Dyadic Behavioral Coregulation and Child Physiological Activity in Homeless/Highly Mobile Parent-Child Dyads: A State-Space Grid Analysis

A Dissertation SUBMITTED TO THE FACULTY OF THE

UNIVERSITY OF MINNESOTA BY

Carrie Elizabeth DePasquale

IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF

DOCTOR OF PHILOSOPHY

Advisor: Dr. Megan R. Gunnar

May 2020

© Carrie Elizabeth DePasquale, 2020

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Acknowledgements

This dissertation would not have been possible without the invaluable contributions of so many people. First and foremost, thank you to the families who participated in the study. Participating in research is far from a top priority, especially for families struggling with poverty and homelessness, and I am incredibly grateful to the families who generously donated their time despite this fact. Thank you also to People Serving People, whose staff has always been helpful, positive, and supportive throughout all of our data collection efforts.

I am incredibly grateful for all of the wonderful mentors I have had the privilege

to work with during my time at the University of Minnesota. A special thank you to Dr. Megan Gunnar, whose thoughtful wisdom and powerful energy cannot go unnoticed. Her commitment to good science that can actually make a difference for children and families is inspiring, and her passionate support for her students is unmatched. I cannot thank her enough. I would also like to thank Drs. Ann Masten and Dante Cicchetti, whose perspectives, support, and mentorship have certainly strengthened both my confidence as a researcher and my understanding of the complex factors that shape children’s developmental trajectories across the continuum of risk. And thank you to my dissertation committee, Drs. Megan Gunnar, Ann Masten, Dan Berry, and Abigail Gewirtz, for your insightful feedback and guidance throughout the dissertation process. Your perspectives have strengthened this dissertation immensely, culminating in the product I am proud to share with you below.

A special thank you to my fellow Mastodons. Thank you to Dr. Rebecca

Distefano, for generously allowing me to collect my dissertation research simultaneously with hers. Thank you to Kayla Nelson and Alyssa Palmer for your amazing help with data collection and RSA collection, cleaning, processing, etc. Dr. Janette Herbers, I cannot thank you enough for your willingness to train me in your coding scheme and the use of state-space grids. Of course, an emphatic thank you to my wonderful state-space grid coders, Kim Knourek and Anna Heinz! And thank you to the rest of the graduate and undergraduate research assistants who helped with this study and made hanging out at the Masten lab table so fun.

Thank you to my fellow Gunnar lab members. Especially Bonny Donzella, who

has never hesitated to help me with anything from talking through an idea out loud to answering my annoying data questions. Dr. Chris Desjardins, thank you for always explaining statistical concepts with such clarity. I owe much of my statistical knowledge and comfort with R syntax to you, which certainly laid the foundation for my dissertation analyses. Thank you to Brie Reid, for being the best cohort- and lab-mate I could have asked for. Thank you also to Dr. Nicole Perry, for always letting me bounce ideas off of you and answering my statistical questions. Thank you to the rest of the Gunnar lab, who have made my graduate training so enjoyable and have helped me in so many ways over the years.

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I would also like to give a huge thank you to my partner, Phil McGuire, for supporting me through all of graduate school. You can always make me laugh, even when I just spent 14 hours in lab trying to get my R syntax to work with variable success. You also generously helped me figure out MATLAB and troubleshoot my code for the supercomputer, all during a global pandemic when we are stuck in a house together for very long periods of time. For so many reasons, this dissertation would not have been possible without your support.

Finally, thank you to my wonderful cohort and all of your dogs. I am so grateful

to have met you all, and I will very much miss you when we all scatter back to our respective corners of the country. Thank you also to my friends and family back home. Getting my Ph.D. has been the hardest thing I have ever done, and I am grateful that you have been understanding about my hectic schedule, and my decision to fly halfway across the country just to keep going to school.

This dissertation was funded by NIMH training grant T32 MH015755 and

Institute of Child Development small grants awarded to myself and Dr. Rebecca Distefano. Funding was also provided by Dr. Ann Masten’s non-sponsored funds. The Minnesota Supercomputing Institute (MSI) at the University of Minnesota also provided resources that contributed to the research results reported within this paper.

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Abstract The quality of parent-child interactions, particularly in toddlerhood, shapes children’s development across the lifespan. This is particularly true for families experiencing chronic stress and adversity, for example homelessness and high mobility (HHM). Evidence suggests that parent-child interaction quality and child physiological self-regulation, specifically respiratory sinus arrhythmia (RSA), can be important protective factors that mitigate the impact of chronic stress on children’s socio-emotional adjustment. However, we do not understand the microsocial dynamics of parent-child behavioral interaction, how this is associated with child physiological regulation in real-time, or how this real-time biobehavioral association predicts broader indices of children’s socio-emotional well-being. In this light, the current study takes a combined developmental psychopathology-dynamic systems approach to assess how microsocial parent-child interaction processes coordinate with child RSA in real-time in N=100 families currently experiencing HHM. This study also investigated the extent to which real-time biobehavioral coordination correlates with broader indices of child adjustment: specifically, observed child executive functioning and parent-reported child socio-emotional adjustment. Children were 3-6 years old (M=4.92, SD=1.21) and families were all currently living in an urban emergency housing shelter at the time of assessment. Microsocial parent-child interaction processes were assessed during three different interaction tasks via state-space grid methodology. Child RSA was measured via ambulatory heart rate monitors during the interaction tasks. Prior to interaction, children completed the Minnesota Executive Functioning Scale and parents reported on their children’s socio-emotional adjustment via the Strengths and Difficulties Questionnaire and a subscale of the Health and Behavior Questionnaire. Multi-level vector autoregressive analyses suggested that child RSA in one moment was positively associated with dyadic behavioral coregulation in the next moment. However, dyadic behavioral coregulation did not conversely predict subsequent child RSA. These associations did not vary across tasks. For individual dyads, the association between child RSA and behavioral coregulation ranged from moderately negative to strongly positive. Still, the magnitude of this within-dyad association did not significantly predict child observed executive functioning or parent-reported socio-emotional adjustment. Results are interpreted in light of their implications for understanding risk and protective factors for families experiencing HHM. Methodological and statistical lessons are also discussed.

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Table of Contents

ABSTRACT.......................................................................................................................................... III

LIST OF TABLES ............................................................................................................................... VI

LIST OF FIGURES............................................................................................................................. VII

LIST OF ABBREVIATIONS ............................................................................................................ VIII

CHAPTER 1: INTRODUCTION .......................................................................................................... 1

THE ROLE OF THE PARASYMPATHETIC NERVOUS SYSTEM ................................................................... 2

PARENTING, RISK, AND HOMELESSNESS .............................................................................................. 4

UNDERSTANDING THE MOMENT-TO-MOMENT DYNAMICS OF PARENT-CHILD INTERACTIONS ................10

METHODOLOGICAL AND STATISTICAL CONSIDERATIONS ....................................................................12

GAPS IN THE CURRENT RESEARCH AND IMPORTANT NEXT STEPS ........................................................15

CHAPTER 2: THE CURRENT STUDY ..............................................................................................17

SPECIFIC AIMS ..................................................................................................................................17

METHODS .........................................................................................................................................19

Participants ...............................................................................................................................19

Study Design and Procedure ......................................................................................................20

Measures and Materials.............................................................................................................23

Data Analytic Plan ....................................................................................................................30

RESULTS ...........................................................................................................................................35

Descriptive Statistics .................................................................................................................35

Exploratory Preliminary Analyses and Covariates .....................................................................36

Aim 1: Association between parent-child behavioral coregulation and child RSA .......................37

Aim 2: Moderation by task context .............................................................................................39

Aim 3: Predicting broader indices of child EF and socio-emotional adjustment ..........................40

CHAPTER 3: DISCUSSION ................................................................................................................43

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LIMITATIONS ....................................................................................................................................52

FUTURE DIRECTIONS .........................................................................................................................54

BIBLIOGRAPHY .................................................................................................................................56

APPENDIX A ........................................................................................................................................75

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List of Tables

Table 1: Sample-wide base rates of each behavior category ……………………26

Table 2: Descriptive statistics of variables of interest …………………………..36

Table 3: Model results for specific aim 1 ……………………………………….38

Table 4: Model results for specific aim 2 [RSA] ………………………………..39

Table 5: Model results for specific aim 2 [BCR] ………………………………..40

Table 6: Model results for specific aim 3………………………………………..41

Table A1: Intercorrelations among all focal variables …………………………..82

Table A2: Fit statistics for all models comparing inclusion of 1-, 2-, and 3-epoch

lag times …………………………………………………………………………83

Table A3: Model results for specific aim 1 using 1-second epoch length ………84

Table A4: Model results for specific aim 1 using 5-second epoch length ………85

Table A5: Model results for specific aim 2 using 1-second epoch length [RSA] .86

Table A6: Model results for specific aim 2 using 1-second epoch length [BCR] .87

Table A7: Model results for specific aim 2 using 5-second epoch length [RSA] .88

Table A8: Model results for specific aim 2 using 5-second epoch length [BCR] .89

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List of Figures

Figure A1: Example empty state-space grid illustrating the 16 possible dyadic

states ……………………………………………………………………………..75

Figure A2: A state-space grid depicting all observed data across all tasks and all

participants ………………………………………………………………………76

Figure A3: Proportion of behavioral coregulation (yellow) compared to

behavioral dysregulation (red) for each dyad [both tasks] ………………………77

Figure A4: Proportion of behavioral coregulation (yellow) compared to

behavioral dysregulation (red) for each dyad [structured play] …………………78

Figure A5: Proportion of behavioral coregulation (yellow) compared to

behavioral dysregulation (red) for each dyad [forbidden toy] …………………..79

Figure A6: RSA for each child participant during the structured play task ……..80

Figure A7: RSA for each child participant during the structured play task ……..81

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List of Abbreviations

PNS: Parasympathetic nervous system

SNS: Sympathetic nervous system

ANS: Autonomic nervous system

RSA: Respiratory sinus arrhythmia

CPS: Child Protective Services

HHM: Homelessness and high mobility

SSG: State-space grid

IBI: Inter-beat interval

EF: Executive functioning

MEFS: Minnesota Executive Functioning Scale

SDQ: Strengths and Difficulties Questionnaire

HBQ: Health and Behavior Questionnaire

ESS: Effective sample size

mlVAR: multi-level vector autoregressive model

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Chapter 1: Introduction

The family system is the central context in which most children develop. In this

system, there is typically one or a small number of caregivers responsible for the child’s

care and wellbeing. Interactions with these caregivers (hereafter referred to as “parents,”

broadly defined to include biological, adoptive, and foster parents, custodial relatives,

etc.) are the primary source of information for children about their environment. This

information provides cues about the safety, stability, and availability of social and

material resources, which influences the development of a wide range of the child’s

biological and behavioral systems (DePasquale & Gunnar, 2018). As these systems

develop, they also set the stage for long-term differences in broader aspects of the child’s

psychosocial functioning over time (Haltigan, Roisman, & Fraley, 2013; Raby, Roisman,

Fraley, & Simpson, 2015).

This dissertation will focus on how microsocial parent-child interaction processes

correlate in real time with child parasympathetic nervous system activity in families

staying at an urban emergency housing shelter, as well as how both of these factors relate

to child socioemotional adjustment. Child parasympathetic activity is consistently

associated with parenting behavior and the quality of the parent-child relationship.

Parasympathetic activity is uniquely suited to be examined on a short, moment-to-

moment time scale, but thus far biobehavioral parent-child interaction processes have

been primarily studied as global task averages. This gap in the literature impedes our

understanding of the complex, dynamic processes that underlie longer-term

developmental changes, particularly for families living in contexts that increase risk for

poorer socioemotional adjustment, such as homelessness and high mobility (HHM).

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The following sections of this Introduction will begin by describing the

organization of the parasympathetic nervous system, its functional niches, and typical

patterns of activity, with a specific focus on respiratory sinus arrhythmia. Then,

associations between respiratory sinus arrhythmia, parent-child behavior and relationship

quality, and socioemotional adjustment are outlined, highlighting studies that include

families living in high-risk contexts (e.g., HHM and other poverty-related stressors).

Further, the particular importance of assessing biobehavioral parent-child interaction

processes during toddlerhood is discussed. The utility of microsocial methods is

explained, in the context of a combined developmental psychopathology-dynamic

systems theory framework. Methodological and statistical issues pertinent to microsocial

research, and the challenges of working with hard-to-reach populations like families

experiencing HHM, are also considered.

