitydwelling preschool children, r = .18. Executive dysfunction may therefore underpin even normative individual differences in early childhood externalizing behaviors. Although associations between externalizing behaviors and EF have been reported in children as young as 2 ½ years old (e.g., Hughes & Ensor, 2005), little is known about younger infants. That said, studies of infant effortful control indirectly support the executive account. Specifically, Kochanska, Murray, and Harlan (2000) found that 22-month-old toddlers who resisted taking a desired snack showed lower levels of anger than peers who did not exert effortful control. Furthermore, effortful control at 22 months was negatively correlated with externalizing behaviors at age 6 (Kochanska & Knaack, 2003). More recently, Adrichem, Huijbregts, Van der Heijden, van Goozen, and Swaab (2019) reported negative associations between infant effortful control at 12 months (observed during a parent-child dyadic interaction) and physical aggression at 20 months. Likewise, Frick, Forslund, and Brocki (2019) reported negative associations between observed sustained attention at 10 months and parent-rated ADHD symptoms at 36 months. We build on these studies and on recent breakthroughs in measuring EF in infancy (e.g., Devine, Ribner, & Hughes, 2019;Miller & Marcovitch, 2015) to investigate the relations between individual differences in EF and externalizing behaviors in the first 2 years of life.
Although EF and externalizing behaviors (e.g. tantrums, physical aggression, defiant noncompliance and persistent rule-breaking) are correlated in early childhood, the heavy reliance on cross-sectional designs (Schoemaker et al., 2013) means that this correlation is open to at least two interpretations. According to Moffitt's (1993) account, executive dysfunction underpins the emergence of externalizing behaviors. If this executive account holds then longitudinal data will reveal a unidirectional link between early EF and later externalizing behaviors. Alternatively, by hindering children's involvement in social activities that foster internalization of strategies to enhance inhibition, flexibility, or forethought, early externalizing behaviors might constrain the emergence of EF (e.g., Hughes & Ensor, 2008).
If externalizing behaviors set the stage for poor EF, then longitudinal data will reveal a unidirectional link between early externalizing behaviors and later EF. Only a small number of longitudinal studies involving children aged over 2½ years (Hughes & Ensor, 2008;Kahle, Utendale, Widamen, & Hastings, 2018;Sulik, Blair, Mills-Koonce, Berry, & Greenberg, 2015) have tested these competing accounts.
The findings to date favor the view that poor EF is a precursor of externalizing behaviors and not vice versa. Using a longitudinal crosslagged model, our first aim was to extend the developmental scope of this work by testing, for the first time, the strength and direction of association between EF and externalizing behaviors in children under the age of 2 years.

| Parent-child interactions and externalizing behaviors
In a recent meta-analysis, Pinquart (2017)

