Computational Modeling of Sequential Dependencies in Mother–Child Social Interaction and Associations to Empathic Responses

ABSTRACT

Understanding how early mother–child interactions are linked to children's social‐cognitive processes requires methods capable of capturing the temporal structure of naturalistic behavior. This study introduces a computational framework based on Bayesian Network modeling to identify sequential dependencies among nonverbal behaviors (smiles, gaze, and social touch) exchanged during free play in mother–child dyads (n = 38; age 3 years). From each network, we derived the Order of Sequential Interaction (OSI), a compact index of interaction complexity. We then examined its associations with behavioral, physiological, and neural measures relevant to cognitive development. Although OSI was not associated with language or executive‐function scores, analyses revealed links between OSI and prosocial behavior, facial EMG, and neural responses (rTPJ, lIFG) during prosocial‐scene viewing. These findings suggest that OSI may capture aspects of interaction structure specifically connected to children's social and affective responsiveness. Building on this, the present framework demonstrates how probabilistic graphical models can structure complex interaction data and support future investigations into multimodal processes in early social cognition.

Summary

• A Bayesian‐network framework is proposed to model multivariate sequential dependencies in naturalistic mother–child interaction.

• The order of sequential interaction (OSI) quantifies interaction complexity from behavioral time‐series data.

• Higher OSI is associated with greater prosocial behavior and with neural (rTPJ, lIFG) and physiological (facial EMG) responses during social processing.

• Interaction complexity is not associated with general cognitive or language measures, suggesting that it reflects a distinct dimension of social behavior.

• The proposed framework provides a basis for studying social‐cognitive development from naturalistic interaction data.

1. Introduction

Early interactions between mothers and children in daily life have a profound effect on the development of children's social cognition Landry et al. (2006); Ginsburg et al. (2007); Rocha et al. (2020). Specifically, the dynamics of behavioral cues exchanged during these interactions influence children's language and social development Bigelow et al. (2010); Csibra and Gergely (2009). Additionally, maternal responsiveness, reflected in contingent and appropriate reactions to a child's behavior, is a robust predictor of children's socio‐emotional, cognitive, and language development, as well as the quality of the parent‐child relationship Mcquaid et al. (2009); Rocha et al. (2020). 

Within this broad domain of social cognition, several interrelated processes contribute to successful interaction. Language development enables the exchange of meaning and perspectives, while executive functions support attention shifting, inhibition, and behavioral regulation. Theory of mind (ToM) represents a more advanced ability to infer others' beliefs and intentions. Closely related to ToM is empathy, commonly described as a multidimensional construct encompassing both cognitive and emotional components. Cognitive empathy refers to the ability to understand another person's thoughts, intentions, or perspectives, whereas emotional empathy involves sharing or resonating with another person's affective state Frith and Frith (2006); Minagawa et al. (2018); De Vignemont and Singer (2006). Together, these processes support early social understanding, interpersonal coordination, and prosocial responding, and develop alongside other socio‐cognitive abilities such as language and perspective taking.

To investigate these mechanisms, previous studies have employed behavioral, physiological, and neuroimaging approaches to examine how children respond to others' emotions and intentions. Behavioral observations show that toddlers spontaneously help or comfort others in distress Warneken and Tomasello (2006), while physiological and neural techniques such as facial electromyography (EMG), electroencephalography (EEG), and functional near‐infrared spectroscopy (fNIRS) have revealed early signatures of affective resonance and social information processing Geangu et al. (2016); Light et al. (2009); Yamamoto et al. (2024); Brink et al. (2011); Shamay‐Tsoory et al. (2009). Despite these advances, our understanding of how these capacities emerge from natural, moment‐to‐moment interactions remains limited. Most studies rely on structured laboratory tasks that isolate specific processes, whereas everyday interactions involve continuous exchanges of smiles, gaze, and touch that unfold dynamically over time. Capturing this temporal complexity requires computational methods capable of modeling sequential dependencies among behaviors. Such approaches represent an important step toward relating observable interaction patterns to the socio‐cognitive and affective processes that support them. In the present study, we use the term sequential dependencies to refer to statistical dependencies among behavioral states observed within the unfolding temporal sequence of interaction. In this sense, the focus is on structured dependencies across time‐indexed interaction states, rather than explicitly modeled lagged transitions between adjacent time points.

Computational models have been employed to map the structure of social interaction by capturing how reciprocal exchanges shape emotional development. Interaction data are often extracted in short time intervals, either through human coding of filmed events or automated sensors (e.g., smile detectors and eye‐contact detectors), generating binary time series that indicate the presence or absence of target behaviors. However, beyond such representations, it is important to capture the dynamics of behavioral exchanges by considering their temporal structure. In addition to relative frequency, the co‐occurrence and dependence of behaviors play crucial roles in describing interaction dynamics Bodner et al. (2018). Network analysis has gained popularity across fields such as computer science, systems biology, and the social sciences, and has increasingly been applied to the study of behavioral and psychological processes, including psychopathology Bodner et al. (2022); Briganti et al. (2022); Hinze et al. (2021); Černis et al. (2021). In these studies, networks have been used to identify relationships between symptoms using cross‐sectional data. For example, one study employed a network‐based approach to analyze binary time‐series data and detect significant co‐occurrences of distinct depressive symptoms Bodner et al. (2022). Similarly, network analysis has been used to explore the relationship between affective family interactions and adolescent depression by modeling observed behavioral cues during social interactions Bodner et al. (2018). More broadly, network approaches provide a practical framework for understanding dynamic systems by simplifying and visualizing complex relationships. For instance, a network analysis of parent‐toddler play showed that children's interaction sequences consisted of a small number of highly repetitive behaviors alongside many infrequent ones, some of which may nonetheless play an important role in exploratory behavior Karmazyn‐Raz and Smith (2023).