The Role of the Parasympathetic Nervous System

An important role the parent-child relationship plays in children’s development is

scaffolding the organization of key biological regulatory systems. For example, the

quality of parenting behaviors has been associated with differences in children’s

parasympathetic nervous system (PNS) activity (Hinnant, Erath, & El-Sheikh, 2015;

Skowron et al., 2011; Smith, Woodhouse, Clark, & Skowron, 2016). The PNS is a

component of the autonomic nervous system (ANS) that controls the neural regulation of

the heart either through the myelinated or unmyelinated portions of the vagus nerve. The

parasympathetic arm of the ANS, coupled with the sympathetic arm of the ANS and

other regulatory systems (Ulrich-Lai & Herman, 2009), operate as an interacting network

to support various adaptive behavioral responses to the environment. In general, the

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activity and function of the parasympathetic and sympathetic arms of the ANS tend to

oppose one another (Thayer & Lane, 2008). PNS activity supports rest and repair

functions, slowing heart rate and reducing stress-related arousal. Conversely, sympathetic

nervous system (SNS) activity tends to increase heart rate and stress-related arousal,

which can be inhibited by increased PNS activation. High PNS activity and low SNS

activity tends to reflect a state of calm and supports exploration and social engagement,

while high SNS activity and low PNS activity reflects a state of heightened arousal,

typically when the body is mounting a response to stress or challenge (El-Sheikh and

Erath 2011; Geisler, Kubiak, Siewert, & Weber, 2013; Gottman and Katz 2002).

A closer look at the three main neural circuits in the ANS (myelinated vagus,

unmyelinated vagus, and sympathetic) indicates that these circuits have evolved over

time as phylogenetically-ordered hierarchical structures designed to facilitate increasingly

complex responses to challenge (Porges, 2007; 2009). Lower-order systems support the

instinctive freezing response (unmyelinated vagus, PNS) and the fight-or-flight response

(SNS). However, the myelinated vagus (PNS) is a more recently-evolved system that

supports adaptive social engagement behaviors and fine-tuned augmentation or

suppression of the lower-order systems in accordance with environmental demands (i.e.,

the “vagal brake”; Porges, 2001). This coordinated process of “lifting” and “pressing” the

vagal brake to modulate autonomic regulation of the heart results in a variable pattern of

heart rate over time. One component of this variability, respiratory sinus arrhythmia

(RSA), represents the high-frequency band of heart rate variability associated with

respiration. RSA is said to be a more direct measure of the specific activity of the

myelinated vagus, while other measures (heart rate, inter-beat interval) are more equally

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impacted by both sympathetic and parasympathetic components of the ANS (Porges,

2007).

The myelinated vagus is directly linked to the neurovisceral control of muscles in

the face and head, which forms an intimate link between autonomic regulation of the

heart and social behaviors like eye gaze, head turning, and facial expressions (Porges et

al., 2007; 2009). Thus, it may not come as a surprise that PNS activity, for example RSA,

is associated with social behavior, emotion regulation, attention, and psychopathology

(Geisler et al., 2013; Hansen, Johnsen, & Thayer, 2003; Hastings et al., 2008; Thayer &

Lane, 2008). Specifically, in infants and young children, higher baseline RSA and

moderate RSA withdrawal (i.e. decrease in RSA) in response to stress or challenge has

been associated with more social engagement, better emotion regulation, higher executive

functioning (EF), and fewer psychopathology symptoms (Calkins & Keane, 2004;

Graziano & Derefinko, 2013; Hastings et al., 2008, Hinnant & El-Shiekh, 2009;

Marcovitch et al., 2010; Stifter & Corey, 2001). Indeed, there has been growing

appreciation for RSA as a biomarker for emotion regulation and risk for psychopathology

(e.g., Beauchaine, 2015). Thus, higher baseline RSA and moderate RSA withdrawal

during challenge (but not too much or too little) that is followed by a rapid return to

baseline levels is presumed to indicate better regulatory adjustment in children

(Marcovitch et al., 2010; Miller et al., 2013).

Parenting, Risk, and Homelessness

As stated above, parenting behaviors have been consistently associated with child

parasympathetic activity and vice versa. Infant RSA patterns during the Strange Situation

Procedure can be differentiated by infant attachment classification (Oosterman, De

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Schipper, Fisher, Dozier, & Schuengel, 2010; Smith et al., 2016) and higher infant RSA

during the Still-Face Paradigm increases risk of later disorganized attachment if their

mothers were also rated as more negative and intrusive (Holochwost, Gariépy, Propper,

Mills-Koonce, & Moore, 2014). During toddlerhood, maternal sensitivity predicts greater

subsequent RSA withdrawal to challenge (Perry, Mackler, Calkins, & Keane, 2014).

Conversely, both higher baseline RSA and greater RSA withdrawal have been found to

predict later increases in sensitive parenting (Kennedy, Rubin, Hastings, & Maisel, 2004;

Perry et al., 2014). More aversive and fewer autonomy-supportive parenting behaviors

during a mild challenge task predicts lower RSA and greater RSA suppression in

preschool children during the same task (Skowron et al., 2011). When watching a video

vignette intended to evoke anger, children of parents reporting authoritative, but not

authoritarian, parenting behaviors are more likely to show a typical pattern of moderate

RSA withdrawal followed by a rapid return to baseline (Miller et al., 2013). In older

children, child-reported harsh parenting was associated with lower, and in some cases

declining, resting RSA across late childhood and adolescence (Hinnant et al., 2015).

From these studies and others, it seems clear that harsh and negative parent

behaviors are associated with dysregulated RSA patterns in children, concurrently and

longitudinally. Improving parenting behaviors may ameliorate this dysregulation. At least

two interventions that target sensitive and responsive parenting behavior for families

referred by Child Protective Services (CPS) also show impacts on child RSA.

Participation in the Promoting First Relationships intervention predicted improvements in

child RSA reactivity to challenge, specifically for children of parents who showed more

sensitive, responsive behavior following the intervention (Hastings et al., 2019). Another

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intervention, Attachment and Biobehavioral Catch-up, showed that children in families

who received the intervention in infancy had higher resting RSA in middle childhood

compared to those who received a control intervention (Tabachnick, Raby, Goldstein,

Zajac, & Dozier, 2019). Thus, RSA is an important biomarker, and a potentially

important biological mechanism, through which parent-child interactions exert their

widespread impacts on children’s development.

These biological mechanisms of parent-child interactions may explain how

deficits in children’s psychosocial functioning emerge in contexts where children are

exposed to frequent, uncontrollable, and severe stressors. Children living in low-

socioeconomic households tend to have lower baseline RSA and excessive RSA

withdrawal, especially when parents are not sensitive and responsive (Johnson et al.,

2017; Lunkenheimer, Busuito, Brown, & Skowron, 2018; Skowron et al., 2011). Greater

early adversity before age 3 is associated with less, but increasing, RSA reactivity across

the preschool period (Conradt et al., 2014). Lower baseline RSA and atypical RSA

reactivity to challenge are associated with deficits in several areas of child functioning,

for example inhibitory control, aggressive behavior, behavioral dysregulation, and

physical health problems, and these associations are exacerbated by chronic adversities

like high socioeconomic risk and maltreatment exposure (Conradt et al., 2014; Eisenberg

et al., 2012; Hagan, Roubinov, Adler, Boyce, & Bush, 2016; Skowron, Cipriano-Essel,

Gatzke-Kopp, Teti, & Ammerman, 2014). Similarly, insensitive and intrusive parenting

has been shown to strengthen the association between low baseline RSA/atypical RSA

reactivity and poorer emotional and behavioral adjustment in early childhood (Gueron-

Sela et al., 2017; Hastings & De, 2008; Hastings et al., 2008; Rudd, Alkon, & Yates,

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2017). As discussed above, interventions designed to promote improved parenting

behaviors in high-risk populations (e.g., CPS-referred families, pre-term infants) have

also shown changes in child RSA (Hastings et al, 2019; Porges et al., 2019; Tabachnick

et al., 2019), though it remains to be tested whether changes in child RSA explain

improvements in behavior regulation and socio-emotional adjustment.

One of the most challenging childhood experiences is homelessness. Families

experiencing homelessness and high mobility (HHM) typically also experience a number

of other risk factors including more frequent stressful life events, fewer social resources,

poor nutrition, more physical and mental health problems, and minority status, even

compared to their low-income but housed peers (Rafferty, Shinn, & Weitzman, 2004;

Samuels, Shinn, & Buckner, 2010). HHM substantially reduces predictability and

stability in the environment, which are known to reduce stress and appraisals of threat

(Gunnar, Leighton, & Peleaux, 1984; Mineka, Gunnar, & Champoux, 1986).

Unpredictability and uncontrollability also amplify the biological stress response

(Dickerson & Kemeny, 2004). When excessive and prolonged, chronic activation of the

biological stress response in early childhood can impact child development across a wide

range of domains (Charmandari, Tsigos, & Chrousos, 2005).

There is little evidence regarding whether young children experiencing HHM

show poorer RSA regulation; however, one study suggests that there are no mean-level

differences in RSA at baseline or during a frustration task compared to housed low- and

middle-income children (Berry, Palmer, Distefano, & Masten, 2019). It is true that not all

children experiencing HMM show poor outcomes in all domains (Cutuli & Herbers,

2014; Masten, Fiat, Labella, & Strack, 2015). Thus, parenting behaviors and child RSA

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regulation may be important protective factors to promote socio-emotional adjustment

despite HHM (Herbers, Cutuli, Monn, Narayan, & Masten, 2014a; Labella, Narayan,

McCormick, Desjardins, & Masten, 2019).

Notably, besides infancy, some of the strongest associations between social-

environmental factors and child RSA and socio-emotional functioning tend to occur

during preschool and early childhood. It is well known that parenting behaviors during

this period can have an outsized impact on long-term child functioning (DePasquale &

Gunnar, in press). Further, recent evidence suggests that the highest rate of change in

RSA reactivity is from approximately ages 2-7, after which changes in RSA start to

plateau (Dollar et al., 2020). The preschool period is characterized by some of the most

rapid increases in behavioral, cognitive, and emotion regulatory functioning (Calkins,

2007; Fox & Calkins, 2003; Zelazo et al., 2003). Better regulatory skills are associated

with later school readiness and better adjustment, setting the stage for a more positive

developmental trajectory compared to children with poorer self-regulatory skills in early

childhood (Blair & Raver, 2015; Casey et al., 2014; Eisenberg, Valiente, & Eggum,

2010). These findings suggest that the preschool period is an important window of

flexibility wherein individual and environmental factors can have an outsized impact on

long-term physiological and behavioral functioning. Therefore, understanding how

parent-child interactions bidirectionally relate to child physiological regulation and

predict broader socio-emotional adjustment during this time, particularly for children

experiencing chronic stress and adversity, is critical.

Though there may be direct associations between parenting behaviors, children’s

RSA, and socio-emotional adjustment, studies tend to assess child RSA as a moderator,

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rather than a mediator, of associations between social-environmental factors and

developmental outcomes. Thus, rather than a direct biological mechanism, RSA may be a

susceptibility or plasticity factor that increases sensitivity to variations in the quality of

the environment, for better or worse. Indeed, differences in RSA may impact children’s

vulnerability to the negative effects of stress and poor parenting (Davis et al., 2017), even

in normative-risk populations (Hastings & De, 2008; Obradović, Bush, Stamperdahl,

Adler, & Boyce, 2010). Several studies have found differential associations between

negative parenting behaviors or socioeconomic risk and child psychosocial functioning at

different levels of baseline RSA and RSA reactivity (e.g., Conradt et al., 2014; Eisenberg

et al., 2012; Gueron-Sela et al., 2017; Holochwost et al., 2014). Typically, low baseline

RSA and inappropriate or excessive RSA withdrawal increase children’s risk for negative

outcomes like poor EF skills and behavioral dysregulation when they also experience

harsh, insensitive parenting, poverty, or related stressors associated with HHM.

Studies finding a moderating effect of RSA tend to assess RSA globally across

several minutes. It is yet unclear if or how moderating effects of RSA would play out at

the moment-to-moment level during an interaction. It may be that certain individual’s

RSA is more responsive to their social environment than others (Muhtadie, Koslov,

Akinola, & Mendes, 2015). Thus, the magnitude of the association between momentary

interaction behavior and momentary physiology would be a better predictor of later

socio-emotional adjustment than associations between broader relationship quality and

overall level of physiological (re)activity. Unfortunately these complex, dynamic, and

likely bidirectional associations between biology and behavior are yet to be well

understood.

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Understanding the Moment-to-moment Dynamics of Parent-child Interactions

Much research looks at global indicators of the parent-child relationship and how

these factors predict child developmental outcomes; however, there is much less known

about moment-to-moment (i.e., microsocial) dynamics of parent-child interactions. We

do not yet know the comparative predictive or explanatory utility of these two

approaches, but some research suggests that global and microsocial methods are

distinctly associated with parental antecedents like prenatal distress (Coburn, Crnic, &

Ross, 2015) and explain unique portions of the variance in child outcomes (Bardack,

Herbers, & Obradović, 2017). In addition, microsocial approaches may reduce the well-

documented “Halo effect” that tends to occur when coders rate parents (or any

individuals) using global scales (Gardner, 2000). Unfortunately, global approaches only

get us so far in terms of predicting, or intervening to enhance, later child functioning

(Barker & Fisher, 2019). As such, there has been increasing interest in the microsocial

dynamics of parent-child interactions as a way to improve predictive and explanatory

power. If successful, we are likely to be able to improve the effectiveness and efficiency

of prevention and intervention programs that target the parent-child relationship.