Research Highlights
• This study examines the unique influences of executive function and parent-child interactions on externalizing behavior at a very young age (24 months).
• The study involves a large longitudinal sample and combines age-appropriate executive function tasks, observational ratings of parent-child interactions, and ratings of temperament and externalizing behaviors.
• Cross-lagged analysis show that poor executive function at 14 months predicts externalizing behaviors at 24 months (but not vice versa).
• High quality parent-child interactions at 14 months predict reduced externalizing behaviors at 24 months, but only among children with low levels of negative affect. externalizing behaviors. That is, increases in parental support were linked with lower levels of externalizing behaviors in children (Pinquart, 2017). Complementing these meta-analytic results, Frick et al. (2019) reported that observed maternal sensitivity at 10 months was associated with reduced child ADHD symptoms at 36 months. These results are consistent with self-determination theory, which proposes that autonomy supportive parenting, aimed at bolstering children's goals, sense of competence, and need for warmth, is crucial for healthy child adjustment (Ryan, Deci, & Vansteenkiste, 2015). Autonomy supportive parenting has been studied from infancy (e.g., Grolnick, Frodi, & Bridges, 1984) through to adolescence using a range of age-appropriate observational measures (Ryan et al., 2015).
Recent meta-analytic data also indicate that a range of parenting measures are associated with variation in children's EF performance (Valcan, Davis, & Pino-Pasternak, 2018). Of note, autonomy supportive parenting (measured using parent-child observations) at 15 months predicted children's performance on tests of EF at 18, 26, and 36 months (Bernier, Carlson, Deschênes, & Matte-Gagné, 2012;Bernier, Carlson, & Whipple, 2010). Moreover, responsive parent-child interactions at 15 months were associated with children's performance on measures of effortful control (e.g. waiting for a desirable snack) at 25 months (Kim & Kochanska, 2012). Interestingly, a more global measure of parental sensitivity at 10 months did not uniquely predict inhibition task performance at 18 months (Frick et al., 2018). In line with self-determination theory, these findings suggest that links between EF and externalizing behaviors may reflect common associations with variation in parenting quality, and more specifically, the degree to which parents support their child's emerging autonomy. Thus, our second aim was to examine the strength, uniqueness and direction of association between observed maternal autonomy support, EF and child externalizing behavior in the first two years of life.
The recognition that adverse or positive family environments can have contrasting effects upon different children has considerably advanced our understanding of how family environments influence child adjustment (Belsky, Bakermans-Kranenburg, & Van IJzendoorn, M.H., 2007). According to the classic 'diathesis-stress' (i.e. vulnerability) accounts (e.g., Monroe & Simons, 1991), some children are more vulnerable to adverse environments than others. Conversely, theorists have called for researchers to investigate variation in the extent to which children benefit from positive environments. This 'vantage sensitivity' is distinct from both classic vulnerability and 'for-better-or-worse' effects of differential susceptibility (Pluess & Belsky, 2013). Infant temperament is a useful marker of children's responsiveness to environments. Infant negative affect, a dimension of temperament, can be measured early in development, exhibits relative stability over time, and reflects variation in infants' responsiveness to environments (Putnam, Rothbar, & Garstein, 2008;Slagt, Dubas, Dekovic, & van Aken, 2016). Moreover, meta-analysis indicates that, compared with other dimensions of temperament including surgency and effortful control, negative affect or 'difficult' temperament is a particularly consistent moderator of parental influences on child outcomes (Slagt et al., 2016). Moderating effects of negative affect on the relations between parenting and child outcomes may explain the relatively weak nature of direct associations between parenting and externalizing reported in Pinquart's (2017) meta-analysis. Several studies have examined this moderating role of infant negative affect on the relation between parenting and externalizing behavior at age 3 years or under. For example, Kochanska and Kim (2013) found that it was only in the context of 'difficult' child temperament that high maternal responsiveness at 30 months predicted low levels of externalizing at 40 months. Likewise, Rochette and Bernier (2016) found that it was only in the context of difficult temperament at 15 months that parent-child positive affect (measured at 12 months) predicted children's EF at 36 months. The third aim of our cross-lagged longitudinal study was to extend existing work by examining the moderating influence of infant negative affect on the link between parental support and child externalizing behavior in the second year of life.

| Participants
We recruited 484 expectant couples from antenatal clinics, ultrasound scans, and parenting fairs in the East of England, New York State, and the Netherlands. To be included in the study, participants had to: (a) be first-time parents, (b) be expecting delivery of a healthy singleton baby, (c) be planning to speak English (or Dutch) as a primary language with their child, and (d) have no history of severe mental illness (e.g. psychosis) or substance misuse. In addition, families were only included if their baby had a healthy full-term delivery.

| Procedure
The

| Executive function
Children completed a short battery of three tasks (for details see: Devine et al., 2019) at 14 and 24 months. Children sat on their parent's lap across a table from the examiner. Parents remained silent during each task. Children received praise at the end of each task regardless of performance to maintain their interest in participating.
Children completed the Prohibition Task (Friedman, Miyake, Robinson, & Hewitt, 2011) during the 14-month visit. Children were required to resist touching an attractive toy for up to 30 s following the examiner's command ('Don't touch!'). Scores were coded into two categories (i.e. 0 = touches before 30s; 1 = does not touch before 30 s). Children completed the Baby Stroop Task (Hughes & Ensor, 2005) during the 24-month visit. Children participated in a 'silly game' in which they pointed to a large spoon when the examiner said 'Baby' and a small spoon when the examiner said 'Mummy'.
Children completed six trials (with feedback) and passed if they performed correctly on 4 or more trials.
Children completed a Multilocation Search Task (Miller & Marcovitch, 2015) during both home visits. Children searched for a number of toy cars (i.e. three at 14 months and five at 24 months) hidden in distinct toy garages after a delay of 5s between each search. The task continued until the child retrieved all cars or made three consecutive errors. Children passed if they retrieved all of the hidden cars.
Children completed the Ball Run Task (Devine et al., 2019) at both visits. In the learning phase, the examiner demonstrated how to activate a musical switch by placing a colored ball (e.g. red) into one of two colored holes (e.g. red hole). The other hole (e.g. green) was sealed from beneath and could not be used to activate the switch.
Children completed six learning trials with feedback. In the reversal phase, the examiner demonstrated how to activate the toy by placing a different colored ball (e.g. green) into the previously unused hole (e.g. green). The original hole was sealed from beneath and could no longer be used to activate the switch. Children completed six reversal trials with feedback. Children passed a phase if they performed correctly on four or more trials.
We created an EF score for each time point by summing together the number of tasks each child passed. Table S1 shows the numbers of children passing each EF task and Table S2 shows the tetrachoric correlation matrix for the EF tasks. The reliability coefficient (i.e. ordinal alpha based on tetrachoric correlations) was modest at 14 months (α = 0.37) and 24 months (α = 0.58). These results were consistent with the modest EF task correlations in this age range reported elsewhere (Johansson, Marciszko, Brocki, & Bohlin, 2016;Kochanska & Knaack, 2003;Miller & Marcovitch, 2015). In addition to reducing the number of variables in our models, we opted for a single aggregate score for EF because these scores exhibit greater stability over time than individual task scores in the second year of life (Miller & Marcovitch, 2015).