Building on these approaches, recent advancements in computational modeling have further contributed to our understanding of children's interactive behaviors, utilizing methods such as Bayesian networks, Hidden Markov Models (HMM), and machine learning to explore cognitive and social processes. For example, machine learning approaches have been used to analyze behavioral data in children with Autism Spectrum Disorder (ASD), demonstrating the potential of computational models to detect subtle movement and interaction patterns related to social functioning Messinger et al. (2022). Dyadic behavioral contingencies, represented as sequential behaviors between mothers and preschoolers, have been used to examine parent‐child coregulation patterns associated with children's emotional self‐regulation Lobo and Lunkenheimer (2020). Similarly, another study introduced multivariate discrete HMM to analyze domain‐based cognitive and behavioral measurements, providing a structured framework for assessing risk factors in child development Zhang et al. (2010). Bayesian networks, in particular, provide a probabilistic framework for modeling dependencies between behavioral and cognitive variables, enabling the representation of latent structure from observable actions. Within developmental research, it has been proposed that children's learning follows principles consistent with Bayesian inference. In this view, Bayesian networks can represent how children construct and refine causal theories from observed evidence and predict social interactions Gopnik and Tenenbaum (2007).

Beyond probabilistic modeling, researchers have also developed frameworks for visualizing and analyzing high‐density multimodal behavioral time‐series data Xu et al. (2020). These approaches include representations of raw time series, burstiness calculations to describe event distribution structures, and cross‐recurrence quantification analysis to examine nonlinear temporal dependencies and determine directional relationships among interdependent behavioral variables. Extending the scope of computational modeling, it has been emphasized that computational models not only serve as predictive tools but can also provide theoretical explanations for cognitive mechanisms Hsiao (2024). These approaches have helped uncover temporal structures in complex behavioral datasets, offering insights into the development of interaction patterns and their role in social and cognitive processes. However, there remains a need to bridge the gap between computational analysis and ecologically valid experimental settings. In particular, experimental designs that assess responses to social and affective stimuli within interactive and naturalistic contexts would enable the collection of richer and more structured interaction data. Advances in computational modeling, machine learning, and real‐time data collection may further facilitate the extraction of fine‐grained temporal patterns of social behavior, helping to identify developmental trajectories of empathy in more naturalistic and socially embedded contexts.

To address this gap, we propose a computational framework that models multivariate sequential dependencies in naturalistic interaction data and introduces the Order of Sequential Interaction (OSI) as a structural descriptor of interaction complexity. Recent literature emphasizes the importance of combining real‐life social interactions with multimodal behavioral, physiological, and neural measures to more comprehensively capture the processes underlying social communicative development. However, many traditional studies still rely on structured laboratory tasks, which may not fully reflect the spontaneous and dynamic nature of everyday social interactions.

The study's main objectives are twofold. First, we examine the application of the proposed framework for modeling mother–child interactions. Bayesian networks provide a probabilistic framework for inferring network structures and modeling dependencies among variables Briganti et al. (2022). For this analysis, we focus on nonverbal interactive behaviors observed during mother–child free‐play sessions. Statistical dependencies among behavioral states within the temporal sequence of interaction are inferred and represented as a Bayesian network for each participant. Building on contingency‐based approaches to temporal dependency, the proposed framework extends the analysis to a multivariate context by modeling statistical dependencies among multiple behavioral states simultaneously. This allows the characterization of higher‐order interaction structure beyond pairwise contingencies within naturalistic behavioral sequences.

Second, we explore how patterns captured by the proposed framework relate to behavioral, physiological, and neural measures relevant to social‐cognitive development. Based on the inferred network structure, we introduce a quantity termed the Order of Sequential Interaction (OSI), a descriptive index of interaction complexity. Because social communicative development is closely related to broader socio‐cognitive and emotional development, we administer several complementary tasks, including theory‐of‐mind assessments, measures of prosocial behavior, and neurophysiological recordings during observation of social stimuli. By comparing these measures between the two OSI‐based groups, we examine whether they vary with the interaction patterns captured by OSI. The set of tasks included in the study was drawn from paradigms previously used and validated in our laboratory to examine children's social‐communicative, affective, and behavioral responsiveness Yamamoto et al. (2019, 2024). Each task captures a distinct modality relevant to interpreting OEI within a broader developmental context.