The developmental psychopathology framework and dynamic systems theory

both necessitate the examination of microsocial dynamics in parent-child relationships. A

core tenet of the field of developmental psychopathology is its focus on complex,

transactional environmental factors that influence an individual’s developmental

trajectory, and the acknowledgement that there are vast individual differences in

outcomes as a result of similar adversity exposures (multifinality and resilience;

Cicchetti, 2010; Masten, 2014; Sroufe & Rutter, 1984). Microsocial analyses of parent-

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child interactions and their bidirectional associations with child physiology in real time

can provide a unique perspective on this environmental complexity and highlight

potential protective factors for resilient functioning in youth experiencing HHM.

Dynamic systems theory emphasizes processes that happen on multiple time scales, from

seconds to years and the flexible, continuous interaction among components of a

particular system (e.g., a family system; Thelen & Smith, 2006).

Both developmental psychopathology and dynamic systems theory place great

importance on examining developmental processes at multiple levels of analysis

(Cicchetti & Toth, 2009; Thelen & Smith, 2006). The two theories provide overlapping

but also unique perspectives that complement one another in the study and interpretation

of developmental processes (Granic, 2005; Lunkenheimer & Dishion, 2009). A combined

developmental psychopathology-dynamic systems framework is particularly relevant to

the development of emotion regulation. Emotion regulation is necessarily understood as a

dynamic process, and must be measured and interpreted in its relational context (Cole,

Ramsook, & Ram, 2019; Heller & Casey, 2016; Silk, 2019). How parents and children

interact and manage each other’s affect in real time lays the foundation for the

development of children’s physiological and behavioral regulation. Many have proposed

that the field must move towards more microsocial, dynamic methodology to better

understand the nuances of how the development of self-regulation and the continuous

processes parents and children contribute to that compound to effect broader changes

over (developmental) time (Cole et al., 2019; Dennis-Tiwary, 2019).

It is particularly interesting to look at dynamic within-dyad associations between

behavior and biology because, while there is plenty of research linking biology and

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behavior over longitudinal, developmental time, there is comparatively little examining

how behavior-biology associations unfold on the order of minutes or seconds, let alone in

the context of a dyadic parent-child interaction. The real-time dynamics of how

individuals influence each other’s behavior and biology have the potential to shed new

light on the development of self-regulation at multiple levels of analysis as well as how

parent-child interactions influence child development at multiple time scales (seconds,

months, years). Any general developmental trend is an emergent property that arises from

a foundation of millions of moment-to-moment interactions that build and shape future

interactions and developmental states in complex, context-dependent feedback loops

(Felmlee, 2007; Ram, Shiyko, Lunkenheimer, Doerksen, & Conroy, 2014; Thelen, 2005).

In other words, development doesn’t happen in years, it happens in moments.

Methodological and Statistical Considerations

There are four important methodological and statistical considerations that should

be acknowledged when choosing a dynamic, microsocial approach to study parent-child

relationships. First, an increasingly popular tool to quantify dyadic microsocial

interactions is the state-space grid (SSG; Hollenstein, 2013). This methodology draws

directly on dynamic systems theory and quantifies dyadic “states” along two dimensions

(e.g., one for parent and one for child). This combination of states occupies a certain

space on the grid, and this allows a lot of flexibility in quantifying interaction dynamics

within the dyad along the two chosen dimensions. SSGs can be used to measure many

aspects of an interaction, including but not limited to dyadic attractor states (“habitual”

regions of the grid), flexibility (how often states change), or frequency in a particular

region of the grid. For the latter, one study applied SSG methodology with families

13

experiencing HHM and found that the proportion of time spent in the “positive co-

regulation” region of the grid (see below for details, and Figure A1) was associated with

children’s better EF skills and higher IQ, which subsequently predicted later teacher-

reported higher academic competence and fewer externalizing behaviors (Herbers,

Cutuli, Supkoff, Narayan, & Masten, 2014b). Positive co-regulation, a construct also

used in this dissertation, has therefore already demonstrated predictive utility in families

experiencing HHM.

Second, when measuring microsocial dynamics of an interaction, it is especially

important to use tasks that more closely approximate real-world settings. Fully

naturalistic settings may not always be feasible due to the high variability of possible

behaviors and situations that would be difficult to code. Furthermore, families

experiencing HHM do not necessarily have an environment conducive to naturalistic

observation. Families living in homeless shelters have very small private living quarters,

if any, with comparatively more communal, public space. While many families

experiencing HHM do not live in shelters (e.g., living in cars, with a friend or family

member, in tents outside; National Coalition for the Homeless, 2009), shelters are the

most practical way for researchers to interact with these families. For example, our

research group partners with a local homeless shelter for families with dependent children

(People Serving People) and use on-site designated research space to minimize burden on

participating families. Thus, laboratory tasks that maximize ecological validity as much

as possible provide a useful alternative.

Traditional laboratory tasks typically give parents a singular objective with

minimal distractions: “play/interact with your child as you normally would” using the

14

specific props or toys I have given you (Gardner, 2000). However, real-world parenting

does not occur in situations when parenting is the only objective in the moment,

especially for families facing adversity. Families experiencing HHM tend to have much

less regularity and predictability in their schedule (Mayberry, Shinn, Benton, & Wise,

2014), and their environments can be chaotic with a lot of distractors (multiple families in

one house, frequently moving from place to place, etc.). Frequently, all parent’s attention

is divided among multiple competing goals, like finishing a transaction at the

supermarket while continuously monitoring your child to ensure you do not get

separated, which increases cognitive demand. Parenting in context takes considerable

amounts of self-regulation (Deater-Deckard, Wang, Chen, & Bell, 2012; Gonzalez,

Jenkins, Steiner, & Fleming, 2012; Monn, Narayan, Kalstabakken, Schubert, & Masten,

2017), and increased task demand has been found to increase harsh and controlling

parenting (Ginsburg, Grover, Cord, & Ialongo, 2006). Traditional laboratory measures

reduce the need to recruit these self-regulatory abilities which likely prevents us from

teasing apart important variation in parenting behavior, especially over short time scales.

Third, dynamic measurement of physiology is inherently difficult, given that most

physiological measures used in research are proxies for the actual constructs of interest.

However, recent advances allow for the quantification of RSA in 1-second intervals via

32-second epochs with 31-seconds of overlap for successive epochs, rather than non-

overlapping 30-second epochs (Gates, Gatzke-Kopp, Sandsten, & Blandon, 2015;

Hansson & Jönsson, 2006). Additionally, parasympathetic activity is modulated in

response to changes in the environment on the order of seconds or even milliseconds,

which makes it a conceptually useful biological marker to measure on such a short time

15

scale. Thus, the PNS is uniquely suited for measuring dynamic physiological activity in

accordance with momentary changes in behavior. Other measures like salivary cortisol (a

measure of hypothalamic-pituitary-adrenocortical activity) would be equally interesting

for the field but operate on a much longer time scale (about 20-30 minutes) from initial

stimulus to measurement in saliva (Kirschbaum & Hellhammer, 1994). Future

technological, and perhaps statistical, advancements are needed to better utilize this type

of a measure in a dynamic way.

Fourth, it is critical to be statistically precise when seeking to answer dynamic,

within-individual research questions. Most pertinent to this dissertation, researchers must

separate portions of variance that are due to between-individual (or between-dyad)

differences in the variable of interest versus within-individual (or dyad) associations over

time. There are many techniques to achieve this, making use of structural equation

modeling or hierarchical linear modeling to model both between- and within-individual

effects (Berry & Willoughby, 2017; Curran, Howard, Bainter, Lane, & McGinley, 2014).

In short, these models tend to parse out the between-individual trend (e.g., differences in

mean levels across individuals) from within-individual fluctuations around that trend

(e.g., variation for a given individual around their own mean). Both are useful and answer

different questions; this allows the researcher to directly compare between- and within-

individual effects and make precise conclusions about which level of analysis their

findings pertain to.

Gaps in the Current Research and Important Next Steps

The extant literature clearly suggests that, moving forward, it will be critical to

understand the moment-to-moment dynamics of how parent-child interactions impact

16

child physiology and vice versa, as well as how those associations relate to broader

indices of child socio-emotional well-being. We do not know how parent-child

interactions correlate with children’s physiology in real-time, nor do we understand how

those momentary interactions build to influence children’s general developmental trend

towards better or worse socio-emotional adjustment. Understanding these dynamics,

particularly for children experiencing HHM and other poverty-related stressors can help

inform mechanisms through which parenting impacts child physiological activity and

regulation. Additionally, this knowledge can be applied to inform parenting interventions,

particularly those that use real-time feedback during parent-child interaction to shape

more desirable parent behavior and high-quality parent-child relationships (e.g., Parent-

Child Interaction Therapy, Attachment and Biobehavioral Catch-up). In theory, a better

understanding of the real-time biobehavioral dynamics of parent-child interactions will

give more context to those providing the parents with real-time feedback, which may in

turn make interventions more efficient and effective.

17

Chapter 2: The Current Study

In an effort to begin to resolve these critical gaps in the extant literature, this

dissertation examined the extent to which momentary dyadic interaction processes are

bidirectionally associated with momentary fluctuations in child RSA and broader indices

of child self-regulatory functioning. To address these questions, this study had three

specific aims.

Specific Aims

Specific Aim 1: Examine the extent to which moments of parent-child behavioral

coregulation predict momentary changes in child RSA activity and, conversely, how

child RSA predicts changes in the likelihood of behavioral coregulation in the next

moment. Hypothesis: Moments of behavioral coregulation will predict within-individual

increases in child RSA in the next moment, while moments not characterized by

behavioral coregulation will predict subsequent within-individual decreases in child RSA.

Conversely, higher child RSA will significantly increase the likelihood that the dyad with

display behavioral coregulation in the next moment, compared to behavioral

dysregulation. This is consistent with prior research that individuals tend to display

higher RSA in low-stress contexts, and higher RSA is associated with more social

engagement (Geisler et al., 2013; Porges, 2009). In line with this, it is expected that

behavioral coregulation will buffer the child’s stress during the tasks and generally be

associated with increases in child RSA (Skowron et al., 2011), reflective of the child’s

calmer, socially-engaged state. This more socially-engaged state, and therefore higher

child RSA, should also predict subsequent instances of behavioral coregulation (as

opposed to dysregulation).

18

Specific Aim 2: Assess whether task context (i.e., structured play versus forbidden toy

task with parent distraction) moderates the moment-to-moment association between

parent-child behavioral coregulation and child RSA (or vice versa). Hypothesis: The

association between parent-child behavioral coregulation in one moment and child RSA

in the next moment will be stronger (more positive) in the forbidden toy task compared to

that in the structured play task. The same is expected to be the case for child RSA in one

moment predicting parent-child behavioral coregulation in the next moment. This is

expected for both conceptual and statistical reasons. First, the forbidden toy task is

intended to model a more ecologically-valid parent-child interaction, with multiple goals

and distractors that increase demand on the parent’s self-regulatory abilities. Thus,

behavioral patterns within the dyad are expected to be more clearly linked to the child’s

physiological state during this task, suggesting greater real-world applicability, compared

to the structured play task. Further, the forbidden toy task is likely more stressful for the

child, giving the parent more opportunities to buffer the child’s physiological response to

this stress during their interaction. For these reasons, I expect to see greater variation in

behavioral coregulation, and possibly child RSA, during the forbidden toy task compared

to the structured play task, which also increases the ability to detect a statistical

association.

Specific Aim 3: Determine the extent to which the strength of the association between

parent-child behavioral coregulation and child RSA (for each dyad) predicts child EF and

socio-emotional adjustment. Hypothesis: The strength of the within-dyad association

between behavioral coregulation and child RSA (or vice versa) will be positively

associated with child EF and socio-emotional adjustment. By this rationale, the extent to

19

which the dyad’s interactive behavior is bidirectionally associated with momentary

changes in child RSA over time provides the basis for how parenting quality more

generally is associated with broader indices of child socio-emotional adjustment in the

long-term.

Methods

Participants

A total of 100 families with children ages 3-6 years old (M = 4.92, SD = 1.21)

currently living in an urban emergency housing shelter participated in this study. For the

following demographic data, counts are the same as percentages (because N = 100) unless

otherwise noted. Children were primarily male (55%, 45% female). Most parents were

birth mothers (94%), with a small number (6%) of birth fathers. Parents were on average

28.77 years old (SD = 4.84, range = 19-42). Parents reported their own race as 69%

Black/African American, 12% American Indian/Alaska Native, 12% White, 1% African

Native, and 6% Multiracial or Other. Four percent of parents reported Hispanic ethnicity

(1% unsure) and 12% of parents reported that they were formally enrolled in a Native

American tribe. Parents reported child race as 69% Black/African American, 18%

Multiracial, 8% American Indian/Alaska Native, 3% White, 2% Other. Seven percent of

parents reported Hispanic ethnicity for their children (1% unsure) and 4% of children

were formally enrolled in a Native American tribe.

