Participants
We used data from the waves of Millennium Cohort Study (MCS) [26] taking place during participants’ adolescence (ages 11, 14, and 17). MCS is a UK-based longitudinal birth cohort study fully documented and available at: https://ukdataservice.ac.uk/. In brief, the first wave of MCS took place in 2000–2002 when participants were aged 9 months old. Participants were sampled using a stratified random sampling design in which individuals were clustered geographically and disproportionately sampled from the three smaller nations of the UK (Scotland, Wales, and Northern Ireland), disadvantaged areas and ethnic minorities. From the age 11 wave of data collection, data were utilised from the 5287 participants (2556 male, 2731 female), at age 14 we used data from 12597 participants (6246 male, 6351 female) and at age 17 we used data from 4918 participants (2891 male, 2126 female).
Measures
ADHD symptoms
ADHD symptoms were measured with the hyperactivity/inattention subscale of the Strengths and Difficulties Questionnaire (SDQ) [27]. The SDQ is one of the most widely used and well-validated behavioural screening instruments for children and [28], including in the current sample where it has shown good psychometric properties, including a high degree of gender, informant and developmental invariance [29, 30]. Though there is some debate around the appropriate cut-point, the hyperactivity/inattention subscale has shown good discrimination with respect ADHD diagnosis [31, 32]. The subscale includes five items that refer to behaviour during the last six months with reference to the following behaviours: ‘restless, overactive, cannot stay still for long’; ‘constantly fidgeting or squirming’; ‘easily distracted, concentration wanders’; ‘thinks things out before acting’; and ‘sees tasks through to the end, good attention span’. Responses were provided on a 3-point Likert-type scale with options: not true (0), somewhat true (1), and certainly true (2). Positively worded items were reverse-coded, and item responses were summed to produce an overall hyperactive/inattentive score with higher scores indicating greater hyperactivity/inattentiveness (possible range = 0–10). We used the parent (age 14), teacher (age 11 and 14), and self-reported (age 17) versions of the SDQ, as available.
Internalising problems
Internalising symptoms were measured with the emotional problems subscale of the SDQ (described above). The emotional problems items refer to: often complaining of headaches, stomach-aches or sickness; having many worries; being often unhappy, down-hearted, or tearful; being nervous or clingy in new situations; and having many fears, being easily scared.
Candidate mediators
Full details of the candidate mediator measures are provided in Supplementary Materials. Mediators included in specific models are listed in the relevant section for each model.
Statistical procedure
Overview
Given that available mediators varied by wave, we fit cross-sectional models to maximise the inclusion of mediators for each age. We began by fitting basic SEMs to estimate the raw association between ADHD symptoms and internalising symptoms at each wave. We then proceeded to add mediators to each model and implement model selection using regularised SEM.
ADHD-internalising problems correlation
For each wave, we first fit a SEM with only ADHD symptoms and internalising problems using diagonally weighted least squares (DWLS) estimation to account for the ordered-categorical nature of the indicators. From these we estimated the correlation between the latent ADHD symptoms and internalising problems factors. These models were fit in lavaan in R statistical software [33].
Exploratory mediation analysis
We next conducted exploratory mediation analysis, adding the set of candidate mediators to the basic SEMs described above. We followed the exploratory mediation analysis with SEM described by [34]. In this method, a path mediation model is fit in which regression paths are specified from ADHD symptoms to the mediators, from the mediators to internalising problems, and from ADHD symptoms to internalising problems. Where relevant, latent variable measurement models for constructs were used (e.g., ADHD symptoms, internalising problems; see Methods section for details). Figure 1 provides a simplified example of the multiple path mediation models fitted. Paths a1-ak label the paths from ADHD symptoms to the mediators, paths b1-bk label the paths from the mediators to internalising problems, and c’ is the direct effect from ADHD symptoms to internalising problems. From the a and b parameters, indirect effects via each mediator are derived by finding the product a*b. The total effect of ADHD symptoms on internalising problems is then the sum of the indirect effects and c’.