In this study, we use the Bayesian‐network‐derived OSI as a descriptive indicator of interaction complexity and examine its associations with a set of developmental measures. While the multimodal measures included in this study were selected for their relevance to social communicative development, OSI quantifies the depth of sequential dependencies among behavioral states, providing a compact summary of interaction structure. The primary aim of this study is therefore to introduce and evaluate a computational framework for modeling the temporal structure of social interaction, with the empirical analyses serving as an initial demonstration of its relevance to socio‐cognitive measures.

2. Materials and Methods

2.1. Bayesian Network Modeling of Interactive Behaviors and Order of Sequential Interaction

Bayesian networks are probabilistic graphical models that represent conditional dependencies among variables using Directed Acyclic Graphs (DAGs). In these graphs, nodes correspond to variables and directed edges indicate statistical dependencies. While such structures can support causal interpretation under additional assumptions, the present study focuses on their use as a descriptive framework for capturing relationships among observed behaviors.

Modeling sequential dependencies among behavioral states in social interaction, as defined above, involved several steps. First, trained video coders identified periods during which targeted behaviors occurred in mother–child free‐play sessions. Binary time‐series data were then generated for each behavioral cue at 1‐s intervals, represented by $S_k(t)$, where $t\in [0,n]$. Here, $S_k(t)=0$ indicates the absence of cue $k$ at time $t$, whereas $S_k(t)=1$ denotes its presence. Each time point therefore represents whether a behavior is present or absent at that moment, so the analysis captures ongoing behavioral states across time rather than only the onset of events. In the present implementation, dependencies were estimated from behavioral states sampled at the same 1‐s time resolution. Thus, the inferred edges reflect statistical dependencies among co‐occurring behavioral states across the interaction, rather than explicitly modeled lagged transitions (e.g., $t_0\to t_1$).

The structure of the Bayesian network was estimated using the Max‐Min Hill‐Climbing (MMHC) algorithm Tsamardinos et al. (2006), a hybrid structure‐learning approach that combines constraint‐based and score‐based strategies to efficiently discover probabilistic dependencies among variables. In the first phase, the Max‐Min Parents and Children (MMPC) algorithm performs a series of conditional independence tests to identify, for each variable, a set of statistically dependent variables, thereby forming an undirected skeleton of potential connections. In the second phase, a greedy hill‐climbing search is applied to this skeleton to orient edges and optimize a global scoring criterion. In this study, the Bayesian Dirichlet equivalent uniform (BDeu) score Heckerman et al. (1995) was used to balance data fit and model complexity. To assess the robustness of the estimated network, we conducted a non‐parametric bootstrap stability analysis following Friedman et al. (2013). Specifically, the MMHC procedure was repeated 1000 times using random sub‐samples comprising 85% of the data (sampled without replacement) in each iteration. For each replication, a new network structure was estimated, and the frequency with which each directed edge reappeared across the 1000 networks was calculated. The resulting edge‐occurrence probabilities provided an empirical measure of structural stability. Edges that reappeared in more than 70% of the bootstrap replications were retained in the final network, representing consistently supported dependencies that were robust to sampling variability.

Finally, the Order of Sequential Interaction (OSI) was defined as the length of the longest directed dependency chain in the inferred network. Because the inferred network is a DAG, the maximum possible OSI is $N-1$, where $N$ is the number of coded behavioral variables. This value quantifies the complexity of dependencies among interactive behaviors observed over time. It provides a simple and interpretable proxy for the depth of the inferred interaction structure, allowing comparison across participants while preserving the sequential organization of interactions. Participants were then classified into low‐ and high‐OSI groups according to their OSI values (see Section 3.1).

In more intuitive terms, the procedure converts the observed mother–child behaviors into parallel binary time series indicating whether each behavior is present or absent at each 1‐s time point. The Bayesian network then estimates statistical dependencies among these behavioral states, providing a compact representation of how behaviors are organized across the interaction. Importantly, these dependencies are derived from the full binarized time series and are not restricted to the onset of behaviors. Based on the resulting network, OSI summarizes the depth of the dependency structure across behavioral states, with higher values indicating richer multi‐step dependency structure within the interaction sequence and lower values indicating simpler interaction patterns. This network‐based representation transforms continuous interaction data into a structured form that captures dependencies among behaviors across time. By encoding behavioral states as a graph, the framework enables the identification of interaction patterns that may not be evident from raw time‐series data alone Hollenstein (2007); Lobo and Lunkenheimer (2020).

2.2. Participants

The study included 38 girls (mean age = 34.6 months, SD = 1.8; range = 33–41 months) and their mothers. All participants were native Japanese speakers residing in the Greater Tokyo metropolitan area, primarily in urban and suburban neighborhoods of Tokyo, Kanagawa, and Saitama Prefectures. The experiments were conducted at the Keio Baby Lab, Keio University, Tokyo, Japan. The sample reflected the demographic profile of middle‐income households in this region. Based on maternal reports, annual household income ranged mostly between 3 and 12 million JPY, consistent with national averages for middle‐class families. All participants identified as ethnically Japanese, consistent with the demographics of the recruitment area. Children were born full‐term (mean gestational age $\approx$ 39 weeks) with an average birth weight of 3.1 kg (SD = 0.3).