Seventy-nine percent of parents were never married, while 11% were married, 6%

were separated, and 4% were divorced. Parents had either some high school with no

degree (28%), High school diploma or GED (65%), or a post-high school degree

(Associates, Masters, Ph.D., M.D.; 6%), with 1% who declined to respond. Most parents

20

were currently employed (76%) and most families had an annual income of less than

$10,000 per year (54%). Eighteen percent had an annual income of $10,000-19,999, 13%

an income of $20,000-49,999, 1% $50,000+, and 14% unsure. Parents reported that the

children participating in this study had been homeless (including the current stay) once

(1%), twice (40%), 3 times (34%), 4 times (15%), 5+ times (5%), with 5% who declined

to respond.

Participants were recruited at a local emergency housing shelter for families,

People Serving People, primarily in person during mealtimes and via flyers placed in the

mailboxes of all residents with potentially eligible children (determined by the daily

shelter census). Families were eligible if they 1) had at least one child between the ages

of 3 and 6 years old, 2) spoke fluent English, and 3) had resided in the shelter for at least

three nights to provide some time for acclimation. However, families reported staying as

long as approximately 2-3 years. In addition, the child must not have had an intellectual

or developmental disability or delay that would interfere with completion of the study

tasks. If a family had more than one eligible child, one child was randomly selected to

participate (the child with the earliest birth month or day; if twins, the child whose name

was first alphabetically).

Of a total of 148 potentially-eligible families with children ages 3-6 residing in

the shelter throughout the entire study period (approximately five months), 73.0% (N =

108) were recruited and a final sample of N = 100 (67.6%) participated.

Study Design and Procedure

All study procedures were approved by the University of Minnesota Institutional

Review Board and People Serving People. Participant sessions lasted approximately two

21

hours overall. After recruitment, parents and children came to a designated research suite

in the same building as the shelter at a predetermined time. During the consent process,

all study procedures and the voluntary nature of the study were described in detail with

multiple opportunities for questions and clarifications. Families could consent to all,

none, or specific parts of the study as desired. Participation in this study (or refusal to

participate) did not impact families’ relationship with the shelter in any way. In addition

to receiving a blank copy of the consent form, families also received a list of resources

including local mental health clinics, job resources, etc.

After consent, children were equipped with ambulatory heart rate monitors and

then parents and children completed individual tasks in separate rooms. Child tasks were

completed with a trained graduate student experimenter, while parent tasks were

completed with a trained undergraduate student experimenter. Children began by

completing a resting baseline task for heart rate analyses while watching a video

narration of the children’s story “Snow Day” by Ezra Jack Keats. Children then

completed several tasks including an EF assessment on a tablet. Simultaneously, parents

completed several questionnaires on a tablet, facilitated by the experimenter to minimize

limitations based on reading ability. After both the child and parent completed individual

tasks, they came together to complete three dyadic interaction tasks: a ten-minute

structured play task, a five-minute forbidden toy task with parent distraction, and a three-

minute free play task. During each task, the experimenters left the room.

For the ten-minute structured play task, parents were given a set of child-friendly

puzzles to complete with their child and were told: “We would like to see what your child

can do on his/her own, but feel free to give him/her as much help as you want.” Each

22

dyad was told to start with the same puzzle, but could proceed to any other puzzle

if/when they completed it. The puzzles were intended to be too difficult for children to

complete on their own, requiring some level of assistance or scaffolding from the parent.

During the five-minute forbidden toy task, parents were given 12 Raven’s

progressive matrices (Bilker et al., 2012) to complete on their own. They were told these

“puzzles” would provide a measure of their problem solving skills to see if they were

related to their children’s self-regulation skills. The Raven’s matrices are quite difficult,

which provided enough of a cognitive challenge that they took some time to complete but

also parents would generally maintain the motivation to keep trying.

Then, the experimenter set up an attractive toy for the child to play with, a fishing

“pond” with magnetic fish, but then pretended to discover that they left the magnetic

fishing rods in another room. This toy has been used in previous studies at the shelter

(Ramakrishnan & Masten, 2019), which have demonstrated that children tend to be very

interested in the toy. The experimenter then told the parent that they needed to go look

for the fishing rods, and to please have the child not touch the toy until the experimenter

came back with the fishing rods, at which time they can play with the toy. The

instructions were explicitly given to the parent, not the child, making it clear that it was

the parent’s job to enforce the rule while the experimenter is gone. The experimenter also

stressed the importance of completing the Raven’s matrices while they went to look for

the toy, so they could move on to the next task when they came back. This task was

intended to give the parent two (potentially competing) goals: the personal goal of

accurately and quickly completing the Raven’s matrices, and the parenting goal of

keeping their child from touching the attractive toy. Parenting does not occur in a vacuum

23

in which the parent is solely focusing on interacting with their child and nothing else. The

distraction of completing the Raven’s matrices is thus intended to make this task a more

ecologically valid representation of naturalistic parenting behaviors assessed in a

laboratory setting.

Finally, during the three-minute free play task parents and children were given a

bin of assorted toys, including the fishing rods for the forbidden toy from the previous

task. Parents were instructed to “play with your child as you normally would” with any of

the toys provided. When the experimenter returned at the end of this task, the interaction

tasks concluded.

Measures and Materials

Parent-child Behavioral Coregulation. Behavioral coregulation was measured

microsocially using SSG methodology. Parents and children were coded separately in

continuous time using the program ProcoderDVÔ (Tapp, 2003). Each individual in the

dyad was classified into one of four mutually exclusive and exhaustive behavioral

categories for both dyadic interaction tasks. These individual states were then

superimposed on one another in a 4x4 SSG, generating 16 possible dyadic states (see

Figure A1 in the Appendix as an example of an empty SSG). Any time the experimenter

was in the room interacting with the parent and/or child was considered transition time

and was not included in the present analyses.

The four parent categories were: positive control, following the child’s lead,

distracted/disengaged, and negative control. Positive control included behaviors like

instructions, suggestions, discussion of emotions, physical or verbal scaffolding of the

child’s behavior, redirecting the child to on-task behavior, etc. Importantly, these

24

behaviors were only considered positive control if they were done without harshness,

criticism, or any other negative affect. Tone could be positive or neutral. Following the

child’s lead described times when the parent is involved and attentive but not driving the

interaction, for example watching the child attempt the task, encouragement or

acknowledgement of the child’s progress, active listening, etc. Distracted/disengaged

was coded when the parent was preoccupied by something other than the task or the

child, for example looking out the window or using their phone while not engaging with

the child, looking at the camera, door, or experimenter, dissociative staring, etc. During

the forbidden toy task, working on the Raven’s matrices while not also interacting with

the child in some way was considered distracted/disengaged. Negative control included

behaviors like yelling, verbal threats/harsh physical contact, criticism, sarcasm at the

child’s expense, aggressive play, or any other behaviors with a harsh or negative tone.

Parents were each placed in one and only one of these four categories at all moments

during the interaction.

The four child categories were: on-task, signaling/bidding, withdrawn, and

defiant. Children were on-task if they are actively engaged in the task, e.g., attempting to

complete the puzzle, listening to parent directives, watching parent engage in the task,

providing suggestions. Signaling/bidding included physical or verbal attempts to get the

parent’s attention, for example tapping on the arm, nonverbal social referencing, requests

for assistance, displaying/verbalizing emotional distress that is not petulant or defiant,

etc. Children were withdrawn if they were distracted by something outside the window,

turning away or avoiding eye contact, dissociative staring, playing with the video camera,

etc. Defiance included verbal refusal to comply or complete the task, breaking a rule set

25

by the parent (regardless of task instructions), yelling, aggressive play, dangerous or

violent behavior, and any other behaviors with an oppositional or negative tone. Children

were each placed in one and only one of these four categories at all moments during the

interaction.

One primary coder was assigned to complete all parent codes and a different

primary coder completed all child codes. Parent and child codes were always completed

by different coders. Primary coders were trained by the master coder (first author,

C.E.D.), who was directly trained by the developer of the coding system (J.E.H.; Herbers

et al., 2014b). Coders were trained on an initial training set of five dyads with additional

dyads added as needed until approximately 80% agreement was achieved. The primary

parent coder showed 78% agreement with the master coder for the training set (7 dyads)

and the primary child coder showed 85% agreement with the master coder (5 dyads).

Following training, coder reliability was monitored via double-coding by the master

coder. Approximately 20% (19.5% parent, 19.6% child) of participants were double-

coded. Coder reliability was calculated as coder accuracy, derived from the kappa

statistic in accordance with observed sample-wide base rates of each behavior category,

as described in Bruckner & Yoder (2006) and Herbers et al. (2014b). As shown in Table

1, the base rates of each behavior category in this study vary considerably, which

influences traditional reliability statistics like kappa independent of the true concordance

among coders. Thus, accuracy may be a more appropriate metric of coder reliability than

kappa (Bruckner & Yoder, 2006). Coder accuracy for all parent and child behavior

categories was above 85%, except for child withdrawn during the forbidden toy task, as

26

this category had too low of an incidence rate, especially during this task, to calculate

kappa.

Table 1. Sample-wide base rates of each behavior category, calculated across all dyads as the overall proportion of time dyads spent in that category where the sum of all four codes for parent and child should each sum to 1. Total Structured Play

(N = 97) Forbidden Toy

(N = 91) Free Play (N = 46)

Parent Positive Control .44 .58 .16 .43 Following .29 .34 .13 .51 Distracted .25 .06 .69 .05 Negative Control .01 .01 .01 .01 Child On-task .86 .87 .82 .92 Signaling .11 .11 .13 .07 Withdrawn .01 .01 .00 .01 Defiant .03 .02 .05 .01

Note. See Figure A2 for a state-space grid depicting all observed data across all tasks and all participants.

Subsequently, parent-child behavioral coregulation was determined based on

simultaneous parent and child individual states. Figures A1 and A2 show the regions of

the grid, determined previously by Herbers and colleagues (2014b), that represent

positive behavioral coregulation. For each second of the interaction, dyads were assigned

a score of 1 (presence of behavioral coregulation) or 0 (behavioral dysregulation) based

on whether they were in this pre-defined region of the grid or not, respectively. For

analyses using 3- and 5-second epochs, behavioral coregulation values were scored in 3-

and 5-second chunks, rather than 1-second chunks, respectively. Using this scoring, no

27

dyad was classified in behavioral coregulation for the entire time across all three tasks.

Seventeen dyads were in behavioral coregulation during the entirety of the structured

play task, while there were only two such dyads for the forbidden toy task, and 23 for

free play. See Figures A3-A5 for bar graphs depicting the proportion of behavioral

coregulation displayed by each dyad overall, and for individual tasks. These figures

demonstrate that the forbidden toy task clearly shows the most within- and between-dyad

variability in behavioral coregulation.

Child Respiratory Sinus Arrhythmia. Child inter-beat interval (IBI) data were

sampled at 1000 Hz using FirstBeat Bodyguard 2Ô ambulatory heart rate monitors with a

modified Lead II electrode configuration. After the relevant areas were cleaned with an

alcohol swab, one electrode was placed under the child’s right collarbone and the second

was placed at the bottom of the left rib cage. Raw IBI data were then cleaned by hand

according to Porges’ method using CardioEdit software (Brain-Body Center, University

of Illinois at Chicago, 2007). All research assistants who took part in the data cleaning

process were trained to reliability on the adult and child IBI training and reliability sets

from Porges’ research group. Sufficient initial reliability was determined if all reliability

files resulted in overall RSA values within +/- 0.1 of the RSA value of the primary

cleaner from Porges’ research group. To monitor drift, 18.6% of data files were double-

cleaned.

Cleaned IBI series for resting baseline were transformed to RSA values in 30-

second epochs for each participant using CardioBatch software (Brain-Body Center,

University of Illinois at Chicago, 2007). The average of all epochs for a given participant

was used as that participant’s resting baseline RSA value. Cleaned IBI series for each

28

interaction task were transformed to second-by-second RSA values using the

RSASeconds graphical user interface (Gates et al., 2015; Hansson & Jönsson, 2006) in

MATLABÒ (2017). RSASeconds uses a peak-matched multiple window technique for

32-second epochs and 31 seconds of overlap between each successive epoch to generate

estimates for RSA at the second-by-second level. This allows the RSA data to be

analyzed on the same time scale as the state-space grid behavioral data coded in

ProcoderDVÔ (described above). To do this, child IBI data were synced to particular

behavioral tasks. Before each participant session the heart rate monitors were linked to

the exact time on a laptop computer, which was then used to record (in HH:MM:SS) the

start and end of each separate task. These timestamps were used to isolate the specific

segments of the IBI series that correspond to each task, time-locked to the beginning of

that task. This allowed me to directly connect the behavioral data to the IBI series (and

subsequently the RSA estimates obtained from RSASeconds) at the second-by-second

level. For analyses using 3- and 5-second epochs, second-by-second RSA values were

averaged into 3- and 5-second chunks, respectively. See Figures A6 and A7 for RSA data

for all child participants for the structured play task and the forbidden toy task,

respectively. Primarily, these figures illustrate the substantial within- and between-person

variability present in the data.