| Maternal support
We observed mother-child dyads in a 4-min play session involving an inset jigsaw puzzle at 14 months and a building block puzzle at 24 months. We measured maternal support by coding the observations using the Autonomy Support Coding manual (Whipple, Bernier, & Mageau, 2011) involved the child as an active participant. Following training and feedback, graduate raters' scores were compared against a reliability set of 30 cases from 14 months and 30 cases from 24 months rated by the lead authors. We calculated a mean autonomy support rating at 14 (α = 0.87) and 24 months (α = 0.83). Inter-rater reliability coeffecients for the mean autonomy support rating at 14 (ICC = 0.73) and 24 months (ICC = 0.74) were acceptable.

Mothers and fathers completed the Brief Infant Behavior
Questionnaire (Putnam, Helbig, Garstein, Rothbart, & Leerkes, 2014) prior to the 4-month visit to measure infant negative affect. We av-   (Rust, 2003). Children pointed to a picture matching a word read aloud by the researcher. We used the total score to provide an index of verbal ability at 24 months.

| Analytic strategy
We used structural equation modeling in Mplus (Version 8) (Muthèn & Muthèn, 2017) to analyse the data. We applied a maximum likelihood estimator with robust standard errors (MLR) in each of our models to account for the non-normal distribution of our indicators.
We evaluated model fit using three primary criteria: Comparative Fit Index (CFI) > 0.90, Tucker Lewis Index (TLI) > 0.90, Root Mean Square Error of Approximation (RMSEA) < 0.08 (Brown, 2015). Table 1 shows the descriptive statistics for each key study measures and the extent of missing data. We used a full information approach (where model parameters and standard errors were estimated using all available data) under the assumption that data were missing at random so that all eligible families who participated in the prenatal and at least one follow-up phase (N = 438; 218 boys) were included (see Online Appendix for information on Missing Data). Table 2 shows the correlations between each variable in the dataset.

| Model results
We tested two cross-lagged autoregressive models to examine the relations between children's EF, maternal support, and child externalizing behavior between the ages of 14 and 24 months. In Model 1, we examined the longitudinal association between each independent variable at 14 months (i.e. 14 month EF, maternal autonomy support, and externalizing behavior) and each dependent variable at 24 months (i.e. 24-month EF, autonomy support, and externalizing   There was no significant association between 14-month maternal autonomy support and children's externalizing behavior at 24 months. We compared the strength of the path between 14-month externalizing behavior and 24-month EF with the path between 14-month EF and 24-month externalizing behavior by constraining these paths to equality. The Wald test revealed a difference in the strength of these two paths, χ 2 (1) = 7.288, p = .007, indicating a unidirectional developmental association between early EF and later externalizing behavior. There was no significant difference between the path linking 14-month maternal autonomy support and later externalizing behavior and the path linking 14-month externalizing behavior and later maternal autonomy support, χ 2 (1) = 1.272, p = .2594.
We conducted follow-up analyses using multiple-groups struc- in which corresponding cross-lagged paths (e.g., path between 14month externalizing behavior and 24-month EF) were constrained to equality in boys and girls (see Table S4). Paths were considered to differ in strength if the constraint produced a decrease in model fit as indicated by a significant increase in the Satorra-Bentler χ 2 difference test and decrease in CFI of > 0.002 (Brown, 2015;Meade, Johnson & Braddy, 2008). The regression path linking negative affect at 4 months and autonomy support at 24 months differed in strength between boys and girls but neither path was statistically significant (see Table S4). Model comparisons revealed that there were no other differences between boys and girls in the strength of regression paths. Patterns of association between variables were therefore similar in boys and girls. TA B L E 2 Robust maximum likelihood estimates for correlations between tasks These paths differed significantly, χ 2 (1) = 7.019, p = .0081, supporting a unidirectional link between early EF and later externalizing behavior.
To assess the moderating effect of child temperament on the relation between maternal autonomy support and child externalizing behavior, we regressed 24-month child externalizing behavior onto the grand-mean centered interaction term for negative affect and 14-month maternal autonomy support using the whole sample (Hayes, 2018). All other features of Model 2 were the same as Model 1. Model 2 provided an acceptable fit to the data, χ 2 (40) = 63.87, p = .009, RMSEA = 0.037, 90%CI [0.018, 0.053], CFI = 0.967, TLI = 0.925. There was a small but significant effect of the multiplicative interaction term on 24-month externalizing behavior. Figure 2 shows the predicted values for externalizing behavior based on the conditional effect of maternal autonomy support for children at the 16th, 50th, and 84th percentile for negative affect. We probed the interaction using a regression centering approach in which we centered the moderator variable around the 16th, 50th, and 84th percentiles (Hayes, 2018).
There was a significant negative association between maternal autonomy support and externalizing behavior among children