We included only girls for two primary reasons. First, previous research has consistently shown that sex‐based differences in toy preferences emerge early in child development Todd et al. (2017). Additionally, our preliminary observations suggested that Japanese boys rarely engaged in play with dolls, which could potentially influence their interactions with them. Second, prior work has documented sex‐related differences in sociocognitive development, including aspects of empathy Christov‐Moore et al. (2014). Sample sizes differ across behavioral, EMG, and fNIRS analyses because each modality has its own data‐quality requirements and can be affected differently by movement artifacts and technical issues. Informed consent was obtained from all mothers prior to participation, and families received compensation for their participation. Consent to publish images containing identifiable information in an open‐access publication was also obtained (Figure 1). The study was approved by the Ethics Committee of the authors' institution (Approval No. 170080001). The experimental protocol was reviewed and approved, and the experiments and data management were conducted in accordance with the relevant guidelines and regulations provided by the ethical committee.

FIGURE 1.

(Left) Participants and their mothers engaged in a free‐play session involving activities such as doll play and puzzle tasks. (Right) Nonverbal interactive behaviors exchanged during the session were video‐coded and analyzed. These signals were converted into binary time‐series data and processed using Bayesian networks to infer sequential dependencies among behavioral states in social interaction.

2.3. Interactive Behaviors in Mother–Child Free Play

During this session, participants were encouraged to play freely with their mothers as they would at home. The behavioral data collected during the session were used to construct a sequential dependency model for each participant. The experiment consisted of two play conditions: one in which participants played freely with a doll and household toys (the “doll condition”) and another in which they engaged in a shape‐puzzle activity (the “puzzle condition”). Each condition lasted 7 min. Two video cameras recorded the interactions throughout the session.

The experimenters observed the mother–child interaction but did not actively participate in the play. The two play conditions were counterbalanced across participants. Nonverbal social signals exhibited during the mother–child interactions were then extracted by two trained video coders using the annotation software ELAN. Targeted behaviors included the following:

• Child smile: The child raises the corners of the mouth and cheeks.

• Mother smile: The mother raises the corners of the mouth and cheeks.

• Eye contact: The mother and child look into each other's eyes.

• Social touch: Physical contact between the mother and child within a social context, such as communication or guidance during play.

To assess coding reliability, the results of the video coding were compared with those of an additional video coder who independently analyzed 10% of the video data. The average inter‐coder agreement was 87%.

2.4. Questionnaire‐Based Assessment

Multiple questionnaires were used to assess child development, language ability, executive functions, and maternal prosociality. The Kinder Infant Development Scale (KIDS), widely used in Japan, provided a comprehensive evaluation of cognitive, language, motor, and social development, including receptive and expressive language abilities relevant to empathic development Miyake et al. (1989). Executive function skills important for social interaction and emotion regulation were assessed using the Behavior Rating Inventory of Executive Function‐Preschool Version (BRIEF‐P), which evaluates domains such as working memory, inhibition, and emotional control Sherman and Brooks (2010). Language ability was further assessed using the Japanese Communicative Development Inventory (JCDI), a culturally adapted version of the MacArthur‐Bates CDI that measures expressive vocabulary, grammar, and syntactic development Watamaki and Ogura (2004). Mothers' tendencies toward prosocial behavior were assessed using an adapted Prosocial Behavior Scale, which measures the frequency of altruistic behaviors within the mother–child relationship Kikuchi (1988).

2.5. Behavioral Assessments

Behavioral assessments play an important role in examining children's emerging capacity for social understanding and prosocial behavior. Studies using structured observational paradigms have shown that young children spontaneously assist others in need from an early age Warneken and Tomasello (2006). These behaviors are often accompanied by early forms of affective coordination, including facial mimicry measured using facial EMG. Such responses indicate children's sensitivity to others' emotional expressions and have also been linked to later prosocial tendencies Geangu et al. (2016).

To evaluate children's prosocial behavior and underlying social‐cognitive skills, we used two complementary assessments: structured helping tasks and a ToM test battery. Prosocial behavior was assessed using the structured helping tasks, which consisted of three scenarios in which children had the opportunity to recognize the experimenter's needs and provide help. The task was adapted from our previous work, in which children's performance was found to correlate with activation in the right temporoparietal junction (rTPJ), a region associated with mentalizing and perspective‐taking Yamamoto et al. (2024). This finding provides both theoretical and empirical motivation for including the task in the present study. Each task followed a structured sequence of three scenes: (1) an introductory scene in which the experimenter encountered a problem, (2) a test scene consisting of five progressively explicit social cues (verbal and nonverbal) presented at 6‐s intervals, and (3) a concluding scene in which the experimenter responded to the child's action. Children's responses were scored on a 0‐15 scale based on how early in the sequence they performed the target helping behavior, capturing their sensitivity to social cues and responsiveness to others' needs.

ToM was evaluated using Wellman's test battery Wellman and Liu (2004), which includes five developmentally relevant tasks: diverse desires, diverse beliefs, knowledge access, false beliefs, and real‐apparent emotions. These tasks assess children's ability to attribute mental states to others, a skill that is foundational for interpreting intentions and engaging in appropriate social responses. The original task instructions were translated and adapted into Japanese.