Child Executive Functioning. Child EF was assessed using the Minnesota

Executive Functioning Scale (MEFS; Carlson & Zelazo, 2014) tablet task, validated for

use with individuals 2-85+. This task is a cognitive flexibility sorting task wherein

participants are asked to sort various shapes or animals into their own boxes based on a

particular feature (size, color, etc.). Partway through each level, the participant is asked to

29

switch their sorting method to a different rule (e.g., size instead of color) or a

contradictory feature (e.g., big animals in the small animal box). Each child starts at a

predetermined level based on their age, and levels are titrated up or down based on the

child’s accuracy. Each level, of which there are 7, also starts with a knowledge check that

must be passed before beginning the level. Scores were calculated based on the child’s

overall accuracy and ceiling level. Additionally, if a child reached the highest level,

reaction time was also taken into account. Scores were then standardized as a z-score

relative to national normative data, which was used in the present analyses as a measure

of children’s EF abilities.

Child Socio-emotional Adjustment. To assess child socio-emotional adjustment,

parents completed two questionnaires: the Strengths and Difficulties Questionnaire

(SDQ; Goodman, 1997) and the Peer Competence subscale of the MacArthur Health and

Behavior Questionnaire (HBQ; Armstrong, Goldstein, & The MacArthur Working

Group, 2003).

The SDQ was designed for 4-10 year olds and assesses five general categories of

child functioning: Emotional problems, Conduct problems, Hyperactivity/Inattentiveness,

Peer problems, and Prosocial behavior. Each scale consists of five items, rated on a scale

from 0-2 (0 = Not True, 1 = Somewhat True, 2 = Certainly True). Items can be positively-

or negatively-valenced and are reverse-scored as needed (0 = Certainly True, 1 =

Somewhat True, 2 = Not True). Example items include: “Often loses temper” and “Shares

readily with other children”. Subscale scores were created based on the average of all

items in that subscale. Cronbach’s alphas were calculated to assess internal consistency:

Emotional problems, a = .63; Conduct problems, a = .65; Hyperactivity/Inattentiveness,

30

a = .74; Peer problems, a = .33; Prosocial behavior, a = .63. A Total Problems score (a

= .66) was also created based on the average of all subscale scores except Prosocial

Behavior.

The HBQ 1.0 parent-report form was designed for 4-8 year olds and assesses

many broad areas of child functioning including social, mental, physical, and academic

well-being. Items were rated on a scale from 1-4 (1 = Not at all like my child, 2 = Very

little like my child, 3 = Somewhat like my child, 4 = Very much like my child). The Peer

Competence subscale, comprised of 31 items related to the child’s prosocial behavior and

the quality of the child’s peer relations, was calculated as the average of all 31 items

included in this subscale (a = .86). Example items include: “Has lots of friends at school”

and “Comforts a child who is crying or upset.”

Data Analytic Plan

Power Analysis. For intensive longitudinal data such as those in this dissertation,

a common method of estimating power is through the calculation of effective sample size

(ESS). The ESS of an intensive longitudinal dataset is derived from the total number of

(dependent) observations (number of participants, n x number of repeated measures

within participant, m) and the magnitude of the within-individual dependency of

observations such that the ESS becomes smaller as the within-individual dependency

(e.g., intra-class correlation, r) becomes larger (Diggle, Liang, & Zeger, 1994; Faes,

Molenberghs, Aerts, Verbeke, & Kenward, 2009). Thus, ESS is determined by the

following formula: n * m / (1 + (m – 1) * r). The result represents the hypothetical

31

number of statistically independent observations needed to achieve the same power as the

actual number of dependent observations.

With a sample size of n = 100 dyads, approximately m = 300 observations per

dyad (e.g., 5 minutes of second-by-second data), and an intra-class correlation of r = .65

for the outcome variable, child RSA, there is an ESS of ñ = 154. Then, a power analysis

was conducted using G*Power to determine the minimum effect size a sample with this

ESS could detect with 80% power and an alpha of .05. For a repeated measures analysis,

this sample has 80% power to detect a within-dyad association (e.g., behavioral

coregulation predicting child RSA) with an effect size of f = .005, which is a small effect

according to Cohen’s conventions (small: f = 0.1).

Primary Analyses. For specific aims 1 and 2, a bivariate multilevel vector

autoregressive (mlVAR) model was fit using the ‘mlVAR’ package in R (Epskamp,

Deserno, & Bringmann, 2019; R Core Team, 2020) to examine time-lagged associations

between parent-child behavioral coregulation and child RSA. This model separately

assesses between-dyad effects, and concurrent and cross-lagged associations between two

variables within a dyad. Between-dyad differences are represented by a random intercept

allowing mean levels of a given variable to vary across dyads. Cross-lagged associations

are modeled by allowing one variable at time t to predict the other variable at time t + 1,

accounting for autoregressive associations within each variable over time. Concurrent

associations are modeled via the correlated residuals of each variable after taking into

account the between-dyad differences, cross-lagged associations, and autoregressive

effects.

32

First, exploratory models were fit using interaction data from the structured play

and forbidden toy tasks combined to determine the cross-lagged lag time that is most

appropriate for analysis. It was originally intended to use the free play task for this

purpose; however, there was insufficient variability in behavioral coregulation during this

task (as shown in Tables 1 and 2). Models were fit, without any covariates, with either a

1-, 3-, or 5-second epoch length and either 1-, 2-, or 3-epoch lag (nine total models).

Models with a 2-epoch lag also included the 1-epoch lag, and the models with a 3-epoch

lag also included both 1-epoch and 2-epoch lags. Model fit was compared across models

and lag time of the best fitting model for each epoch length was used in the subsequent

analyses. The model with the lowest values for comparative fit indices Akaike

Information Criterion (AIC) and Bayesian Information Criterion (BIC) was chosen. To

address specific aim 1, a model with the above-determined lag time and all relevant

covariates was fit for all observations across the structured play and forbidden toy tasks.

A random intercept was included for both behavioral coregulation (representing each

dyad’s mean level of behavioral coregulation across both tasks) and child RSA

(representing each child’s mean level of RSA across both tasks).

Then, based on the best fitting model determined above, the appropriate lag time

was used for all future analyses. Primary results are provided using the 3-second epoch

length; results for 1- and 5-second epoch lengths are provided in Appendix A. To assess

whether behavioral coregulation predicts child RSA and vice versa (specific aim 1), a

bivariate mlVAR model was fit with the relevant covariates (see below), and two focal

predictors: one representing the dichotomous behavioral coregulation variable for each

epoch, and the second representing average child RSA for each epoch. To assess whether

33

the association between behavioral coregulation and child RSA differed by task, two

interaction terms were created to be included in separate models. First, the task x

behavioral coregulation interaction was calculated as the product of dichotomous

behavioral coregulation for each epoch (0 or 1) and a dichotomous moderator

representing the structured play (-1) and forbidden toy (1) tasks. The task x child RSA

interaction was calculated as the product of child RSA for each epoch (centered on the

mean for each child) and the same dichotomous task moderator.

Finally, to assess whether the magnitude of the association between behavioral

coregulation and child RSA (or vice versa) predicted child EF and socioemotional

adjustment (specific aim 3), the estimates for the association between behavioral

coregulation and RSA in the mlVAR model were extracted for each dyad and used as

predictors in a multiple linear regression model (with the relevant covariates), with child

EF, SDQ, and HBQ scores as correlated dependent variables. For specific aim 3, the

association between behavioral coregulation and child RSA was determined based on the

results of specific aim 2. If the moderation was significant, the estimates were derived

from the task which showed the strongest association between behavior and RSA (or

RSA and behavior). If the moderation was non-significant, the estimates were derived

from both tasks combined.

Covariates. Child gender and age were investigated as potential time-invariant

covariates for all analyses. Child RSA during resting baseline was investigated as a

potential time-invariant covariate for all analyses with child RSA as a dependent variable

(specific aims 1 and 2). The total percent of time the child was classified as

defiant/disobedient was also investigated as a potential covariate (for specific aims 1 and

34

2) to account for child-evocative effects on dyadic interaction states. For parsimony,

covariates were only retained in final models if it significantly predicted at least one of

the two dependent variables.

Missing Data. Three dyads did not complete the structured play task and nine did

not complete the forbidden toy task. Only 46 dyads had usable behavioral coregulation

data for the free play task, either due to not completing the task or poor video recording

quality. Aside from not completing the tasks in the first place, partial missing behavioral

coregulation data was typically due to interactions with the experimenter during the task,

an individual going off camera with insufficient information to determine their behavioral

state, or briefly exiting the room (e.g., bathroom breaks). Seventeen dyads had any partial

missing behavioral coregulation data (M = 44 seconds, SD = 51). Because child RSA was

derived from moving averages, there was no partial missing data for this variable.

Twenty-one, 25, 31, and 30 children did not have RSA data for the resting baseline,

structured play, forbidden toy, and free play tasks, respectively. This was either due to

refusal to participate in this portion of the study or poor data quality determined in the

cleaning process (i.e., over a third of recorded IBIs needed manual editing). Six children

did not have MEFS scores and three children did not have HBQ data primarily due to

refusal to participate in this portion of the study. There was no missing data for SDQ

scores.

For mlVAR analyses, missing data were handled using listwise deletion at the

level of the observation, where each dyad has as many observations as the duration of

their parent-child interaction (in seconds). Thus, mlVAR analyses (Specific Aims 1 and

2) were conducted using a reduced sample of N = 77 that had usable child RSA data for

35

the structured play and/or forbidden toy tasks and at least partial behavioral coregulation

data. For Specific Aim 3, multiple linear regression analyses used listwise deletion at the

level of the dyad. Thus, linear regression analyses were conducted using a reduced

sample of N = 70 when child MEFS score was the dependent variable, N = 72 when

parent-reported child SDQ score was the dependent variable, and N = 72 when parent-

reported child HBQ score was the dependent variable.

Results

Descriptive Statistics

Descriptive statistics for all variables of interest can be found in Table 2.

Intercorrelations among these variables can be found in Table A1. As expected, there was

more variation in behavioral coregulation during the forbidden toy task compared to both

the structured and free play tasks due to the lower frequency of behavioral coregulation

and thus fewer dyads at ceiling levels (100% behavioral coregulation). Child age was

significantly, positively associated with child EF and child RSA across all three tasks,

though the association was marginally significant for RSA during the forbidden toy task.

Behavioral coregulation during the structured and free play tasks were significantly

positively correlated, though neither of these variables were significantly correlated with

behavioral coregulation during the forbidden toy task, suggesting that they represent

different aspects of the parent-child relationship. Overall percent time of child

defiance/disobedience was significantly, negatively correlated with behavioral

coregulation during the structured play and forbidden toy task, but not the free play task.

Child RSA, on the other hand, was strongly positively correlated across all three tasks.

36

Table 2. Descriptive statistics of variables of interest. Mean SD Range Child age 58.99 14.48 36.04 – 83.84 Behavioral coregulation (% time) Structured play

96.45

6.08

64.59 – 100.00

Forbidden toy 87.16 13.57 17.52 – 100.00 Free play 97.10 5.30 71.96 – 100.00 Child defiance/disobedience (total % time)+ 6.38 7.71 0.14 – 30.94 Child respiratory sinus arrhythmia Resting baseline

5.60

1.24

2.73 – 8.75

Structured play 4.74 1.24 1.58 – 7.94 Forbidden toy 4.82 1.20 1.70 – 8.31 Free play 4.81 1.21 1.77 – 7.70 Child MEFS Score -0.52 0.76 -2.60 – 1.20 SDQ Total Problems 11.99 5.88 1.00 – 28.00 HBQ Peer Competence 2.52 0.31 1.72 – 2.96

Note. MEFS: Minnesota Executive Functioning Scale; SDQ: Strengths and Difficulties Questionnaire; HBQ: MacArthur Health and Behavior Questionnaire. +Statistics provided excluding children who showed no defiance/disobedience (n = 10).

Exploratory Preliminary Analyses and Covariates

When comparing bivariate mlVAR models with 1-, 2-, and 3-epoch lags, models

with 3-epoch lags consistently showed the best model fit according to AIC and BIC

relative fit indices. This was generally true regardless of whether epoch length was set to

1 second, 3 seconds, or 5 seconds. See Table A2 for AIC and BIC for all nine models.

Thus, 3-epoch lags were included in all models described below.

As expected, child RSA resting baseline was associated with mean levels of RSA

during the two interaction tasks (p < .001) but was not associated with the overall

proportion of time each dyad spent in behavioral coregulation (p = .35). Child age was

also positively associated with RSA (p < .001) but not behavioral coregulation (p = .58).

37

Total proportion of child defiance/disobedience significantly predicted behavioral

coregulation (p < .001) and RSA (p = .003). Because RSA resting baseline, child age, and

proportion defiance/disobedience were all associated with either behavioral coregulation

or child RSA, all were included as covariates for all models with behavioral coregulation

and RSA as dependent variables (specific aims 1 and 2). Child gender was not

significantly associated with behavioral coregulation or RSA (ps = .23 and .15,

respectively), so it was not included in further analyses.

