Childhood dysregulation is conceptualized as impaired self-regulation and associated difficulties with internal modulation of physiological arousal in response to stressors (Althoff et al., 2010). Children with externalizing difficulties, including disruptive and conduct problems, have been shown to experience heightened dysregulation (e.g., Frick et al., 2003). According to Dodge and Pettit’s (2003) biopsychosocial model on the development of conduct problems, externalizing behavior arises from the complex multidirectional and additive influences of psychophysiological, emotional, and cognitive (inhibitory) dysregulation. In line with this model, considerable empirical work has investigated the (dys)regulatory correlates of externalizing psychopathology, particularly parasympathetic physiological correlates (e.g., Deutz et al., 2019; Kahle et al., 2018). However, much of this work has focused on point-in-time measures and absolute mean levels of physiology, which do not capture the dynamic fluctuations in physiology that characterize dysregulation in real life.

In the present work, we examined fluctuations in children’s physiological responses to social transgression scenarios across 15 short-term measurement occasions (independent of their mean levels of physiology). This novel, exploratory approach allowed for characterization of our physiological response measurements as intensive longitudinal data, which uncovers dynamic processes that take place over a relatively short span of time (e.g., seconds; Hamaker & Wichers, 2017). Our goal was to assess whether physiological dysregulation characterized by momentary fluctuations rather than mean levels would differentiate between children with and without clinical levels of externalizing behavior.

Dysregulation and Externalizing Difficulties

Challenges with self-regulation are central to the development of emotional and behavioral difficulties (Houben et al., 2015; Kuppens & Verduyn, 2017). In the context of elevated externalizing difficulties, such as conduct and oppositional defiant disorders, children have been shown to be more dysregulated based on both parent and self reports (see meta-analysis by Card & Little, 2006). For example, Frick et al. (2003) found that third- to seventh-grade children with conduct problems and their parents tended to report more emotional and behavioral dysregulation compared to age-matched controls. Further, observed dysregulation during a lab task in toddlerhood has longitudinally predicted more parent-reported externalizing behavior two years later (Rubin et al., 2003).

Dysregulation in children with externalizing behavior has also been measured physiologically via the autonomic nervous system (ANS), including its parasympathetic (PNS) and sympathetic (SNS) branches. For example, researchers have assessed skin conductance and heart rate variability as indices of dysregulated responding to stress (Bunford et al., 2017; Evans & Kim, 2007; Fenning et al., 2019; Hankin et al., 2010). In the present work, we focus on respiratory sinus arrhythmia (RSA) in the PNS branch, which has emerged as a widely used and reliable indicator of cardiac regulatory capacity (Beauchaine & Bell, 2020). RSA is an indicator of activity in the vagus nerve and acts as a brake on the heart, with increases in RSA or RSA augmentation having a regulatory effect and decreases in RSA or withdrawal of the vagal brake permitting increased arousal (see Porges, 2011).

Contrasting the consistent links between questionnaire-based dysregulation scores and externalizing behavior, physiological dysregulation as measured by RSA reactivity to social or moral conflict situations has shown inconsistent links with child externalizing behavior (see Beauchaine & Bell, 2020). For example, Shader et al. (2018) demonstrated with a large sample of 4- to 17-year-old children that dysregulation as indicated by overall RSA withdrawal (in heart rate variability; HRV) differentiated between children with versus without clinically elevated externalizing difficulties. However, other works have shown that externalizing symptoms correspond with little to no RSA withdrawal, at least as indicated by HRV. For example, Erath et al. (2012) found no associations between mean RSA during a video-mediated emotional evocation task and verbal and behavioral aggression. Meanwhile, Obradović et al. (2010) reported modest concurrent links but no longitudinal links between mean RSA reactivity as indicated by HRV and externalizing difficulties in their study of community children. Beauchaine et al. (2007) further found that 8- to 12-year-old children with disruptive behavior disorders experienced the same level of mean RSA withdrawal indicated by HRV compared to controls while watching an emotionally evocative video.

These inconsistencies were also reflected in a meta-analysis by Fanti et al. (2019), in which pooled results of case-control studies showed that RSA was reduced during emotional tasks in children with conduct problems compared to those without. However, no such pooled link between RSA and conduct problems was found in correlational studies. In their recent review, Beauchaine and Bell (2020) suggest that these inconsistencies may be due to high variability in the psychophysiological methods used across studies, including in the statistical approaches used to measure physiological change and in the types or contexts of tasks used to elicit RSA reactivity.