2.6. Physiological and Neural Measurement

Neuroimaging and psychophysiological methods have further advanced our understanding of the neural and physiological bases of early social behavior. Techniques such as EEG, fNIRS, and functional magnetic resonance imaging (fMRI) have identified brain regions associated with affective responsiveness, social perception, and emotion regulation during early childhood Light et al. (2009); Brink et al. (2011); Shamay‐Tsoory et al. (2009). For example, prefrontal EEG asymmetry has been linked to positive affect and affective regulation Light et al. (2009), whereas orbitofrontal and inferior frontal regions show increased activation during the observation of socially and emotionally salient scenes Brink et al. (2011); Shamay‐Tsoory et al. (2009). In previous work Yamamoto et al. (2024), we used fNIRS and facial EMG to examine children's neural and physiological responses to video stimuli depicting prosocial and antisocial interactions. Both facial EMG amplitude and rTPJ activity were found to correlate with the degree of prosocial behavior observed during subsequent assessments, suggesting that individual differences in social responsiveness are evident across multiple physiological and neural levels. This evidence underscores the value of multimodal approaches to studying early social cognition.

In the present study, children's neural and physiological responses to social stimuli were measured using a combination of fNIRS and EMG, focusing on brain regions associated with social understanding and emotional responsiveness. Children first participated in a brief warm‐up session to familiarize themselves with the experimenter and the laboratory environment. Following this, fNIRS was used to measure brain activity in the TPJ, inferior frontal gyrus (IFG), and medial prefrontal cortex (mPFC), while EMG was used to record facial muscle activity. EMG electrodes were placed bilaterally on the face, targeting the temporalis and zygomaticus major muscles, which allow the detection of facial muscle activity associated with smiling Hess et al. (2017).

The experiment took place in a soundproofed room equipped with a stimulus‐presentation monitor. A digital video camera (HC‐V300M, Panasonic) was mounted above the monitor to monitor children's engagement and support data‐quality checks during stimulus presentation. During the experiment, children watched eight videos, each lasting 17.5 s, depicting two individuals engaged in a social scenario. In each video, one individual encountered a problem (e.g., spilled water, feeling cold, or needing a writing tool), while the second individual had access to an item that could resolve the issue (e.g., a cleaning cloth, gloves, or a pen). Each video comprised:

• 1)A 9‐s introductory phase establishing the context (e.g., a person appearing cold).
• 2)An 8.5‐s ending phase in which the second person performed a helping action.

The fNIRS‐EMG measurements were collected over eight trials. Each trial began with a 1‐s attention‐getting stimulus, followed by the video presentation. To control for order effects, the sequence of videos was randomized for each participant. The data‐collection procedures used in this study follow and adapt methods established in Yamamoto et al. (2024).

2.6.1. Physiological Measurement: Facial EMG

Facial EMG provides a precise method for detecting subtle muscle activity that may not be easily observable through visual assessments alone Gruebler and Suzuki (2014). By capturing and amplifying small electrical impulses generated during muscle contractions, EMG enables the measurement of nuanced facial expressions with high temporal resolution. This technique has been shown to effectively detect facial muscle activity in response to mildly evocative emotional stimuli Perusquia‐Hernandez et al. (2017). Although some studies have reported variability in the internal consistency of EMG signals, overall reliability remains high Larsen et al. (2003); Hess et al. (2017). Furthermore, research has confirmed the suitability of this technique for use in children, supporting its applicability in developmental studies Geangu et al. (2016); Turati et al. (2013).

In this study, surface EMG signals were recorded at a sampling rate of 1 kHz using a commercially available measurement device (Biolog DL‐4000, S&ME Inc.). To minimize noise interference, the four‐channel signals were bandpass filtered in the 50–350 Hz range. For the analysis, the average absolute EMG value during the final 3 s of the introductory phase was used as the baseline (${\theta }_b$). The relative EMG change ($X_{\text{rc}}$) during the ending phase was then computed as follows:

$$X_{\text{rc}}(t)=\frac{|X_{\text{rc}}(t)-{\theta }_b|}{{\theta }_b}$$

where the baseline (${\theta }_b$) was defined as:

$${\theta }_b=\frac{1}{N_b}\sum _{\tau }|x(t_0-\tau )|,\tau \in [0,3\mathrm{s}]$$

Here, $\tau$ represents time within the last 3 s of the introductory phase, $t_0$ marks the onset of the ending phase, and $N$ (N = 3000) denotes the total number of samples in the baseline segment.

2.6.2. Neural Measurements: fNIRS

From the channels recorded by the fNIRS system, we selected those corresponding to cortical regions that (a) have been previously linked to social cognition and affective processing and (b) were compatible with the spatial constraints and configuration of the fNIRS hardware. The ability to infer the mental states of others has been associated with activity in key regions of the mentalizing network, particularly TPJ and mPFC Gweon et al. (2012); Van Overwalle and Baetens (2009); Yamamoto et al. (2024). Additionally, IFG plays an important role in social and emotional processing, supporting the interpretation of others' intentions and affective states Zhao et al. (2021); Rizzolatti and Sinigaglia (2010). Signal quality was assessed across recorded channels as part of standard preprocessing. Main analyses were restricted to predefined regions of interest: rTPJ (channels 1 and 2), mPFC (channel 20), and the right and left IFG (channels 12 and 25), selected on the basis of their a priori relevance to social‐cognitive and affective processing during early development.

