The study of the developmental interdependencies between and within the domains of internalising and externalising mental health symptoms can be guided by theoretical research on the co-occurrence of childhood psychopathology [8]. Evidence coming from correlational [10,11,13] and behavioural genetics [14,15] empirical studies have shown a substantial correlation between the domains of internalising and externalising symptoms. However, co-occurrence does not only occur between domains but also within domains of internalising and externalising symptoms [7,16,17]. The within-domain co-occurrence is called homotypic, whereas the between-domain co-occurrence is called heterotypic and is more important from a substantive perspective [7].

Empirical explanations for this phenomenon of co-occurrence have been presented in the literature. One account, coming from the behavioural genetics literature, suggests that there is a genetic factor underpinning these associations that accounts for a large proportion of shared variance between externalising and internalising symptoms [12,15]. Another view suggests that internalising symptoms precede and predict subsequent externalising symptoms [7], whereas conduct problems in the form of antisocial behaviour can also give rise to internalising symptoms [7]. A dynamic mutualism view has been introduced, which suggests that symptoms of different mental health classifications can reinforce each other through direct causal links and interactions, instead of a common underlying cause [18]. This basically means that once weakly correlated symptoms can grow to be strongly associated over time as they influence each other across the development [18]. This dynamic mutualism viewpoint is usually examined through the ‘cascade effects’ model in psychopathology [18,19], which describes how psychopathology factors interact and transact between and within different developing levels (e.g., externalising and internalising) to modify the developmental course of a process [20]. So, a problem in one area can spread and cause issues in other areas, creating a chain reaction of difficulties.

Another explanation of the co-occurrence comes from studies using dimensional analyses through latent variable models that propose a general underlying psychopathology factor (usually called p-factor) that accounts for the co-occurrence within the domains of internalising [16] and externalising [21], as well as between the domains of internalising and externalising [18]. This general psychopathology factor is assumed to stem from higher-order dimensions of personality or temperament [7].

The study of the longitudinal developmental relations between facets of internalising and externalising mental health has attracted the attention of researchers. However, as will be shown, the results from the longitudinal studies are, to date, inconclusive and sometimes point in different directions.

Some early studies have noted no significant predictive effects (also known as cascading effects [20]) between internalising and externalising mental health in children or adolescents [22–24]. In contrast, other evidence has come to light indicating a unidirectional predictive effect [10,25,26]. Nevertheless, a few studies have also shown some small reciprocal effects. Such an example is the study by Wiggins et al. [27] that found a reciprocal association between internalising and externalising symptoms between ages 5 and 9. Similarly, another study reported significant reciprocal cascading effects between the two domains from age 3 to age 9 [13]. These findings suggest that a reciprocal cascading model might serve as a possible explanation of the long-term relations between children’s internalising and externalising mental health.

Beyond the studies on the between-domain relations, the evidence on relations within the domains of internalising and externalising mental health symptoms is also inconclusive and scarce. In the internalising domain, for example, a study found no longitudinal associations between emotional symptoms (i.e., depressed affect) and peer problems within children [28], whereas other studies have shown a longitudinal link between peer problems and emotional symptoms [29]. Some other evidence points toward a reciprocal longitudinal relation only between specific time points [30]. In the externalising domain, the evidence regarding the bidirectionality between conduct problems and hyperactivity is rather scarce, especially at the within-child level. A study from the behavioural genetics literature has reported a shared genetic underpinning to the relation between conduct problems and hyperactivity [31]. Longitudinal evidence has also highlighted the long-term predictive effect from hyperactivity indicators to conduct problems [32–34]. In short, some of the above evidence is rather short-term and does not cover all the developmental stages between early childhood and mid-adolescence.

The discrepancies in the conclusions reached across the empirical investigations suggest the need for replicating the findings through cross-validation. The importance of cross-validation of structural relations is a well-known property [35,36]; however, to the best extent of my knowledge, there are no previous studies on the cascading dynamics between and within internalising and externalising domains that have employed cross-validation cross-cohort approaches.

Having discussed the evidence coming from previous empirical studies on the longitudinal links between and within the domains of internalising and externalising symptoms, I now discuss the importance of trait-state approaches to the study of these longitudinal interdependencies. As mentioned in the literature, it is hard to think of psychological factors that are not simultaneously characterised by stability and change over the course of development [37]. Latent state-trait theory suggests that emotional responses, cognitions, and behavioural reactions in humans can be distinguished by stable traits, which describe stability over the course of development, and states, which reflect momentary deviations from the traits [38].