With regard to child EF and socio-emotional adjustment, child age was

significantly positively associated with EF (p = .01) and marginally positively associated

with SDQ Total Problems (p = .06), but was not significantly associated with HBQ Peer

Competence (p = .54). Child gender, on the other hand, was only significantly associated

with SDQ Total Problems (p = .007), such that male gender was associated with higher

problem scores compared to females. Child gender was not significantly associated with

EF (p = .39) or HBQ Peer Competence (p = .28). Because child age and gender were

each associated with at least one index of child socio-emotional adjustment, and to

maintain consistency across all models, child age and gender were included in all models

regarding socio-emotional adjustment (specific aim 3).

Aim 1: Association between parent-child behavioral coregulation and child RSA

See Table 3 below for final model results for aim 1, illustrating the cross-lagged,

autoregressive, concurrent, and between-dyad effects of behavioral coregulation on child

RSA and vice versa. Behavioral coregulation did not significantly predict subsequent

child RSA, but child RSA did significantly predict subsequent behavioral coregulation.

Specifically, child RSA was positively associated with subsequent behavioral

38

coregulation at a 1-epoch lag, but negatively associated at a 2-epoch lag. See Tables A3

and A4 for model results for aim 1 for 1-second and 5-second epoch lengths,

respectively.

Table 3. Model results for specific aim 1. Cross-lagged effects Estimate SE p-value RSA à BCR: Lag 1 .159 .071 .03 RSA à BCR: Lag 2 -.254 .124 .04 RSA à BCR: Lag 3 .103 .068 .13 BCR à RSA: Lag 1 .000 .001 .79 BCR à RSA: Lag 2 .000 .001 .88 BCR à RSA: Lag 3 .000 .001 .98 Autoregressive effects Estimate SE p-value RSA: Lag 1 1.982 .010 < .001 RSA: Lag 2 -1.500 .014 < .001 RSA: Lag 3 .483 .007 < .001 BCR: Lag 1 .337 .026 < .001 BCR: Lag 2 .037 .016 .02 BCR: Lag 3 .041 .013 .001 Concurrent effects Partial correlation p-value RSA ßà BCR -.115 .12 Between-dyad effects Partial correlation p-value Average RSA ßà Average BCR .003 .36 Average RSA ßà Age .161 .004 Average RSA ßà Defiance .139 .15 Average RSA ßà RSA baseline .724 < .001 Average BCR ßà Age .270 .47 Average BCR ßà Defiance -.952 < .001 Average BCR ßà RSA baseline -.047 .79

Note. Epoch length = 3 seconds. Bolded rows indicate statistically significant associations (p < .05). BCR: behavioral coregulation; RSA: respiratory sinus arrhythmia.

39

Aim 2: Moderation by task context

See Tables 4 and 5 below, which build on the model shown in Table 3 above by

adding an interaction term between child RSA and task or between behavioral

coregulation and task, respectively. Task (structured play vs. forbidden toy) did not

moderate the association between child RSA and subsequent behavioral coregulation, nor

did it moderate the association between behavioral coregulation and subsequent child

RSA. See Tables A5-A8 for model results for aim 1 for 1-second and 5-second epoch

lengths, respectively.

Table 4. Model results for specific aim 2, moderation between task and child RSA. Cross-lagged effects Estimate SE p-value RSA à BCR: Lag 1 .068 .041 .10 RSA à BCR: Lag 2 -.112 .071 .11 RSA à BCR: Lag 3 .047 .038 .22 Task x RSA à BCR: Lag 1 .020 .044 .65 Task x RSA à BCR: Lag 2 -.058 .075 .44 Task x RSA à BCR: Lag 3 .040 .040 .31 BCR à RSA: Lag 1 -.001 .002 .76 BCR à RSA: Lag 2 .000 .002 .96 BCR à RSA: Lag 3 .000 .002 .72 Autoregressive effects Estimate SE p-value RSA: Lag 1 1.981 .010 < .001 RSA: Lag 2 -1.500 .015 < .001 RSA: Lag 3 .484 .007 < .001 BCR: Lag 1 .331 .026 < .001 BCR: Lag 2 .036 .016 .02 BCR: Lag 3 .039 .013 .002 Concurrent effects Partial correlation p-value RSA ßà BCR .012 .08

40

Task x RSA ßà BCR .012 .16 Note. Epoch length = 3 seconds. Bolded rows indicate statistically significant associations (p < .05). BCR: behavioral coregulation; RSA: respiratory sinus arrhythmia. Table 5. Model results for specific aim 2, moderation between task and behavioral coregulation. Cross-lagged effects Estimate SE p-value RSA à BCR: Lag 1 .081 .035 .02 RSA à BCR: Lag 2 -.131 .062 .04 RSA à BCR: Lag 3 .063 .036 .08 BCR à RSA: Lag 1 -.001 .002 .63 BCR à RSA: Lag 2 .001 .002 .56 BCR à RSA: Lag 3 .000 .002 .82 Task x BCR à RSA: Lag 1 .010 .006 .13 Task x BCR à RSA: Lag 2 -.013 .007 .08 Task x BCR à RSA: Lag 3 .004 .005 .44 Autoregressive effects Estimate SE p-value RSA: Lag 1 1.977 .010 < .001 RSA: Lag 2 -1.494 .014 < .001 RSA: Lag 3 .477 .007 < .001 BCR: Lag 1 .306 .027 < .001 BCR: Lag 2 .042 .015 .005 BCR: Lag 3 .043 .012 < .001 Concurrent effects Partial correlation p-value RSA ßà BCR .007 .38 RSA ßà Task x BCR .003 13

Note. Epoch length = 3 seconds. Bolded rows indicate statistically significant associations (p < .05). BCR: behavioral coregulation; RSA: respiratory sinus arrhythmia.

Aim 3: Predicting broader indices of child EF and socio-emotional adjustment

Because the moderation by task context was not significant, B estimates for the

random effect of the association between child RSA and behavioral coregulation (lag 1)

were extracted from the model using 3-second epochs (depicted in Table 3) for both tasks

41

combined. In other words, each dyad was assigned one value based on their own within-

dyad association between child RSA and behavioral coregulation with a 1-epoch lag.

Positive scores indicate that when a particular child shows increases in RSA, that same

dyad is more likely to display behavioral coregulation in the next epoch. Negative scores

indicate that when a child shows increases in RSA, that same dyad is less likely to

display behavioral coregulation in the next epoch. Estimates close to zero indicate

minimal association between child RSA and dyad behavioral coregulation for a given

dyad.

B estimates were generally normally distributed, with a mean of .16 (the overall

main effect) and a standard deviation of .22. Estimates ranged from moderately negative

(-.20) to highly positive (.83) suggesting significant between-dyad variation in

associations between child physiology and dyadic behavior. However, when this estimate

was used to predict child EF and socioemotional adjustment in multivariate multiple

linear regression (with correlated dependent variables, controlling for child age and

gender), it was not significantly associated with child MEFS score, SDQ Total Problems,

or HBQ Peer Competence (see Table 6 for details).

Table 6. Model results for specific aim 3, with behavioral coregulation-RSA association derived from model using 3-second epoch length (see Table 3 above). MEFS Score ~ B (SE) t-value Intercept -1.35 (.44) -3.06** Age .02 (.01) 2.50* Gender -.17 (.19) -0.90 RSA à BCR: Lag 1 -.08 (.46) -0.17 SDQ Total Problems ~ B (SE) t-value Intercept 2.31 (3.25) 0.71

42

Age .11 (.05) 2.29* Gender 3.49 (1.37) 2.55* RSA à BCR: Lag 1 2.62 (3.40) 0.77 HBQ Peer Competence ~ B (SE) t-value Intercept 2.72 (.19) 14.71*** Age -.00 (.00) -0.87 Gender -.08 (.08) -0.97 RSA à BCR: Lag 1 -.06 (.19) -0.32

Note. Multivariate multiple linear regression was used to account for the correlations among the dependent variables. Bolded rows indicate statistically significant associations (p < .05). BCR: behavioral coregulation; RSA: respiratory sinus arrhythmia; MEFS: Minnesota Executive Functioning Scale; SDQ: Strengths and Difficulties Questionnaire; HBQ: Health and Behavior Questionnaire. Gender: 0 = female, 1 = male. *p < .05, **p < .01, ***p < .001.

43

Chapter 3: Discussion

The overarching goal of this dissertation was to contribute to better understanding

the real-time biobehavioral dynamics of parent-child interactions for families

experiencing chronic stress and adversity. Specifically, this dissertation aimed to 1)

assess whether moment-to-moment dyadic behavioral coregulation would be associated

with moment-to-moment changes in child RSA and vice versa, 2) examine whether these

associations would vary by task context, and 3) determine the extent to which the

magnitude of a dyad’s behavior-RSA association would predict children’s EF and socio-

emotional adjustment. I hypothesized that behavioral coregulation in one moment would

be positively associated with subsequent child RSA, and vice versa, within dyads. I also

hypothesized that these behavior-RSA associations would be stronger (more positive)

during the forbidden toy task that is supposedly more ecologically valid and better able to

detect variation in dyadic interaction quality. Lastly, I hypothesized that the magnitude of

the behavior-RSA association would positively predict observed child EF and parent-

reported peer competence, and negatively predict parent-reported behavior problems.

My first hypothesis was partially supported, in that child RSA positively predicted

subsequent dyadic behavioral coregulation at a 1-epoch lag when the epoch length was 3

seconds. This association varied significantly across dyads, ranging from moderately

negative to strongly positive. However, behavioral coregulation did not significantly

predict subsequent increases in child RSA. Neither behavioral coregulation nor RSA

predicted changes in the other if the epoch length was set to 1 second or 5 seconds.

Behavior-RSA associations also did not significantly vary between the two interaction

tasks. Finally, the strength of the association between child RSA and subsequent dyadic

44

behavioral coregulation (that was found to be significantly positive in the analysis for aim

1 – see Table 3 for details) was not significantly correlated with child EF or either index

of socio-emotional adjustment. Thus, my second and third hypotheses were not

supported.

Regarding aims 1 and 2, it was somewhat surprising that child RSA would

significantly predict subsequent behavioral coregulation but not vice versa. It was also

not expected that the associations would not differ by task, especially when considering

the increased variability in dyadic behavioral coregulation in the forbidden toy task

compared to the structured play task (see Figures A4 and A5). However, there is the

obvious issue of statistical power. Adding a moderation term to an mlVAR model

exponentially increases the complexity of the model and may have limited the power to

detect such task-related differences, even though there was a notably large number of

repeated measures for each dyad (approximately 900 total seconds of data per dyad).

Indeed, perhaps the association between behavior and subsequent RSA (compared to

RSA and subsequent behavior) more strongly differs by task, masking its effect in the

aim 1 model and lacking power to detect it in the aim 2 models.

Aside from statistical power, there are a number of other reasons why this pattern

of findings may have emerged. The chosen behavioral measure may possibly better

reflect the child’s own emotional and behavioral state, and the parent’s response to that

state, rather than more dyadic interaction processes. In this study behavioral coregulation

is discussed as a dyadic behavior measure, because both parent and child behaviors

contribute to the classification of behavioral coregulation states (Herbers et al., 2014b).

However, it is still possible that one individual in the dyad exerts a stronger influence on

45

the interaction than the other. For example, we know that children experiencing HHM

tend to show increased behavior problems and poorer self-regulation and cognitive

abilities compared to children of lower-risk families and even compared to low-SES but

stably housed children (Buckner, 2008; Masten et al., 1993; Monn et al., 2013; Rafferty

& Shinn, 1991; Rubin et al., 1996). In these situations, difficult child behaviors may

dominate the parent’s attention, shifting from a more bidirectional exchange to a more

child-driven exchange where parents are primarily reacting/responding to their child’s

behaviors. Thus, if a child experiences increased arousal, there may be an increased

likelihood that they display off-task or possibly defiant behavior, which may increase the

likelihood of parent frustration and insensitive behavior. This would be reflected in a

significant, positive RSA to subsequent behavioral coregulation association, consistent

with the findings in this dissertation.

However, one would still expect that real-time sensitive and supportive parental

responses should help the child successfully modulate their emotional experience, lessen

physiological arousal, and reduce problem behaviors (Lunkenheimer, Lichtwarck-

Aschoff, Hollenstein, Kemp, & Granic, 2016). If parents do not respond sensitively and

supportively, the dyad may enter into a coercive cycle, where negative behavior in one

individual begets more negative behavior in the other individual and vice versa

(Patterson, 1982; Snyder, Edwards, McGraw, Kilgore, & Holton, 1994). Parents play an

important role in either exacerbating or interrupting a coercive cycle (Lunkenheimer,

Ram, Skowron, & Lin, 2017; Scaramella, Sohr-Preston, Mirabile, Robison, & Callahan,

2008; Smith et al., 2014), given that they have a better-developed regulatory capacity that

young children typically rely on for external regulatory support (Fox & Calkins, 2003).