A fNIRS system (ETG‐7000, Hitachi, Japan) was used to measure fluctuations in oxyhemoglobin (oxy‐Hb) and deoxyhemoglobin (deoxy‐Hb) concentrations. The system emits near‐infrared light at two wavelengths (780 and 830 nm) to detect changes in these hemoglobin concentrations, which reflect variations in local cerebral blood flow. The probe consisted of a 2 $\times$ 11 optode array forming 27 channels covering the frontal region and rTPJ. To ensure consistent positioning, the fourth optode from the right in the lower row was aligned with $F_{\text{pz}}$ according to the International 10–20 system, and the distance between each emitter‐detector pair was 2.5 cm. To determine the brain regions associated with each measurement channel, the virtual spatial registration method was employed Tsuzuki et al. (2007), which probabilistically maps the cortical structures underlying each channel without requiring individual structural brain imaging, using the Talairach and AAL atlases for anatomical labeling. To enhance signal quality, a noise‐reduction procedure was applied to obtain corrected activation signals for oxy‐Hb and deoxy‐Hb dynamics Cui et al. (2010). Data preprocessing was performed using the Optical Topography Analysis Tools (POTATo) developed by Hitachi Ltd., and subsequent analyses were conducted in MATLAB 2012 (MathWorks, Natick, MA, USA).

Following the extraction of corrected activation signals from oxy‐Hb and deoxy‐Hb dynamics, additional filtering was applied to enhance data quality. To remove pulse‐related fluctuations and minimize noise, a high‐pass filter (0.02 Hz cutoff) and a low‐pass filter (1 Hz cutoff) were used. A three‐point moving average filter was further applied for signal smoothing. For the analysis, the baseline period was defined as the 3.5‐s interval preceding the onset of the ending phase, while the test period corresponded to the interval between 5 and 8 s after the onset of the ending phase. Corrected activation signals during the test period were compared with their respective baseline levels for each trial. The average relative change in these signals was then computed to characterize neural responses associated with the experimental tasks.

3. Results

The following sections present the behavioral, questionnaire‐based, physiological, and neural measures examined in relation to OSI.

3.1. Grouping Participants Based on the Order of Sequential Interaction

Mother–child dyads participated in play sessions involving a doll and a puzzle, during which their nonverbal interactive behaviors were recorded and analyzed through video coding (Figure 1 (Left)). To model relationships among these behaviors within the temporal sequence of interaction, we employed a Bayesian network, where nodes correspond to behavioral cues and directed edges encode statistical dependencies. For this study, we focused on four key behaviors commonly observed during the play sessions: child's smile, mother's smile, eye contact, and social touch. In the resulting network, each behavioral cue is represented as a node, while directed edges denote statistical dependencies among behavioral states observed across the interaction (Figure 1 (Right)). These dependencies were inferred from binary time‐series data sampled at 1 Hz. For example, a directed edge from child's smile $\to$ mother's smile indicates a statistical dependency between these behaviors within the inferred network structure. To quantify the complexity of these interactions, we introduced the OSI metric, which measures the maximum number of sequential dependencies within a network (Figure 2). The distribution of OSI values across dyads was concentrated between 1 and 2 (Table 1), supporting a descriptive distinction between dyads with minimal dependency structure ($\le 1$) and those with richer multi‐step dependencies ($\ge 2$). Given the observed distribution of OSI values, we used OSI $\ge 2$ as a descriptive cutoff for the present analysis. Based on this metric, dyads were categorized into two groups:

• 1)Lower OSI group (Group L): Dyads with fewer than two sequential dependencies per network.
• 2)Higher OSI group (Group H): Dyads with two or more sequential dependencies per network.

FIGURE 2.

Participants were categorized into two groups based on OSI. The lower OSI group included pairs with fewer than two sequential dependencies within a network (e.g., a and d), whereas the higher OSI group included pairs with two or more sequential dependencies (e.g., b and c).

TABLE 1.

Distribution of OSI

OSI	0	1	2	3
Number of dyads	2	19	16	1

Following this classification, 17 dyads were assigned to Group H and 21 to Group L. Notably, while most dyads exhibited smile‐based dependencies, Group H showed additional dependencies involving touch and/or eye contact, indicating more complex interaction patterns within the network representation.

3.2. Questionnaire‐Based Assessment and OSI Groups

Next, we investigated the relationship between OSI groups and commonly used developmental scales described in Section 2.4. Specifically, we compared scores from the CDI Watamaki and Ogura (2004), BRIEF‐P Sherman and Brooks (2010), KIDS Miyake et al. (1989); Hashimoto et al. (2013), and the MP scale Kikuchi (1988). For each measure, $n_L$ and $n_H$ denote the number of valid samples in the lower and higher OSI groups, respectively. Given the ordinal nature of the questionnaire data, we used the Mann‐Whitney U test to assess group differences.