Theoretically, it would be reasonable to expect that higher physiological arousal would be closely linked to more externalizing difficulties. However, children with externalizing tendencies may also experience a blunted physiological response to certain emotional stimuli (e.g., in response to the fear shown by victims), reflecting atypicalities in the regulation and processing of important social cues gleaned from emotional information (Colasante et al., 2021). Thus, children with externalizing difficulties may not only be disinhibited in their own emotional and aggressive tendencies, but also inhibited in their capacity to respond to others’ emotional expressions and responses in social situations (e.g., Marsh et al., 2008). Echoing Beauchaine and Bell’s (2020) discussion, the mixed findings in extant literature reviewed above suggest that there may be a previously unconsidered approach that better captures the role of physiological dysregulation in childhood externalizing behavior.

Physiological Fluctuations as a Marker of Dysregulation

In the present study, we propose that an examination of intra-individual fluctuations in physiological data across a rapid array of data points, sequentially unfolding across seconds, may provide regulatory information not available from traditional approaches focused on mean-level data. The mixed findings from previous research have been largely derived from mean levels of physiological response, which average variability. Fluctuations lost in such approaches may actually reveal the dynamic physiological processes underlying dysregulation. Dysregulation is not static, but rather is inherently characterized by moment-to-moment variability in response to unfolding situations (Beauchaine & Bell, 2020). Thus, it may be best captured through intensive longitudinal measurement of physiology across short time scales that allows for consideration of the fluctuations connecting data points within children, rather than averaging absolute scores across data points and assuming that children’s resulting mean-level physiology relative to others’ levels are indicative of dysregulation. The same argument may be applied to assessing simple mean-level changes in physiology from one time point to another (i.e., physiological change or reactivity scores); such approaches often dilute meaningful variability within each time period when constructing the change score.

Intensive longitudinal data (ILD), wherein multiple datapoints are collected in sequence over a relatively short and defined period of time, is growing in popularity in physiological research due to its unique ability to capture complex biopsychological processes as they unfold over time within a given person (Dunton et al., 2021; Hamaker et al., 2018). A variety of extant studies have explored self-regulation constructs using ILD. For example, Hoeppner and colleagues (2007) collected multiple heart rate reactivity measurements amidst a series of stressful events and rest periods for children with autism. ILD can also be used to examine (dys)regulation in non-physiological data, such as through questionnaire-based ecological momentary assessment (EMA). Roos and colleagues (2020) have reviewed studies using EMA to examine use of self-reported cognitive regulation strategies in substance users, while studies reviewed in Bentley and colleagues (2021) used EMA to examine self-injurious thoughts and behaviors unfolding in daily life.

The appropriate time scale for ILD depends on the type of measure being used. Studies employing EMA, for example, largely collect data using time scales of hours or days (Bentley et al., 2021). Certain biomedical measures, including electrocardiography and electroencephalography, can leverage high sampling rates to obtain datapoints of rapidly changing physiology on ultra-short time scales of seconds or shorter (Nakamura et al., 2016). For cardiac measures, it is standard practice to capture datapoints on a timescale of seconds, most commonly utilizing 10-second (s) time bins (Goldberger et al., 2017).

A reliable physiological indicator of regulation that can be used on ultra-short time scales is the root mean square of successive differences (RMSSD) of beat-to-beat intervals (Shaffer & Ginsberg, 2017). RMSSD is a quantification of respiratory sinus arrhythmia (RSA), a measurement increasingly preferred in the biopsychological literature as it indicates activity in the parasympathetic regulatory branch of the autonomic nervous system (Beauchaine & Bell, 2020). Since parasympathetic activity reflects a ‘rest-and-digest’ regulatory response or lack thereof, assessing fluctuations in RMSSD across a series of ultra-short time points may serve as a useful approach to measuring each child’s physiological (dys)regulation in the moment. In the present study, we adopted an exploratory approach of measuring RMSSD in 5-s intervals to ensure sufficient measurement occasions for ILD across our experimental task.

Despite increasing use of RMSSD in the biopsychological literature, work reporting on RMSSD as a marker of dysregulation in children with externalizing difficulties has only begun to emerge in recent years (see Houben et al., 2015). Similar to research on RSA, extant studies have generally used point-in-time measurements and mean levels of RMSSD (Beauchaine & Bell, 2020). While informative in expanding knowledge regarding overall tendencies for dysregulation, such measures do not permit adequate assessment of within-child variability or momentary swings in physiological responding that would more appropriately capture dysregulation dynamics (Hamaker et al., 2015). Considering that dysregulation is central to both theorizing about and diagnosis of externalizing disorders, examining RMSSD variability across time in children with and without clinical levels of externalizing difficulties may contribute to our understanding the role of physiological dysregulation in childhood externalizing, and how to best capture such dysregulation moving forward as the field progresses toward better identification, measurement, and prevention of dysregulation and associated clinical difficulties (Beauchaine & Bell, 2020).