| D ISCUSS I ON
Our study yielded three main findings about individual differences in externalizing behavior in the second year of life. First, there was a modest but significant unidirectional negative association between EF at 14 months and externalizing behavior at 24 months. Second, this unique predictive association held up even when potential effects of verbal ability or maternal support were considered. Third, only infants with low levels of negative affect benefitted from maternal autonomy support, such that only this group showed an inverse association between 14-month maternal autonomy support and externalizing behavior at 24 months.

| EF predicts externalizing behavior in the second year of life
Although externalizing behaviors are more common among 2 year olds than among 4 year olds, there are striking individual differences in the extent to which children engage in externalizing behaviors even in the second year of life (Alink et al., 2006).
Understanding individual differences in externalizing in toddlerhood matters because longitudinal studies show that externalizing behaviors are moderately stabile across childhood (Campbell et al., 2006;Cote et al., 2006;Rose et al., 1989;Smith et al., 2004).
Converging support for Moffitt's (1993) proposal that EF sets the stage for early externalizing behavior comes from three previous longitudinal studies that have adopted cross-lagged designs in preschool and school-aged children (Hughes & Ensor, 2008;Sulik et al., 2015;Kahle et al., 2018). While prior studies point to a link between related constructs like effortful control and externalizing behavior in the second year of life (e.g., Adrichem et al., 2019;et al., 2000), to date cross-lagged analyses in this age range have not been undertaken. The current study extends the developmental scope of research on the executive account of externalizing behavior by examining the nature and direction of this association in children under the age of two. Our findings indicate that individual differences in toddlers' externalizing behavior and EF performance each show modest temporal stability. Cross-lagged models permitted comparison of the strength of developmental associations between these two constructs. EF at 14 months predicted externalizing behavior at 24 months, even when 14-month externalizing behavior was considered. In contrast, there was no reciprocal association between toddler externalizing behavior at 14 months and EF at 24 months. These findings support the executive account, expand the developmental scope of previous work (Schoemaker et al., 2013), and strengthen the view that EF provides a useful focus for interventions aimed at mitigating externalizing F I G U R E 2 Child negative affect moderates the association between maternal support and child externalizing behavior behavior. Our results also suggest that the correlation between EF and externalizing in the first two years of life is similar in magnitude to that reported for community-based preschool children (Schoemaker et al., 2013). While beneficial for understanding predictors of between-person individual differences, autoregressive cross-lagged panel models do not provide insight into how withinperson changes in EF lead to within-person changes in externalizing behavior (or vice versa) (Berry & Willoughby, 2017). Future studies, incorporating three or more time points will permit researchers to examine the links between within-person change in each domain using autoregressive latent trajectory models (Berry & Willoughby, 2017).
Note that our protocol included three EF tasks. This relatively small EF task battery was useful in minimizing demands upon