The majority of the above studies on the interplay between internalising and externalising mental health symptoms have adopted a state-trait perspective [10,24,26], recognising that childhood internalising and externalising mental health symptoms are characterised by both stability and change over time. Hence, it is important to distinguish between inter-individual (also known as between-child) associations from intra-individual (also known as within-child) associations between and within the domains of internalising and externalising symptoms. To achieve this, the random-intercept cross-lagged panel model (RI-CLPM) [37,39] is deployed in the current study. The path configuration of a conceptual bivariate RI-CLPM is shown in Fig 1. In the RI-CLPM, the bi-factor reflects the stable trait-like aspects of symptoms, whereas the residual factors attached to the observable measures reflect the state-like aspects that are transient and subject to change [40]. The dynamic mutualism hypothesis of co-occurrence can be tested using the cross-lagged paths in the RI-CLPM, which indicate cascades between the different states.

In the framework of the state-trait approach [10,41], the general psychopathology underlying factor (p-factor) that emerges is conceptually similar to the correlation between the trait-like bi-factor structure of the RI-CLPM [37]. If the correlation between the different traits is very large and close to unity, then the traits will be indistinguishable, and the hypothesis of a common underlying trait factor over the course of development would hold [42]. Thus, the current study contributes to the ongoing discussion about the co-occurrence of internalising and externalising symptoms. This contribution stems from the examination of the co-occurrence at the within-child level and at the between-child /trait level over the course of the development from early childhood to mid-adolescence.

The present study weaves together the theoretical perspectives on the co-occurrence between and within the internalising and externalising mental health domains [7,16,18] and the longitudinal state-trait perspective [38,41] to address two important questions. First, the study queries whether internalising symptoms drive developments in the externalising symptoms or vice versa. Second, the study explores whether these domains are mutually reinforcing as children develop over time. Reciprocal associations between and within the domains of internalising and externalising symptoms would lend support for the hypothesis of dynamic mutualism over time [18]. In contrast, a unidirectional flow of effects would indicate that one domain or component of psychopathology is the leading cause of the co-occurrence between and within the psychopathology domains [7].

The state-trait theoretical and modelling approach adds to the above viewpoints by disentangling the developmental dynamics of the symptoms within the children’s development from the general traits of psychopathology that remain stable over time [10]. Therefore, the current study provides insights into how children with greater than average symptoms in one domain might display greater than average increases in the other domain. In addition to the above, the study contributes by cross-validating the findings through a cross-cohort comparison, which can provide more conclusive evidence regarding the stability of the findings over time (2004–2014 vs. 2008–2018). Overall, the present study is guided by two research questions and the following hypotheses:

Provided that different longitudinal cohort studies reached competing conclusions, it is expected that cohort membership would moderate the longitudinal dynamic interplay between internalising and externalising symptoms (H1). The second research hypothesis assumes a positive relation between different facets of mental health symptoms (H2). Given the past findings, it is more likely that externalising symptoms will positively predict internalising symptoms (H3). However, some studies have also reported a positive reciprocal association between internalising and externalising mental health symptoms at specific ages; hence, a reciprocal association might be possible only between specific time points (H4).

The data come from the longitudinal accelerated Growing Up in Australia dual-cohort, also known as the Longitudinal Study of Australian Children (LSAC) [43]. Detailed information about the dual-cohort design and its methodologies can be found at https://growingupinaustralia.gov.au. Both the kindergarten (K) and the baby (B) cohorts’ data were utilised, leaving a total sample size of 5998 children. The baby cohort contributed 2722 (48.38% female) children, and the kindergarten cohort contributed 3276 (49.27% female) children. The baby cohort (infant) sampled children born between March 2003–February 2004, whereas the kindergarten cohort sampled children born between March 1999–February 2000 [43]. A two-stage stratified cluster sampling design was employed, whereby the clustering was with respect to the postal codes, and the stratification ensured the proportional selection from different geographical areas [43]. Children in both cohorts had approximately equal probabilities of selection [43]. About 60% of the parents were born in Australia, and more than 90% of the children were also born in Australia. The children in the current study were assessed biennially at ages 4, 6, 8, 10, 12, and 14. The baby cohort’s children were 4, 6, 8, 10, 12, and 14 years old between the calendar years 2008–2018, whereas the kindergarten cohort’s children were 4, 6, 8, 10, 12, and 14 years old between the calendar years 2004–2014.

Weighted descriptive statistics (means, standard deviations) were calculated for the kindergarten and baby cohorts and are presented in Table 1.