Emotional and Cognitive Correlates of Externalizing Behavior

Beyond dysregulation, demographic characteristics, such as being a boy (gender) or being a younger child (age), have been linked to greater risk for externalizing behavior (Bongers et al., 2004). Models outlining the multifaceted influences along the pathway to developing externalizing behavior (e.g., Dodge & Pettit, 2003; van Goozen et al., 2007) further suggest that cognitive and emotional processes work together with biological processes (such as those reflected by RMSSD dysregulation) to increase the likelihood of externalizing difficulties. Some of these processes have been shown to also differentiate between clinical and community samples. In the emotional and cognitive domains respectively, sympathy and inhibitory control are two characteristics that appear to be lower in children with externalizing difficulties. Sympathy is defined as empathic concern for others, particularly in response to others’ negative emotional states, such as sadness or distress. Children experiencing externalizing difficulties exhibit less sympathy compared to those without similar difficulties (e.g., de Wied et al., 2005; Miller & Eisenberg, 1988). Inhibitory control is a higher order cognitive process that marks the ability to regulate dominant or automatic impulses. Children with externalizing behavior show more inhibitory control difficulties compared to those without similar behavioral challenges (e.g.,Raaijmakers et al., 2008; Schoemaker et al., 2013).

However, given issues with multifinality—that is, the combinatorial effect of multiple risk factors being associated with any given set of outcomes—Dodge and Pettit (2003) highlight that researchers should articulate the conditions under which a specific component may be associated with externalizing outcomes, accounting for other components that may also be associated. The authors recommend simultaneously testing multiple risk factors, highlighting the specific component under investigation. Such approaches would allow for robust testing of the unique contributions of one component of the model under investigation—in the present case, physiological dysregulation—above and beyond other components of theoretical importance. Following this guidance, in the present work, we investigated the effect of physiological dysregulation on clinical externalizing status while controlling for the previously well-documented roles of sympathy (emotional component) and inhibitory control (cognitive component).

The Present Study

In this work, we assessed how dynamic RMSSD across short-term intervals may distinguish 8- to 12-year-old children with versus without externalizing difficulties. We collected intensive longitudinal electrocardiogram data from children as they responded to hypothetical social transgression scenarios, and compared clinical and community samples of children in two ways: (1) absolute or mean levels of RMSSD across the scenarios and (2) variability or fluctuations in RMSSD across the scenarios. The latter was a novel component of particular interest, as we binned children’s RMSSD into 15 5-s intervals across the transgressions, resulting in an intensive longitudinal dataset that could be used to accurately model short-term variability (Hamaker et al., 2015). With 5-s intervals, we adopted an exploratory approach that used shorter timespans compared to typical physiological regulation studies. Our initial assessments demonstrated that with our sample size (120 participants), 15 timepoints of measurement would be sufficient to satisfy the minimum requirements of DSEM (McNeish & Hamaker, 2020; Schultzberg & Muthen, 2018). In order to extract this number of timepoints from our experimental task, our data was parsed into 5-s intervals.

We adopted dynamic structural equation modelling (DSEM; McNeish & Hamaker, 2020) to assess within-person fluctuations in RMSSD over time in addition to averaged values, and, in turn, to model the predictive utility of these two RMSSD calculations on clinical status. We controlled for sympathy and inhibitory control in the model, as these constructs often differentiate between clinical and community samples in the context of externalizing difficulties (e.g., de Wied et al., 2005; Schoemaker et al., 2013), and leading theories advocate for the inclusion of multiple risk factors when attempting to establish the unique role of any single risk factor (Dodge & Pettit, 2003).

Considering the centrality of dysregulation to clinical externalizing difficulties (Houben et al., 2015), we expected that dysregulation, as captured by lower mean levels of RMSSD and higher fluctuations in RMSSD, would be higher in children with clinical referral for disruptive behavior disorders compared to those without. Based on the rationale that dysregulation—a dynamic process by definition—would be better captured by momentary fluctuations than static mean levels of RMSSD, we further expected that RMSSD fluctuations would be more strongly associated with clinical status than RMSSD mean levels, controlling for the expected effects of sympathy and inhibitory control.

Method

Participants

A community sample (N = 60; Mage = 9.11 years, SD = 1.54; 13% female) and a clinical sample (N = 60; Mage = 9.17 years, SD = 1.56; 15% female) from the Greater Toronto Area in Ontario, Canada, were assessed. All children and caregivers were fluent in English as deemed by recruitment and consent procedures. The community sample was a 60-child subset from a sample of 300 children that were assessed annually for four years. As the community and clinical samples could potentially differ on basic demographic variables (sex and age), we used propensity score matching (PSM) to ensure that the 60 community sampled children ultimately included in the data would best match the 60 clinical sampled children. PSM is a regression-based matching process in which select variables (in this case, sex and age) are used to create a regression coefficient representing a propensity score. This propensity score is then used to match each participant from one group (clinical) to one participant from another group (community) that exhibits a similar profile on those select variables. In the present work, we conducted PSM in R (package Matching; Sekhon, 2011, 2021) and selected participants without replacement so that a clinical sample child would be matched to a community sample child without duplicate draws from the larger community sample.