As shown in Figure 3, no significant differences were observed across any of the scales (CDI: $n_L=21,n_H=17,U=399.5,p=0.78$; BRIEF‐LP: $n_L=21,n_H=17,U=368.5,p=0.23$; KIDS: $n_L=21,n_H=17,U=427.0,p=0.62$; MP: $n_L=17,n_H=17,U=280.5,p=0.57$).

FIGURE 3.

Score distributions between the higher OSI group (H) and lower OSI group (L) were compared across multiple questionnaire‐based measures using Mann‐Whitney U tests. No statistically significant differences were observed between the groups for any measure (CDI: $U=399.5,p=0.78$; BRIEF‐LP: $U=368.5,p=0.23$; KIDS: $U=427.0,p=0.62$; MP: $U=280.5,p=0.57$).

3.3. Behavioral Measures and OSI Groups

ToM was assessed using Wellman's test battery introduced in Section 2.5. As shown in Figure 4, the Mann‐Whitney U test revealed no significant difference in ToM scores between the two OSI groups ($n_L=21,n_H=14,U=357.5,p=0.49$). The plot represents kernel density estimates, where the width of the shaded area indicates the relative distribution of the data.

FIGURE 4.

Theory of Mind (ToM) scores were compared between the higher and lower OSI groups, with no statistically significant difference in median values ($U=357.5,p=0.49$).

Children's prosocial tendencies were examined using three tasks, each presenting a scenario in which a person faced a problem. A task was considered complete once the child exhibited the targeted helping behavior. Figure 5 (Left) shows the score distributions for the three tasks. A ceiling effect was observed in Task 3, with a large proportion of participants achieving the maximum score; therefore, it was excluded from further analysis. Figure 5 (Right) shows the distribution of combined scores from Tasks 1 and 2 across the two OSI groups. Given the limited sample size, we used the Mann‐Whitney U test, which indicated a significant difference between groups H and L ($n_L=17,n_H=17,U=225.5,p=0.012$).

FIGURE 5.

(Left) Score distributions across participants in the three prosocial tasks, comparing the higher OSI (H) and lower OSI (L) groups. Scores from Task 3 were excluded due to a ceiling effect. (Right) The summed scores were significantly higher in Group H than in Group L ($U=225.5,p=0.012$).

3.4. Physiological Measures and OSI Groups

Facial EMG and fNIRS data were collected while children watched video stimuli depicting two individuals. Each video presented a scenario in which one person faced a problem and another resolved it. The videos followed a structured format, consisting of a 9‐s introductory phase to establish the context and an 8.5‐s ending phase depicting the helping action.

Figure 6 illustrates changes in EMG activity during the ending phase relative to the mean activity in the last 3 s of the introductory phase. To define the ROI for analysis, we computed the average EMG response across all participants (dashed‐dotted line) and identified a 2‐s time window centered around its peak (white area). We then compared the mean EMG change within this time window between the two OSI groups (Figure 7). Given the limited sample size, we used the Mann‐Whitney U test, which indicated a significant difference between groups ($n_L=12,n_H=12,U=185.0,p=0.023$).

FIGURE 6.

Facial EMG activity during the ending phase was analyzed relative to the introductory baseline. The solid red line shows the mean activity of Group H, and the dashed blue line that of Group L. The hatched area indicates the standard deviation, and the black dashed line the global average across both groups. The region of interest (ROI) was defined as $\pm 2\mathrm{s}$ around the peak of the global average (filled black circle).

FIGURE 7.

Mean EMG change within the selected time window was compared between Group H and Group L. A Mann‐Whitney U test indicated a statistically significant difference between the groups ($U=185.0,p=0.023$).

Similarly, we analyzed fNIRS‐derived neural responses based on OSI group classification. Figure 8 shows the average change in oxy‐Hb across four regions of interest: rTPJ, mPFC, lIFG, and rIFG. The rationale for selecting these regions is provided in Section 2.6.2. Group differences were assessed using a permutation test with 1000 permutations, a commonly used non‐parametric approach in neuroimaging and fNIRS analysis Nichols and Holmes (2002); Pinti et al. (2020), which is well‐suited for small sample sizes and does not rely on distributional assumptions. The results indicated significantly stronger activation in rTPJ ($n_L=13,n_H=16,MD=-0.0391,p=0.008$) and lIFG ($n_L=15,n_H=14,MD=-0.0255,p=0.035$) in Group H compared to Group L. In contrast, no significant differences were observed in mPFC ($n_L=17,n_H=17,MD=-0.0115,p=0.16$) or rIFG ($n_L=16,n_H=14,MD=-0.0069,p=0.56$). Here, $MD$ denotes the mean difference between groups.

FIGURE 8.

Average neural activity changes across channels 1, 2 (rTPJ), 12 (rIFG), 20 (mPFC), and 25 (lIFG) were compared between Groups L and H. A permutation test ($n=1000$) indicated significant differences in rTPJ ($MD=-0.0391,p=0.008$) and lIFG ($MD=-0.0255,p=0.035$), with no significant differences in mPFC ($MD=-0.0115,p=0.16$) or rIFG ($MD=-0.0069,p=0.56$).