Multigroup longitudinal invariance analyses were first conducted to compare the dynamic interplay between the four mental health indices over time across cohorts and to ensure comparability of measurements [62]. The results of the multigroup longitudinal invariance analyses are presented in Table 2. As shown in Table 2, emotional symptoms, peer problems, and hyperactivity were strictly invariant across cohorts over time. Probably due to the two different item wordings of the conduct scale at age 4, conduct problems were only partially strictly invariant over time, with the problem of non-invariance being located at the items’ thresholds at age 4. The non-invariant thresholds at age four years signal that the first timepoint is likely to be an inefficient predictor in the cross-lagged modelling.

The results of cross-cohort multigroup RI-CLPM model comparisons are presented in Table 3. As shown in Table 3, the multigroup models’ comparisons revealed no differences in the within-child structural relations across cohorts, given the statistically insignificant Satorra-Bentler tests. In fact, the constrained models exhibited a better fit in all models. This suggests that time had no moderating effect on the relations within and between the domains of internalising and externalising mental health and that any findings of relations hold across cohorts.

Having compared the within-child effects across cohorts, the standardised structural parameters were inspected next. The standardised regression coefficients were derived from the constrained multigroup models, which calculated separate but comparable covariance matrices and are presented in Table 4. I reiterate here that only the autoregressive and cross-lagged coefficients, respectively, were specified to be 1:1 equal across cohorts. Overall, rather modest within-child autoregressive carry-over effects were found between adjacent ages. This suggests that children’s mental health development fluctuated substantially over time; that is, those children who initially faced greater than usual difficulties did not necessarily persist in facing difficulties over time. In general, strong positive reciprocal relations were observed between emotional symptoms and peer problems from age eight years onwards. Reciprocal relations were also observed between emotional symptoms and hyperactivity only in the transitions between middle childhood (age 8) to early adolescence (age 10) and between early adolescence (age 12) to mid-adolescence (age 14). Between conduct problems and emotional symptoms, there were no significant reciprocal links. In contrast, consistent reciprocal relations were found between peer problems and hyperactivity from middle childhood (age 8 years) onwards. Higher than usual peer problems were moderately to strongly reciprocally associated with greater conduct problems from age eight years onwards. Within the externalising domain, the evidence was rather mixed, with few statistically significant reciprocal effects between hyperactivity and conduct problems, which were mostly concentrated in the adolescent years (between ages 12 and 14 years). Most effects from age 4 years to age 6 years were rather ambiguous, being insignificant or the opposite than expected sign. Finally, the trait correlations (i.e., correlations between random intercepts) consistently revealed that there was a robust positive association between children between and within the different components of internalising and externalising mental health.

The present study has several strengths, such as the representative samples, the cross-cohort comparative approach, the invariant measures with good psychometric properties, and the trait-state approach. Nevertheless, some limitations should be noted. For instance, the SDQ measure is a screening tool designed for the general population of children and does not necessarily accurately capture all aspects of children’s mental health [66]. Additionally, the data predate the COVID-19 pandemic and may, thus, not accurately reflect the current state of children’s mental health. Finally, a replication of the current findings with teacher- and self-reports, as well as with more refined measures of children’s mental health, is needed.

The current findings contribute to the theory of children’s mental health development by clearly examining the developmental cascades within and between the internalising and externalising mental health domains. The results indicate that the transitions from middle childhood to early adolescence and to mid-adolescence are critical periods for children’s mental health development since most of the bidirectional associations occurred in these stages. On the practical side of things, the findings would suggest that children facing emotional difficulties typically have troubled peer relationships. However, children with higher-than-usual hyperactivity do not necessarily exhibit conduct problems (e.g., bullying or stealing), except in the transition from early to middle adolescence, between ages 12 and 14 years. Provided the consistent bidirectionalities between peer problems and externalising symptoms, professionals should be aware that potentially troubled peer relationships are associated with conduct problems and hyperactivity, and vice versa. Interventions are needed particularly in adolescence to prevent exacerbating mental health symptoms due to the tendency for dynamic mutualism between and within the two domains of psychopathology. Children and adolescents could be taught coping skills and socio-emotional skills to become more resilient against the development of increased mental health symptoms. However, educators, parents, and practitioners also have a role to play by being vigilant in identifying children and adolescents who need additional support. Finally, researchers need to raise the awareness that the manifestation of childhood and adolescent mental health symptoms is a fluid process that takes time and may be reversed due to potential discontinuities and particular life experiences [67]. Hence, long-term monitoring of children’s and adolescents’ mental health status is recommended in schools and communities.