Community sample participants were recruited from local community centers, events, and summer camps. They were excluded if they were reported as having an autism spectrum disorder due to associated elevated difficulties in social information processing and perspective-taking (Lockwood et al., 2013), which would deter fulsome engagement with the social-emotional tasks included in this study. Parents reported externalizing difficulties below clinical cut-off for all children with the exception of one child who met criteria for ODD and CD. Community sample caregivers reported their highest level of education as: 52% bachelor’s, 25% master’s, 15% college, 3% doctoral, 5% apprenticeship/trade level. Caregivers reported their ethnic origins as 27% Western/Eastern European, 18% multiethnic, 17% Central/South American & Caribbean, 10% South/Southeast Asian, 12% East Asian, 5% African, and 2% Middle Eastern, and 3% other (7% missing/chose not to report).

The clinical sample was comprised of children with elevated externalizing behaviors referred by clinicians to partake in a specialized program at a mental health hospital. Children presented significant externalizing difficulties after a psychiatric assessment or met criteria for treatment at the clinic during the intake assessment. To be included in the clinical sample, children met the following criteria:

  1. 1.

    diagnosis of oppositional defiant or conduct disorder based on the Clinical Diagnostic Interview Schedule for Children (C-DISC; Shaffer et al., 2000);

  2. 2.

    borderline/clinically at risk scores in externalizing difficulties on the Child Behavior Checklist (CBCL 6–18; Achenbach et al. 2001), which was determined by a T score ≥ 60 on the Externalizing Problems scale or a T score ≥ 65 on the Oppositional Defiant or Conduct Disorder scales;

  3. 3.

    parent rating of ≥ 3 on questions 1, 6, and/or 7 of the Impairment Rating Scale, Narrative Description of Child section (e.g., “How your child’s problems affect his or her relationship with playmates”; IRS; Fabiano et al., 2006); and

  4. 4.

    as part of the overall clinic structure, referral to the Centre for Addiction and Mental Health for services relating to externalizing behavior difficulties after a psychiatric assessment.

Children were excluded from the clinical sample if they met any of the following criteria: (1) a KBIT-2 (Kaufman & Kaufman, 2004) Verbal and/or IQ Composite Standard Score < 80, or (2) query or diagnosis of a pervasive developmental disorder or autism spectrum disorder. Based on CBCL T-scores, 31% of children in this sample were comorbid for clinically elevated anxiety and 48% met criteria for ADHD.

Clinical sample caregivers reported their highest level of education as: 28% bachelor’s, 30% college, 20% master’s, 5% high school, 5% apprenticeship/trade level, and 2% no diploma (10% missing/chose not to report). Caregivers reported their child’s ethnic origins as: 47% White-North American/European, 13% multiethnic, 8% East Asian, 8% Black-Caribbean/North American, 5% South/Southeast Asian, 2% Latin American, 2% Middle Eastern, and 14% other (2% missing/chose not to report).

Procedures

Ethical approval was granted by the University of Toronto and the Centre for Addiction and Mental Health. Children and caregivers visited the laboratory (community sample) or a psychiatric hospital (clinical sample) for 60- to 90-minute appointments. They were assessed by trained research assistants and graduate students, and in the clinical sample, children were also interviewed by clinicians for the questionnaire components. Oral assent was obtained from children and written informed consent was obtained from caregivers prior to beginning the study. Child assessments took place in a designated testing room while caregivers remained in a waiting area while filling out the questionnaires. At study completion, caregivers and children were debriefed and children were compensated with an age-appropriate book (community and clinical samples) and $20 CAD (clinical sample).

Measures

Hypothetical Transgression Vignettes

The Social-Emotional Responding Task contains seven pre-recorded audio-visual, first-person vignettes that prompt children to imagine they are the transgressors in the stories (SERT; Malti, 2017; for reliability and validity, see Malti et al., 2021). Three of these stories were chosen due to clinical testing time constraints and because they best captured disruptive externalizing behaviors characteristic of the clinical sample.  The three stories involved the following social or moral violations of conventions and/or others’ rights or well-being: (1) disobeying a rule and walking around during lunchtime, (2) stealing a chocolate bar from a peer’s backpack while they were not looking, and (3) pushing a peer out of line to get the last remaining lollipop from the teacher. Each story was 25 s, with 10 to 15 s pre-transgression time and 15 to 20 s transgression time. Stories were presented on a computer screen and children were instructed to sit still and face the computer screen while the audio and visuals directed them to imagine themselves engaging with the stories as the transgressor. Visual content was matched to children’s respective sex and skin tone and the order of the stories was randomized.