| Comparing effects of EF and maternal support on externalizing behavior in the second year of life
With notable exceptions focused on outcomes later in childhood and externalizing behavior at 24 months remained significant even when variation in maternal autonomy support was considered.
Self-determination theory predicts that parents who support their infant's emerging volition, competence, and need for relationships, will exhibit fewer externalizing behavior and better EF than their peers (Ryan et al., 2015). Our results present a challenge to this account. While there were significant correlations between autonomy support and EF at 24 months and between autonomy support and externalizing behavior at 14 and 24 months, observed maternal autonomy support at 14 months did not uniquely predict either EF or externalizing behavior at 24 months. These results contrast with evidence indicating direct associations between parental behavior and EF in preschool children (e.g., Hughes & Devine, 2017) but echo recent work showing no unique association between parental sensitivity at 10 months and EF at 18 months (Frick et al., 2018).
One possibility worthy of future study is that emerging EF may become more susceptible to parental influence with the growth of language in the second year of life.
Investigations of early family relationships have overlooked childdriven effects (Davidov, Knafo-Noam, Serbin, & Moss, 2015). In this regard, it is worth noting that Pinquart's (2017) meta-analytic findings from studies of in school-aged children and adolescents indicate contrasting results for different aspects of parenting in relation to externalizing behavior. Specifically, while harsh parental control showed a bidirectional link with child externalizing behavior, maternal support showed a weak unidirectional effect upon child externalizing behavior.
Note that the association between maternal support and child externalizing behavior in the current study was similar in magnitude to that reported by Pinquart (2017) (i.e., r = −0.06, as compared with −0.05), but was not statistically significant, indicating the potential interplay with child characteristics.

| Maternal support predicts reduced externalizing behavior for infants with low levels of negative affect
Our model showed no direct effect of maternal support upon children's externalizing behavior. This is consistent with a study reporting no direct association between autonomy supportive parenting at 15 months and child aggression at age 6 (Sirois & Bernier, 2018). While these findings may challenge self-determination theory (Ryan et al., 2015), the results are consistent with predictions from vantage sensitivity (e.g., Pluess & Belsky, 2013). Infants with low levels of negative affect at 4 months benefitted more from high levels of maternal support at 14 months than those with average or high levels of negative affect, such that for this group alone there was a significant inverse association between early maternal support and later externalizing behavior. Interestingly, prior work on related domains (e.g., maternal responsiveness and externalizing) has shown that children with 'difficult temperaments' were more susceptible to responsive parenting such that there was an inverse association between parental responsiveness at 30 months and child externalizing at 40 months (Kochanska & Kim, 2013). One possibility, suggested by the between-study contrast in child age periods is that the moderating effects of child temperament are developmentally specific.
That is, in late infancy, children with easy temperaments may gain most from high quality maternal support whereas by the preschool years, maternal support may have most impact on children with difficult temperaments.
It is also worth noting that infant negative affect at 4 months showed an inverse association with maternal support at both 14 and 24 months. Mothers of infants prone to distress may have attempted to minimize frustration by providing greater assistance during goal-directed tasks and thereby inadvertently limiting their child's autonomy. This correlation could indicate child-driven effects (Belsky et al., 2007), rather than an example of vantage sensitivity. Further work is needed to investigate this interaction effect. Vantage sensitivity for infants with low negative affect may indicate limits on the extent to which maternal support can influence children's externalizing behavior, with weaker benefits for infants prone to distress.

| C AVE ATS AND CON CLUS I ON S
It is worth acknowledging that the low-risk nature of the sample potentially limited the generalizability of study findings and the sensitivity of some of our analyses. Effects of environmental adversity on child externalizing behavior may display a threshold effect, such that the limited demographic diversity in our sample may explain the lack of association between family affluence and child outcomes. That said, maternal education was positively related to maternal support in our model, indicating that there was variation in family background. Note also that the large sample size precluded the collection of observational data on child externalizing behavior and temperament. It is reassuring that our results are consistent with previous studies involving smaller samples that have included multi-informant ratings of externalizing behavior (e.g., Hughes & Ensor, 2008). The two-wave crosslagged design allowed us to examine the direction of developmental associations in our data but did not allow tests of mediation hypotheses linking parent-child interaction, EF and externalizing behavior (e.g., Roman, Ensor, & Hughes, 2016). Future studies involving at least three time-points are required to investigate whether EF might mediate the relations between parent-child interaction and later externalizing behaviors (Cole & Maxwell, 2003).
To our knowledge, this is the first study to adopt a cross-lagged design to investigate the nature and direction of associations between EF and externalizing behavior in children under the age of 2 years. Our results show that early difficulties with EF contribute to the individual differences in externalizing behavior, even before children's second birthdays. These findings support the executive dysfunction account of child externalizing behavior. Our results underscore the need to examine how the effects of maternal support on early externalizing behavior are moderated by temperamental factors such as negative affect. By including both experimental measures of child EF and direct observations of parental support our study extends existing work on toddlers and preschoolers by bridging two disparate approaches in investigating the origins of externalizing behavior in the first two years of life and provides a comprehensive model to be tested in future studies involving diverse samples.

CO N FLI C T S O F I NTE R E S T S TATE M E NT
There are no conflicts of interest.