46

There is evidence to suggest that children can also elicit more negative behavior in

parents, particularly in infancy and toddlerhood (Smith, Calkins, Keane, Anastopoulos, &

Shelton, 2004; Verhoeven, Junger, van Aken, Deković, & van Aken, 2010), but this

simply underscores the expected bidirectionality of dyadic interaction effects.

Nevertheless, the absence of a significant association between dyadic behavioral

coregulation and subsequent child RSA in this dissertation does not support this

bidirectional hypothesis.

Also of note, there was a positive association between RSA and behavioral

coregulation at a 1-epoch lag (3-second epochs), but a negative association at a 2-epoch

lag. This was true of autoregressive effects for child RSA as well, and generally

consistent regardless of epoch length (see Tables 3, A3, and A4). This pattern of results,

particularly for the autoregressive RSA associations, may suggest that RSA levels are

fluctuating up and down around a consistent mean, rather than systematically increasing

or decreasing throughout the task. Therefore, it may make sense why child RSA would

show this counterbalancing effect, but it is not immediately clear why this would also be

reflected in the cross-lagged association between RSA and behavioral coregulation. One

possible explanation is that the counterbalancing positive and negative autoregressive

associations for RSA are indicative of the child’s broader self-regulation abilities. Then,

the extent to which a child’s RSA counterbalances (i.e., shows alternating positive and

negative associations with each additional measurement lag) in order to maintain a stable

mean level would be associated with dyadic behavioral coregulation. However, this was

not hypothesized and research in this area is sparse, preventing me from drawing

conclusions to this effect.

47

One theory that has recently gained traction that may explain such a

counterbalancing effect is cardiac fractality (e.g., Berry et al., 2019). Fractal patterns

show recursive self-similarity across space and/or time at multiple, nested levels of

observation (Mandelbrot, 1977). Cardiac fractality was recently found to be positively

associated with better behavioral and emotional regulation during a frustration task in 4-6

year old children at varying levels of risk, including a subsample of children currently

experiencing HHM (Berry et al., 2019). Thus, it is especially interesting that, in this

dissertation, the counterbalancing pattern of RSA was displayed regardless of epoch

length. This suggests a self-organizing, recursive pattern that exists at multiple time

scales of measurement (in this case, 1-, 3-, and 5-second epochs). It is important to note

that the idea that autonomic activity displays a “pattern of organized variability” is not

new (Thayer & Sternberg, 2006). Indeed, the widely known concept of allostasis is

predicated on the idea of stability through physiological or behavioral change, such that

adaptive plasticity and flexibility of a system is typically associated with resilience in that

system (Karatsoreos & McEwen, 2011; Masten, 2014; Thayer & Sternberg, 2006).

Therefore, future studies should explore the associations between cardiac fractality,

individual self-regulatory abilities, and dyadic interaction quality in more depth. It will

also be interesting to see if these patterns are consistent across families experiencing

chronic stress and adversity (like HHM) and families experiencing more normative levels

of stress.

Contrary to expectations, analyses for aim 3 revealed no significant associations

between the magnitude of RSA-behavior correlation and child EF or socio-emotional

adjustment. This may suggest that the nature of real-time physiology-behavior

48

associations during dyadic interactions does not directly associate with broader indices of

child functioning. Alternatively, it is possible that real-time RSA-behavior associations

predict other, unmeasured indices of child adjustment, for example emotion regulation

(Cole et al., 2019). Further, the RSA-behavior association used as a predictor in aim 3

was determined by the significance of all RSA-behavior and behavior-RSA associations

tested in aims 1 and 2. This variable showed substantial variability across dyads, ranging

from moderately negative to strongly positive. Other RSA-behavior (or behavior-RSA)

associations showed similar variability across dyads, but if there is an even distribution of

negative and positive correlations, the main effect will wash out to near zero. Even if the

main effect is zero, this between-dyad variability may predict child adjustment in ways

not seen in this dissertation due to the a priori decision to focus on parameters that

showed significant main effects. Future analyses could explore other RSA-behavior

associations, like the converse behavior-RSA association, that were hypothesized but not

found to be significant across the entire sample.

Dyadic physiology-behavior associations should also be measured longitudinally.

It is not yet known whether the relation between physiology and behavior during a dyadic

interaction is stable across several years, months, or even days. Is it a trait-like

phenomenon, like a stable relationship characteristic, or does it fluctuate based on factors

like the environmental context and the emotional state of the individuals in the dyad? The

RSA-behavior association was not found to predict concurrent child EF or socio-

emotional adjustment, but does it predict change in these characteristics over time? Does

this differ at across levels of family risk? A recent review (DePasquale, 2020) shows that

dyadic physiological synchrony in parent-child dyads (e.g., the within-dyad association

49

between parent and child RSA over time) may be less beneficial for dyads experiencing

chronic stress and adversity. Assuming that dyadic interaction behavior is the mechanism

through which RSA synchrony arises (child RSA influences child behavior, which

influences parent RSA and behavior, and so on), a similar pattern may exist for the RSA-

behavioral coregulation associations measured in this dissertation. Thus, findings may

differ in a more normative-risk population. The field of dyadic, real-time, biobehavioral

synchrony is still in its infancy, and much more research needs to be done to fully

understand these constructs and how they relate to parent-child relationship quality and

child adjustment across levels of risk.

In this dissertation, there are multiple worthwhile methodological and statistical

takeaways. First, we have preliminary evidence of a recommended epoch length and lag

time that may be best suited for real-time biobehavioral analyses. Including 1-, 2-, and 3-

epoch lags in autoregressive and cross-lagged paths almost universally provided the best

fit to the data regardless of epoch length (see Table A2), though the significant cross-

lagged associations were found for 1- and 2-epoch lags and only when epoch length was

3 seconds. While we cannot directly compare AIC and BIC for models with different

numbers of observations, model fit may suggest that 1-second epochs are most desirable

for RSA while 5-second epochs are most desirable for behavioral coregulation. These

conclusions are consistent with the assumption that a meaningful time interval of

behavior may need to be larger than that of RSA, which operates and changes on the

order of seconds or milliseconds. Behavior like that assessed in this dissertation may

show less meaningful change in such a small time window. The fact that significant

biobehavioral associations were only found for 3-second epochs suggests that this is a

50

sufficient “compromise” between the ideal modelling parameters for each of the

individual variables. However, conclusions cannot be drawn from one study. Some

studies have tested multiple lags (e.g., Lunkenheimer et al., 2018); however, no study to

my knowledge has systematically varied epoch length as done here, besides more

dramatic differences (e.g., whole-task vs. microsocial assessment; Bardack et al., 2017).

These findings should be interpreted as preliminary guidance for future analyses and need

to be replicated in a variety of samples before determining best practices for measuring

real-time dyadic biobehavioral associations.

Second, as mentioned above, many of the cross-lagged effects assessed in aims 1

and 2 showed substantial between-dyad variability, but main effects close to zero. There

may be meaningful between-dyad variability in these within-dyad biobehavioral

associations that may not come to light when only looking at main effects. Variation in

the magnitude of the association may be an important indicator of dyadic interaction

quality. Even more informative may be the distinction between positive and negative

associations between the same two variables. For example, when one dyad shows a

positive association between child RSA and behavioral coregulation, this suggests that

higher child RSA increases the likelihood of dyadic behavioral coregulation in the next

moment. Conversely, for a dyad that shows a negative RSA-behavioral coregulation

association, there may be fundamentally different interaction processes occurring that

may be driven by differences in certain relationship characteristics like maltreatment

history (DePasquale, 2020). Both positive and negative biobehavioral associations may

be adaptive in different contexts (e.g., stressful or calm activity, dyads with and without

maltreatment history), though this remains to be clearly understood.

51

Finally, the structured play and forbidden toy tasks were chosen on the premise

that the structured play task represents a more typical laboratory interaction task, with

one clear parenting goal and minimal distractions, while the forbidden toy task

incorporated multiple goals for the parent with distractors. It was hypothesized that the

forbidden toy task would be better able to identify variability in parent-child interaction

quality, and would represent a more ecologically valid interaction task that is more

representative of real-world parenting experiences. Indeed, there was more variability in

behavioral coregulation during the forbidden toy task compared to the structured play

task, but the majority of dyads still showed behavioral coregulation the majority of the

time (see Figure A5). Variability would likely be even smaller in a normative-risk

population, as parenting quality tends to be negatively associated with risk factors like

poverty and HHM (Perlman, Cowan, Gewirtz, Haskett, & Stokes, 2012). Even if this is

an accurate reflection of how each dyad interacts in the real world, this lack of variability

hinders the assessment of how behavioral dysregulation is associated with child

physiology and other individual/relationship characteristics. Future studies should

identify other microsocial coding schemes that maximize meaningful variability in

interaction behavior while still reflecting real-world dyadic interactions as accurately as

possible.

This dissertation had several strengths. Microsocial techniques have increased in

popularity in recent years, though few studies measure both biological and behavioral

measures in real-time in parent-child dyads. This study uses the association between

dyadic behavior and child RSA to begin to understand how small, moment-to-moment

processes can influence broader developmental trajectories of children’s self-regulation

52

and socio-emotional adjustment. Studies such as this have great potential for ultimately

improving the effectiveness of real-time feedback in parenting interventions by

delineating how real-time parent-child interactions affect child physiology. In this way,

we may be better able to identify important points in the interaction where, for example, a

parent can shift a coercive cycle to a more positive trajectory. We may also better

understand how and when clinicians and program providers should scaffold these

interactions for maximal uptake and retention of program principles. This research is

especially important in populations like families experiencing HHM who are typically

hard-to-reach, yet exhibit high need for support programs like parenting interventions.

Finally, this dissertation is strengthened by its use of both observed and parent-reported

indices of child functioning, and the inclusion of both biological and behavioral levels of

analysis during the parent-child interaction.

Limitations

Though this dissertation had many strengths, there are also several limitations that

must be considered. It is valuable to understand real-time biobehavioral processes in

parents and children experiencing HHM; however, because all families in this sample

were currently living in emergency housing, I am unable to compare findings with

normative-risk families or even families that are similarly high-risk but stably housed. In

these other populations, parent-child interaction processes may differ substantially, which

limits the generalizability of the present findings. Also, as stated above, the behavioral

coregulation measure does not encompass all of the many potentially-relevant dimensions

of interaction behavior that can influence the biobehavioral associations of interest. Other

dimensions like affect, intrusiveness, active vs. passive engagement, or verbal

53

communication, among others, may better capture meaningful variability that is

associated with other individual/relationship characteristics. Further, this study used a

categorical measure of behavior (behavioral coregulation vs. dysregulation), though a

continuous metric may be more fruitful.

This dissertation also had a relatively small sample with substantial missing data,

which resulted in only N = 77 dyads for the primary analyses. The possibility of

insufficient power (Type II error) is probable, though this was likely more apparent for

the between-dyad-focused analyses (aim 3) than the within-dyad-focused analyses (aims

1 and 2). Conversely, there is a possibility of false positives (Type I error) due to the

large number of models tested (when considering all epoch lengths that were included)

with few significant findings. Thus, the results of this dissertation need to be replicated

with larger samples to ensure that Type I and Type II errors are not responsible for the

current findings.

Another limitation is that this dissertation did not account for the impact of speech

or speech rate on spontaneous respiratory changes that could have artificially inflated or

deflated child RSA values (Bernardi et al., 2000; Reilly & Moore, 2003). Once issues

related to data privacy and the identification of multiple speakers are resolved, future

analyses will quantify speech rate to be included as a covariate to ensure that any

significant findings are not due to the confounding factor of speech. This study also does

not consider the role of interrelated biological systems that influence and are influenced

by the PNS (e.g., SNS, hypothalamic-pituitary-adrenocortical axis). Complex cross-

system activity may better reflect child self-regulatory processes during parent-child

interactions, though this substantially complicates modelling procedures and would

54

require a much larger sample size to adequately measure. Future studies could consider

cross-system measures like sympathovagal balance (Sturge-Apple, Skibo, Rogosch,

Ignjatovic, & Heinzelman, 2011) or cortisol-salivary a-amylase ratio (Ali & Pruessner,

2012) instead of single-system measures like RSA.

Future Directions

Some of the most important future directions of this work will be to incorporate

the biobehavioral associations with the burgeoning literature on parent-child

physiological synchrony (DePasquale, 2020). Measuring real-time behavior in addition to

biology in both individuals in the dyad may yield a more complete understanding of how

parents and children influence and are influenced by one another. It will also be

interesting to directly assess the role of stress (both acute and chronic) and how it is

associated with dyadic biobehavioral synchrony. Stress may alter biobehavioral

processes, but biobehavioral synchrony/coregulation could also reduce or exacerbate the

experience of stress (DePasquale, 2020). Additionally, there are several common metrics

used with SSGs that may prove informative, like predictability/consistency (i.e. entropy)

and flexibility (Dishion, Nelson, Winter, & Bullock, 2004; Lunkenheimer et al., 2016)

that may predict relationship quality and long-term child adjustment. If these metrics

could be meaningfully operationalized on a small enough time scale to examine

associations with real-time fluctuations in child physiology, they might shed additional

light on the moment-to-moment interaction processes that support the parent-child

relationship, particularly in infancy and early childhood. Finally, and most importantly,

future studies of dyadic biobehavioral synchrony should be longitudinal to understand if

or how these factors change over time, and to identify their antecedents and consequences

55

for child adjustment over time. Longitudinal studies can also identify whether

biobehavioral synchrony is a risk factor for or a protective factor against

psychopathology in children and/or parents, the mechanisms that explain this risk or

protective process, and whether the process differs as a function of socioeconomic risk or

experiences of adversity.