RMSSD

Three-lead electrocardiogram data were recorded from children at a sampling rate of 2 kHz using the BIOPAC MP150 data acquisition system (community sample), BioNomadix modules (community and clinical samples), and BioNomadix Logger (clinical sample; BIOPAC Systems, Goleta, CA, USA). Electrocardiogram (ECG100C) monitoring electrodes were secured slightly below children’s right clavicle and below their ribs. Leads from the electrodes were connected to a module fastened around their midsection that wirelessly transmitted the data to a computer equipped with AcqKnowledge 4.2 software (BIOPAC Systems, Goleta, CA, USA) in an adjacent room via the MP150, or the data was stored directly in the logger and transferred to a computer afterwards. If children moved during a data collection interval, they were prompted to remain as still as possible. All instructions to minimize movement were given before, in between, or after key data collection intervals—never during them—to ensure that the data under study was not confounded.

To acclimate children to the tester and testing environment, physiology equipment was worn for approximately 10- to 15-min prior to physiological data collection. Immediately prior to the transgression stories, a 2-min aquatic video was played to measure children’s resting arousal (not included in the present analysis; Piferi et al., 2000).

The Observer XT (Noldus Information Technology, Leesburg, VA, USA) was used to synchronize electrocardiogram recordings with the stories. Within AcqKnowledge, data were subject to a bandpass filter with a 1-Hz low-frequency cut-off and a 35-Hz high-frequency cut-off. Data were then imported to HRV 3.0.25 software (Mindware Technologies, Gahanna, OH, USA) for artifact cleaning and RMSSD calculation/extraction. The HRV software automatically flags abnormal electrocardiogram peaks, which were reviewed by a trained researcher. Flagged R-peak points were either confirmed to be accurate and left unaltered, manually altered to the correct peak location, or interpolated based on the interbeat intervals (i.e., spacing) of correct peaks in the rest of the interval. RMSSD was extracted in 5-s bins across the full length of the three stories, resulting in 15 RMSSD bins/time points for each child and thus fulfilling the suggested range for intensive longitudinal data (Bolger & Laurenceau, 2013). If greater than 20% of a child’s data required cleaning, it was excluded from analyses. In the clinical sample, n = 3 had no usable physiology data, while n = 4 from the community sample did not have any usable physiology data for one to three of the stories, but their data were included and estimated using FIML.

Sensitivity Analyses

Following the methods reviewed by Shaffer and Ginsberg (2017) with the data available only for the 60 community-sample children, we ran a sensitivity analysis with the goal of demonstrating the reliability and validity of our 5-s RMSSD bins. Approaches in Shaffer and Ginsberg (2017) typically compared ultra-short term measurements to contextually invariant, longer-term measurements in the same children to demonstrate the robustness of the short-term measures. The longest continuous measure we had from our physiological measurement battery was a 120-s baseline period. For our community sample, we had this data outputted in 24 5-s bins as well as in a single 120-s bin. Results of the sensitivity analyses showed that the average of the 24 5-s bins was strongly and significantly positively correlated with the single 120-s bin (r = 0.87, p < 0.001). Furthermore, the 24 5-s bins were extremely reliable (α = 0.98), suggesting that they were excellent indicators of a broader average. In terms of validity, both the average of the 24 5-s bins and the single 120-s bin were correlated with parent-reported inhibitory control to a similar degree in the theoretically expected direction, rs = 0.33 and 0.29, ps = 0.016 and 0.039, respectively). The findings of this sensitivity analysis supported the viability of calculating RMSSD using 5-s bins within an intensive longitudinal framework in this study.

Sympathy

Caregivers completed a five-item dispositional sympathy scale adapted from Eisenberg and colleagues (1996, e.g., “My child feels sorry for other children who are being teased”). Caregivers rated their children’s sympathy on a 7-point scale (0 = never to 6 = always; community α = 0.91, clinical α = 0.91), and a mean score was used for analyses.

Inhibitory Control

Caregivers completed an eight-item scale from the Temperament in Middle Childhood Questionnaire (Simonds, 2006; e.g., “Has an easy time waiting to open a present”). Caregivers rated their children’s inhibitory control on a 7-point scale (0 = never to 6 = always; community α = 0.76, clinical α = 0.82) and a mean score was used for analyses.