In the approach proposed by Serang et al.(2017) the above-described multiple model is fit using regularised SEM [35]. Regularised SEM incorporates a penalty term into the maximum likelihood function used for model fitting:
$$\:F=\text{log}\left(\left|\varSigma\:\right|\right)+tr\left(C*{{\Sigma\:}}^{-1}\right)-\text{log}\left(\left|C\right|\right)-p+\lambda\:P\left(.\right)$$
(1)
where \(\:\varSigma\:\) is the expected covariance matrix, C is the observed covariance matrix, p is the total number of manifest variables, \(\:\lambda\:\:\)is a tuning parameter, and \(\:P\left(.\right)\) is a function for summing over the absolute value of the penalised coefficients. In exploratory mediation applications of SEM this is the a and b coefficients. We used a general purpose optimiser (rsolnp) which provides an approximate solution and thresholding to set parameters very close to 0 to 0 [36]. This was implemented within the regsem R package [37].
First, all continuous variables standardised (for the constructs specified using latent variables this was achieved by fixing the latent variable variance to 1). Next, the tuning parameter value was found by testing 100 \(\:\lambda\:\:\) values (0 to 1 in 0.01 increments) and identifying the model with the smallest Bayesian Information Criterion (BIC). BIC provides a more practical solution to tuning by cross-validation, which can become impractical for large models due to the computation time involved. The model was then re-fit without regularisation, using only the subset of mediators with non-zero indirect effects from the model with the optimal \(\:\lambda\:\:\) value. Statistical significance of the indirect effects was assessed using the 95% confidence interval of the bootstrapped standard errors of the indirect effect coefficients (using 1000 bootstrap samples).
Age 11 exploratory mediation model
At age 11, the following mediators were included in the cross-sectional model: prosociality, peer problems, conduct problems (all with parent and teacher reports); school happiness and parental discipline (parent reports), self-esteem, school motivation, well-being (self-reports), academic performance, injuries, parental closeness, physical activity, gaming screen time, surfing screen time, messaging screen time, social networking screen time, happiness, peer conflict, antisocial behaviour, self-reported academic performance, victimisation, aggression and risk-taking based on the Cambridge Gambling Task (risk-taking, quality of decision-making, deliberation time, risk adjustment, delay aversion) and parental mental health problems latent factor (parent self-reports).
Age 14 exploratory mediation model
At age 14, the following mediators were included in the cross-sectional model : risk decision making based on the Cambridge Gambling Task (risk-taking, quality of decision-making, deliberation time, risk adjustment, delay aversion), physical activity, screen time (TV time, gaming time, social media time), academic self-concept, educational motivation, relationships with parents (maternal conflict, maternal closeness, paternal conflict, paternal closeness), parental monitoring, parental discipline, social support, smoking, gambling, bullying (traditional bullying perpetration, cyberbullying perpetration, traditional bullying victimisation, traditional bullying perpetration), victimisation, antisocial behaviour, willingness to take risks, patience, trust, wellbeing, self-esteem, general health, parental mental health, prosociality, peer problems, and conduct problems.
Age 17 exploratory mediation model
At age 17, the cross-sectional model candidate mediators were: self-reported prosociality conduct problems, peer problems, self-esteem, smoking, alcohol use, binge drinking, victimisation, risky behaviours, and antisocial behaviour, self-control, TV screen time, gaming screen time, social media screen time, gambling, sleep quality, social provision, overall health, physical activity, and parental psychological distress.
Some candidate mediators that were considered in these models such as criminal justice involvement and the use of specific drugs other than cannabis were not included due to high levels of missingness or low category endorsement. Further, while the measurement models included some categorical indicators, for pragmatic reasons (the large number of mediators) the models were fit with maximum likelihood estimation, treating the categorical indicators as if continuous. Complete case analysis was used based on pragmatic considerations given the computation time that would be needed to combine FIML or multiple imputation with tuning (and bootstrapping).