56

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Appendix A

Chi

ld B

ehav

ior

On-task

Signals/ Bids

Withdrawn/ Distracted

Defiant/ Disobedient

Negative Control

Distracted/ Disengaged

Following Child’s Lead

Positive Control

Parent Behavior

Figure A1. Example empty state-space grid illustrating the 16 possible dyadic states determined by the microsocial coding described in Measures and Materials. The region outlined in bold is the behavioral coregulation region.

76

Chi

ld B

ehav

ior

On-task

Signals/ Bids

Withdrawn/ Distracted

Defiant/ Disobedient

Negative Control

Distracted/ Disengaged

Following Child’s Lead

Positive Control

Parent Behavior

Figure A2. A state-space grid depicting all observed data across all tasks and all participants. The region outlined in red is the behavioral coregulation region. Empty circles represent starting states for each dyad. Filled in circles represent subsequent states. The size of the circle represents the duration spent in that state without transitioning to another state. Placement of the circles within each of the 16 states in the grid is random.

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Figure A3. Proportion of behavioral coregulation (yellow) compared to behavioral dysregulation (red) for each dyad, sorted by proportion behavioral coregulation. Data include both the structured play and forbidden toy tasks.

78

Figure A4. Proportion of behavioral coregulation (yellow) compared to behavioral dysregulation (red) for each dyad, sorted by proportion behavioral coregulation. Data included only from the structured play task.

79

Figure A5. Proportion of behavioral coregulation (yellow) compared to behavioral dysregulation (red) for each dyad, sorted by proportion behavioral coregulation. Data included only from the forbidden toy task.

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Figure A6. RSA for each child participant during the structured play task.

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Figure A7. RSA for each child participant during the forbidden toy task.

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Table A1. Intercorrelations among all focal variables (total N = 100). 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 1. Child age 100 2. BCR – Structured play .13 97 3. BCR – Forbidden toy .12 .09 91 4. BCR – Free play .02 .56*** -.15 46 5. Child percent defiant/disobedient

-.12 -.62*** -.27** -.12 97

6. Child RSA – Resting baseline

.12 .13 -.03 .06 -.01 79

7. Child RSA – Structured play

.26* .09 .02 -.05 .12 .84*** 75

8. Child RSA – Forbidden toy

.22+ .17 .05 .10 .05 .78*** .86*** 69

9. Child RSA – Free play .44*** .12 .13 -.01 .06 .65*** .76*** .74*** 70 10. Child executive functioning

.33** .26** .02 .20 -.06 .08 .05 .12 .04 94

11. Child SDQ Total Problems

.10 -.13 -.05 -.09 .09 -.13 .04 -.03 .11 -.04 100

12. Child HBQ Peer Competence

-.07 .11 -.01 .00 -.13 .03 -.05 -.13 -.02 .03 -.59*** 97

Note. Sample size for each variable is presented in italics on the diagonal. All correlations shown are Pearson correlations. BCR: behavioral coregulation; RSA: respiratory sinus arrhythmia; SDQ: Strengths and Difficulties Questionnaire; HBQ: Health and Behavior Questionnaire. +p < .10 *p < .05, **p < .01, ***p < .001. Significant values (p < .05) are shown in bold.

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Table A2. Fit statistics for all models comparing inclusion of 1-, 2-, and 3-epoch lag times. Behavioral coregulation RSA

AIC BIC AIC BIC

Epoch length: 1 second 1-epoch lag 97411.2 97510.5 -207321.1 -207221.8 1-, 2-epoch lags 95689.0 95887.6 -357231.7 -357033.1 1-, 2-, 3-epoch lags 94436.3 94770.4 -461645.8 -461311.7 Epoch length: 3 seconds 1-epoch lag 41693.6 41780.7 -25934.4 -25847.3 1-, 2-epoch lags 41500.2 41674.4 -40308.6 -40134.4 1-, 2-, 3-epoch lags 41297.1 41590.2 -45610.1 -45317.1 Epoch length: 5 seconds 1-epoch lag 25930.7 26012.1 -5435.1 -5353.7 1-, 2-epoch lags 25833.4 25996.1 -9473.7 -9311.0 1-, 2-, 3-epoch lags 25782.5 26056.2 -9605.6 -9332.0

Note. Fit statistics were calculated for the separate univariate components (behavioral coregulation, respiratory sinus arrhythmia) of each bivariate model. Bolded values indicate the best fitting model for each variable and each epoch length. RSA: respiratory sinus arrhythmia; AIC: Akaike Information Criterion; BIC: Bayesian Information Criterion.

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Table A3. Model results for specific aim 1 using 1-second epoch length. Cross-lagged effects Estimate SE p-value

RSA à BCR: Lag 1 .074 .197 .71 RSA à BCR: Lag 2 -.007 .390 .99 RSA à BCR: Lag 3 -.059 .201 .77 BCR à RSA: Lag 1 .000 .000 .73 BCR à RSA: Lag 2 .000 .000 .87 BCR à RSA: Lag 3 .000 .000 .34

Autoregressive effects Estimate SE p-value

RSA: Lag 1 2.810 .003 < .001 RSA: Lag 2 -2.718 .006 < .001 RSA: Lag 3 .907 .003 < .001 BCR: Lag 1 .649 .014 < .001 BCR: Lag 2 -.036 .015 .02 BCR: Lag 3 .054 .011 < .001 Concurrent effects Partial correlation p-value

RSA ßà BCR -.002 .99

Between-dyad effects Partial correlation p-value

Average RSA ßà Average BCR .003 .21 Average RSA ßà Age .187 < .001 Average RSA ßà Defiance .136 .003 Average RSA ßà RSA baseline .728 < .001 Average BCR ßà Age .259 .58 Average BCR ßà Defiance -.951 < .001 Average BCR ßà RSA baseline -.071 .35

Note. Bolded rows indicate statistically significant associations (p < .05). BCR: behavioral coregulation; RSA: respiratory sinus arrhythmia.

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Table A4. Model results for specific aim 1 using 5-second epoch length. Cross-lagged effects Estimate SE p-value

RSA à BCR: Lag 1 .049 .061 .42 RSA à BCR: Lag 2 -.054 .103 .60 RSA à BCR: Lag 3 .001 .060 .98 BCR à RSA: Lag 1 .001 .003 .65 BCR à RSA: Lag 2 -.001 .002 .77 BCR à RSA: Lag 3 .000 .002 .99

Autoregressive effects Estimate SE p-value

RSA: Lag 1 1.444 .014 < .001 RSA: Lag 2 -.673 .020 < .001 RSA: Lag 3 .098 .011 < .001 BCR: Lag 1 .262 .030 < .001 BCR: Lag 2 .016 .017 .35 BCR: Lag 3 .018 .012 .14

Concurrent effects Partial correlation p-value

RSA ßà BCR .024 .02 Between-dyad effects Partial correlation p-value

Average RSA ßà Average BCR .004 .55 Average RSA ßà Age .235 .007 Average RSA ßà Defiance .158 .13 Average RSA ßà RSA baseline .883 < .001 Average BCR ßà Age .300 .29 Average BCR ßà Defiance -.929 .004 Average BCR ßà RSA baseline -.044 .99

Note. Bolded rows indicate statistically significant associations (p < .05). BCR: behavioral coregulation; RSA: respiratory sinus arrhythmia.

86

Table A5. Model results for specific aim 2 using 1-second epoch length, moderation between task and child RSA. Cross-lagged effeƒcts Estimate SE p-value

RSA à BCR: Lag 1 .061 .105 .56 RSA à BCR: Lag 2 -.055 .210 .79 RSA à BCR: Lag 3 -.004 .111 .97 Task x RSA à BCR: Lag 1 .163 .107 .13 Task x RSA à BCR: Lag 2 -.310 .213 .15 Task x RSA à BCR: Lag 3 .150 .113 .18 BCR à RSA: Lag 1 .000 .000 .89 BCR à RSA: Lag 2 .000 .000 .94 BCR à RSA: Lag 3 .000 .000 .43

Autoregressive effects Estimate SE p-value

RSA: Lag 1 2.812 .002 < .001 RSA: Lag 2 -2.721 .004 < .001 RSA: Lag 3 .909 .002 < .001 BCR: Lag 1 .647 .014 < .001 BCR: Lag 2 -.037 .015 .02 BCR: Lag 3 .054 .011 < .001 Concurrent effects Partial correlation p-value

RSA ßà BCR -.003 .79 Task x RSA ßà BCR -.003 .48

Note. Bolded rows indicate statistically significant associations (p < .05). BCR: behavioral coregulation; RSA: respiratory sinus arrhythmia.

87

Table A6. Model results for specific aim 2 using 1-second epoch length, moderation between task and behavioral coregulation. Cross-lagged effects Estimate SE p-value

RSA à BCR: Lag 1 .069 .105 .51 RSA à BCR: Lag 2 -.072 .208 .73 RSA à BCR: Lag 3 .010 .108 .93 BCR à RSA: Lag 1 .000 .000 .94 BCR à RSA: Lag 2 .000 .000 .90 BCR à RSA: Lag 3 .000 .000 .29 Task x BCR à RSA: Lag 1 .000 .000 .71 Task x BCR à RSA: Lag 2 .000 .000 .45 Task x BCR à RSA: Lag 3 .000 .000 .59

Autoregressive effects Estimate SE p-value

RSA: Lag 1 2.811 .002 < .001 RSA: Lag 2 -2.720 .004 < .001 RSA: Lag 3 .908 .002 < .001 BCR: Lag 1 .639 .013 < .001 BCR: Lag 2 -.039 .015 .01 BCR: Lag 3 .063 .011 < .001 Concurrent effects Partial correlation p-value

RSA ßà BCR -.003 .50 RSA ßà Task x BCR .001 .86

Note. Bolded rows indicate statistically significant associations (p < .05). BCR: behavioral coregulation; RSA: respiratory sinus arrhythmia.

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Table A7. Model results for specific aim 2 using 5-second epoch length, moderation between task and child RSA. Cross-lagged effects Estimate SE p-value

RSA à BCR: Lag 1 .010 .034 .76 RSA à BCR: Lag 2 .002 .056 .97 RSA à BCR: Lag 3 -.016 .034 .63 Task x RSA à BCR: Lag 1 -.022 .031 .47 Task x RSA à BCR: Lag 2 .072 .052 .17 Task x RSA à BCR: Lag 3 -.052 .031 .09 BCR à RSA: Lag 1 .002 .005 .74 BCR à RSA: Lag 2 -.002 .005 .67 BCR à RSA: Lag 3 .000 .004 .91

Autoregressive effects Estimate SE p-value

RSA: Lag 1 1.445 .015 < .001 RSA: Lag 2 -.674 .021 < .001 RSA: Lag 3 .099 .012 < .001 BCR: Lag 1 .252 .030 < .001 BCR: Lag 2 .013 .017 .46 BCR: Lag 3 .015 .012 .22

Concurrent effects Partial correlation p-value

RSA ßà BCR .016 .10 Task x RSA ßà BCR .007 .39

Note. Bolded rows indicate statistically significant associations (p < .05). BCR: behavioral coregulation; RSA: respiratory sinus arrhythmia.

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Table A8. Model results for specific aim 2 using 5-second epoch length, moderation between task and behavioral coregulation. Cross-lagged effects Estimate SE p-value

RSA à BCR: Lag 1 .024 .027 .38 RSA à BCR: Lag 2 -.027 .048 .74 RSA à BCR: Lag 3 .010 .027 .70 BCR à RSA: Lag 1 .000 .005 .95 BCR à RSA: Lag 2 .001 .005 .89 BCR à RSA: Lag 3 .001 .004 .81 Task x BCR à RSA: Lag 1 .032 .017 .06 Task x BCR à RSA: Lag 2 -.031 .018 .10 Task x BCR à RSA: Lag 3 .007 .016 .65

Autoregressive effects Estimate SE p-value

RSA: Lag 1 1.426 .014 < .001 RSA: Lag 2 -.657 .019 < .001 RSA: Lag 3 .079 .011 < .001 BCR: Lag 1 .232 .032 < .001 BCR: Lag 2 .018 .018 .31 BCR: Lag 3 .013 .012 .29

Concurrent effects Partial correlation p-value

RSA ßà BCR .005 .13 RSA ßà Task x BCR .002 .45

Note. Bolded rows indicate statistically significant associations (p < .05). BCR: behavioral coregulation; RSA: respiratory sinus arrhythmia.