Analytic Approach

We employed dynamic structural equation modeling (DSEM; McNeish & Hamaker, 2020) using the Bayes estimator in Mplus 8.7 to investigate variability in children’s RMSSD while they imagined transgressing, irrespective of their mean levels of RMSSD. DSEM combines time-series analysis, multilevel modeling, and structural equation modeling, which allowed us to isolate the dynamics of each child’s RMSSD across 15 short-term time points and then compare children on the basis of their pooled fluctuations. First, we ran an unconditional DSEM to characterize fluctuations in RMSSD across the full sample. At level 1 (within children), RMSSD scores were auto-regressed onto RMSSD scores at the prior segment (lag = 1) and a mean-centered time/segment order variable to detrend the data. The autoregression and time/segment slopes were treated as fixed effects. The residual variance (representing segment-to-segment variability in RMSSD) and intercept (representing mean levels of RMSSD across all segments) were treated as random effects to be modeled at level 2 (between children).

To determine the predictive value of these fluctuations in explaining clinical levels of disruptive behavior above and beyond more established predictors of sympathy and inhibitory control, we then tested a conditional model that regressed sample membership (categorical outcome: 0 = community sample, 1 = clinical sample) onto RMSSD variability (higher value = greater segment-to-segment variation), the RMSSD intercept (higher value = higher mean level) and caregiver reports of sympathy and inhibitory control (all at level 2). The inclusion of sympathy and inhibitory control as control variables allowed us to assess their respective associations with group membership. The Bayes estimator uses a probit link function for categorical outcomes. Thus, regression coefficients for level-2 predictors can be interpreted as the degree to which the latent propensity to belong to the clinical sample is expected to change as a function of changes in the predictor, holding all other predictors constant.

For each model, we requested four Markov Chain Monte Carlo (MCMC) chains with a potential scale reduction factor set to 0.05. Convergence was first obtained based on 5,000 total iterations, and then confirmed by doubling the number of iterations to 10,000. We also ensured convergence by manually inspecting all trace- and auto-correlation plots. Auto-correlation plots initially revealed elevated autocorrelations (> 0.10) among the iterations for some parameters; every 10th iteration was subsequently used to form the posterior distributions using the THIN option.

For each parameter, we report the median point value and standard deviation of the posterior distribution, Bayesian p value, and 95% credibility interval (CI). A Bayesian p value reflects the proportion of the posterior distribution that includes or is greater/less than zero (for negatively/positively signed parameters, respectively). Thus, p < 0.05 signifies that there is a less than 5% chance that the null hypothesis is true (e.g., that an effect is zero) given the data. The 95% CI indicates that there is a 95% chance that the value of a parameter in the population falls within that given range (van de Schoot et al., 2014). In line with traditional conventions, 95% CIs that did not contain zero were interpreted as statistically significant. RMSSD data were available for over 95% of the time points, and caregiver-reported data were available for over 90% of children. Missing data were therefore estimated under a missing-at-random assumption using the full sample of 120 participants.

Results

Descriptive statistics and bivariate correlations are reported in Tables 1 and 2, respectively. Relative to the community sample, the clinical sample had significantly lower overall levels of sympathy (p < 0.001) and inhibitory control (p < 0.001). Age and sex were not significantly associated with any of the core study variables. See Fig. 1 for a visual depiction of RMSSD fluctuations generated from the unconditional DSEM. The mean intercept of RMSSD—representing the average estimated RMSSD score across all participants—was 60.43, 95% CI [54.78, 66.05]. The variance of the intercept—representing individual differences in overall levels—was 752.04, 95% CI [529.39, 1009.72]. The log of the residual variance—representing the average amount of intraindividual fluctuations around each child’s own mean—was 6.18, 95% CI [5.90, 6.44]. The variance of the log residual variance—representing individual differences in intra-individual fluctuations—was 2.11 [1.57, 2.75].

Table 1 Descriptive Statistics and Sample Differences
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Table 2 Zero-Order Correlations for the Community and Clinical Samples
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Fig. 1
figure 1

RMSSD Fluctuations Across Children: Clinical (n = 60) and Community (n = 60) Samples. Note. Time points 1 through 15 on x-axis represent consecutive 5-s bins of RMSSD while children responded to randomized hypothetical social/moral transgressions

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Conditional DSEM results are reported in Table 3. In line with our hypothesis, greater RMSSD fluctuations predicted a higher likelihood of belonging to the clinical sample (relative to the community sample). Importantly, this effect held while controlling for mean levels of RMSSD, sympathy, and inhibitory control. With respect to the latter predictors, the effect of mean level RMSSD was in the expected direction: lower mean RMSSD levels, which are thought to reflect a dispositional tendency for physiological dysregulation (Beauchaine, 2012), were associated with a higher likelihood of belonging to the clinical sample, but this effect did not reach significance as per its 95% credibility interval. Effects of sympathy and inhibitory control did reach significance and were in the expected direction as lower levels of these capacities coincided with a higher likelihood of clinical sample membership (Table 3).

Table 3 Results of Dynamic Structural Equation Model Predicting Clinical Externalizing Status
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Discussion

In this study, we examined whether physiological dysregulation during social transgression scenarios differentiated 8- to 12-year-old children with and without clinical referral for externalizing behavior. Physiological dysregulation was indexed by two measures: mean levels of RMSSD and RMSSD fluctuations. Additionally, we investigated whether physiological dysregulation was a unique predictor of clinical status even after controlling for sympathy and inhibitory control—two capacities that are theoretically well-established as core to externalizing behavior and for which deficits have been shown to predict clinical externalizing status (e.g., Dodge & Pettit, 2003). Our results revealed that greater RMSSD fluctuations while transgressing, lower sympathy ratings, and lower inhibitory control ratings each uniquely and significantly predicted a higher likelihood of belonging to the clinical sample. Further, these effects held after controlling for the traditional physiological indicator of mean levels of RMSSD, which only bordered on significance.

Though exploratory, this study’s use of RMSSD fluctuations as a dynamic indicator of physiological dysregulation represents a novel innovation for research in this field. Literature over the past few decades has frequently examined physiological data, including RSA and related measures like RMSSD, in relation to externalizing behavior in children (see meta-analyses by Ortiz & Raine, 2004; Houben et al., 2015). In such research, however, measurements (whether obtained at rest or during stress-inducing tasks) typically reflect a cruder, averaged glimpse of one’s physiology over a period of time and are less equipped to provide insight into within-person variability in physiology over time. While averaged physiological data is undoubtedly informative to some degree, as well as methodologically simpler and less labour-intensive to collect and analyze, such data do not capture the moment-by-moment course of physiological dysregulation that a child may be experiencing as their situation naturally unfolds in daily life (Hamaker et al., 2015; Houben et al., 2015). Further, collapsing data into simple mean levels renders a researcher unable to distinguish whether a participant experienced relatively stable physiology over a period of time versus larger ‘peaks and valleys’ or swings in physiology, as both could potentially average out to the same mean value. When researching a clinical population for whom dysregulation is so central to the core symptomatology, such as for those with externalizing disorders (Althoff et al., 2010), peaks and valleys should be studied rather than averaged over and/or disregarded as statistical noise. Thus, examining within-child variability in regulation may provide rich and dynamic detail that would otherwise be obscured when using averaged data.

In this study, in contrast to much past research, we engaged this more detailed approach of examining within-person variability by including RMSSD fluctuations in our central model (alongside mean RMSSD levels). Adopting DSEM as an analytic approach allowed us to isolate and quantify the temporal dynamics of children’s RMSSD, regardless of the respective mean level of RMSSD that each child fluctuated around. Complementing the theoretical discussions of Beauchaine and Bell (2020), our finding that RMSSD fluctuations more strongly predicted clinical status than RMSSD mean levels lends further support to our argument for the importance of examining physiological fluctuations as an indicator of dysregulation, perhaps most especially when examining samples for whom self-regulation is a central challenge.

In externalizing samples specifically, examining fluctuating physiology in the context of disrupting or harming others (as illustrated in the social transgression scenarios presented in the present study) helps to shed light on links between dysregulated physiology and the impaired socioemotional behaviors associated with externalizing disorders. For instance, previous research has indicated that children with externalizing difficulties show deficits in empathic responding to others (see de Wied et al., 2010). Our results suggest that dysregulation, operationalized as fluctuations in RMSSD, may disrupt children’s capacity for attuning to or processing moral cues, or other-oriented cognitive capacities such as perspective-taking. Prior research demonstrates that the cognitive capacity to understand others’ perspectives in morally relevant situations is attenuated under conditions of physiological instability (Barkley, 1997; Deuter et al., 2018), lending confirmatory support to this study’s findings on the link between variability-based dysregulation and moral responding. However, these findings using 5-s measurement intervals are highly novel and exploratory in nature, requiring replication in future works with more measurement points (i.e., more than 15) or greater second-order sample sizes (i.e., more than 120).

Further developmental research on within-individual fluctuations in physiological responding with externalizing populations may better clarify the meanings and roles of different formulations of dysregulation in disrupting social, emotional, cognitive, or other abilities, both in contexts of social transgressions and other life contexts. In particular, given that there exists heterogeneity in the nature, etiology, and developmental course of different externalizing problems, and behavioral difficulties often co-occur with attentional inhibition difficulties (e.g., ADHD), understanding dysregulation in different symptom group contexts and comorbidities would be an important next step in uncovering the usefulness of short-term fluctuations in RMSSD to assess dysregulation.

Also of note in our findings is that RMSSD fluctuations predicted clinical status while controlling for similarly robust effects of caregiver-rated sympathy and inhibitory control. Both sympathy and inhibitory control are centrally featured in eminent theoretical models of externalizing behavior. For example, Dodge and Pettit (2003) describe sympathy-related interpersonal challenges (e.g., low social competence, minimal parental modelling of socioemotional skills, greater exposure to aggression and violence, and underexposure to prosociality) and an underactive emotional and behavioral inhibition system as contributing factors to the development of conduct problems in their Biopsychosocial Model. Beauchaine and colleagues (2016) similarly highlight social problems and poor emotional socialization alongside trait impulsivity as contributing factors to externalizing behavior in their Ontogenic Processing Model. Empirically, both constructs are understood to be closely related to externalizing behavior; children who exhibit behavior challenges are reliably found to exhibit lower levels of both sympathy and/or empathy and inhibitory control (see APA, 2013 and meta-analyses by Bonham et al., 2021; Lovett & Sheffield, 2007; Malti & Krettenauer, 2013; and Miller & Eisenberg, 1988 for a review of related literature).

That we found an effect of RMSSD fluctuations on clinical status while replicating the longstanding literature linking emotional and cognitive factors like sympathy and inhibitory control to externalizing further underscores the unique role that fluctuations in physiology may play in externalizing problems. With this in mind, in order to further our understanding of the development and maintenance of externalizing behavior, we recommend that future research continue to examine RSA fluctuations alongside mean RSA scores. The effect of mean RSA in our model neared significance in the expected direction based on past research (e.g., Shader et al., 2018), and other researchers in the field have expressed the importance of maintaining mean levels in dynamic models to develop a base of evidence that will help researchers understand the relative explanatory roles of traditional vs. dynamic measurements (e.g., Houben et al., 2015). Relatedly, researchers (e.g., McNeish & Hamaker, 2020; Sharpe, 2013) have called for greater engagement of statistical techniques such as DSEM to appropriately analyze and unlock the predictive potential of intensive longitudinal data. Such skills would complement trends in data collection, storage, and statistical processing that permit more robust analysis of intensive data.

There are several limitations of the present study that future research should aim to address. Despite sensitivity analyses suggesting robustness of the novel and experimental 5-s interval RMSSD measurements in our data, we recognize that there are currently few studies using such ultra-short term measures of physiology. Thus, our findings provide preliminary evidence for short-term physiological measurements in ILD frameworks, but further studies using such short-term measurements to conceptualize dysregulation would be important, particularly those focused on replicating the current findings. For several reasons, including feasibility within a larger project design, we chose to examine externalizing behavior via a binary variable of clinical status (i.e., clinical sample vs. community sample). Doing so prohibited us from examining externalizing behavior symptoms via an array of items on a continuous scale, which may have enabled more nuanced insight into the factors impacting severity of externalizing problems. Future research might instead choose to examine a more general and continuous measure of externalizing difficulties, such as Child Behavior Checklist (CBCL; Achenbach, 1991) scores, and adjusting the analytic strategy of the study to suit this variable-centered approach to contrast findings with our current person-centered approach. Further, while our sample consisted of somewhat diverse families (e.g., approx. 75% non-White/European origins were reported in the clinical sample), assessing the phenomenology of physiological dysregulation patterns in specific ethnoracial groups would provide important information on improving the sensitivity of its clinical applications for externalizing difficulties.

In addition, this study did not actively exclude children from the community sample who may have exhibited undiagnosed or subclinical levels of externalizing behavior. While our samples did significantly differ in all variables of interest in the expected directions, a future study with a clearer distinction between clinical and community samples may be useful. An additional direction for future research would be to incorporate ILD-style measurements of physiological responses in systems beyond the PNS. For example, Fenning et al. (2019) found that certain interactions of elevated or attenuated sympathetic and parasympathetic responses elevate the risk behavior problems in middle childhood. Employing similar holistic, multisystem physiological measurements in ILD form would be a natural extension of existing works, including the present work.

Limitations notwithstanding, our results provide deeper, albeit preliminary, insights into dynamic physiological regulation patterns, which have implications for interventions with children who experience elevated behavioral difficulties. In earlier works on dysregulation characterized by RSA, Beauchaine and colleagues (2007) found that dysregulation may precede externalizing problems in children 4 to 18 years of age. Our findings further suggest that consideration of dynamic patterns of dysregulation over time provides an alternative, sharpened perspective for understanding child outcomes above and beyond mean levels of dysregulation. Further, success of clinical interventions targeting reductions in dysregulation may be evaluated using dynamic assessments of physiological dysregulation, which may provide an alternative indicator of improvement.

In summary, this study employed a novel technique to characterize physiological dysregulation in greater detail: examining children’s moment-to-moment and fluctuating physiological responses to transgression tasks via DSEM. Resulting physiological variability scores were a more robust predictor of children’s externalizing than traditional scores of mean-level physiology. We encourage further research that adopts a similar approach in order to better evaluate and understand the unique role that physiological dysregulation plays in the genesis and development of children’s externalizing behavior.