Because the study included behavioral, physiological, and neural outcomes, a total of 11 statistical tests were conducted across modalities. To control for multiple comparisons, we applied the Benjamini–Hochberg false discovery rate (FDR) correction Benjamini and Hochberg (1995); Storey (2002) with the threshold set at $q=0.10$. This relatively lenient threshold was chosen to balance sensitivity and Type I error control with a limited sample size. After FDR adjustment, four findings remained statistically significant.

4. Discussion

This study introduces a computational framework based on Bayesian networks to model sequential dependencies among interactive behaviors during naturalistic mother–child interactions. By focusing on non‐verbal cues in free‐play scenarios, the proposed approach characterizes how interaction patterns are structured and how behavioral states are statistically related within the unfolding interaction sequence, enabling the analysis of multivariate and higher‐order dependencies beyond traditional contingency‐based methods. Within this framework, we defined OSI as a descriptive metric of interaction complexity, capturing the stability and richness of behavioral sequences. The empirical analyses serve as an initial demonstration of this approach: OSI showed associations with behavioral, neural, and physiological measures in prosocial‐related tasks. These findings highlight the potential of the framework to reveal links between interaction structure and broader socio‐cognitive processes. The primary contribution of this work is the proposed computational framework for modeling multivariate dependency structure in naturalistic interaction data, with the following analyses serving as an initial evaluation of its relevance across modalities.

The proposed framework can be understood in relation to prior contingency‐based approaches, which examine how one partner's behavior tends to follow or co‐occur with the other's over time during interaction Hsu and Fogel (2003); Lobo and Lunkenheimer (2020). Classical methods quantify the likelihood that one partner's behavior follows another, providing insight into dyadic coordination. In contrast, the Bayesian‐network framework extends this logic to a multivariate setting, allowing multiple behaviors to be modeled simultaneously and enabling the identification of dependencies involving multiple interacting behaviors beyond simple pairwise relationships. Within this perspective, OSI was associated with patterns of contingent responding across modalities such as smiles, gaze, and touch, providing a quantitative description of how behaviors are organized and related during interaction. The observed convergence across behavioral (prosocial responses), neural (rTPJ and IFG activation), and physiological (facial EMG) measures suggests that this structural representation may align with aspects of children's social and affective responsiveness, including sensitivity to others' emotional states and readiness to engage in socially responsive actions. These associations should be interpreted cautiously, as the present design does not allow inferences about causality or underlying mechanisms. Within the proposed framework, OSI characterizes the structural organization of interaction rather than broader developmental ability. Consistent with this interpretation, questionnaire‐based assessments did not reveal significant differences between OSI groups in general development (KIDS), language ability (CDI), executive functioning (BRIEF‐P), or maternal prosocial behavior (Figure 3). These findings provide contextual support, suggesting that variations in interaction complexity, as indexed by OSI, are not clearly accounted for by general cognitive or linguistic development or by maternal characteristics.

Given this, we next examined how interaction complexity relates to observable social responsiveness. Children with higher OSI scores tended to show greater prosocial tendencies, particularly in immediate helping behaviors (Figure 5). These patterns are consistent with previous findings suggesting that spontaneous helping is associated with empathy‐related processes and with children's understanding of others Eisenberg et al. (2013); Mizokawa and Koyasu (2015). In contrast, performance on ToM tasks did not differ between OSI groups (Figure 4), suggesting that explicit mentalization abilities alone do not account for the observed variation in interaction structure. These patterns suggest that different components of social responsiveness should be considered separately when interpreting OSI, and motivate further examination of how interaction complexity relates to both emotional and cognitive processes. To further explore these relationships, we next consider neural and physiological patterns.

Previous research has identified key brain regions associated with empathy‐related cognition. In this context, fNIRS measures offer a way to examine potential neural correlates of interaction structure (Figure 8). The rTPJ and mPFC are commonly described as core components of the mentalizing network, involved in inferring others' mental states Gweon et al. (2012); Van Overwalle and Baetens (2009); Frith and Frith (2006). Within this framework, increased rTPJ activation in the higher OSI group may suggest greater sensitivity to predictive social cues or a stronger tendency to anticipate others' actions. In contrast, the absence of consistent effects in the mPFC may indicate that processes such as higher‐order perspective taking and self‐other differentiation, often associated with medial prefrontal regions, were not strongly related to variation in interaction complexity in the present dataset Frith and Frith (2006); Rothmayr et al. (2011). A similar interpretive perspective can be applied to the lIFG findings. Given its proposed role in emotional resonance and action understanding within the mirror neuron system Iacoboni et al. (1999); Zhao et al. (2021); Rizzolatti and Sinigaglia (2010), increased lIFG activation in the higher OSI group may be consistent with stronger automatic responsiveness or mimicry during the observation of social interactions. This interpretation is further supported by the accompanying increase in facial EMG responses to prosocial stimuli (Figures 6 and 7), suggesting tighter coupling between perceptual and motor components of social behavior. Such coupling has been linked to facial mimicry processes supported by networks involving the IFG, superior temporal sulcus (STS), and middle temporal gyrus (MTG) Dimberg et al. (2011); Sasaki et al. (2012). By contrast, the absence of group differences in rIFG activation may relate to the relatively passive nature of the task, which did not place strong demands on processes such as attention to socially relevant cues or the integration of communicative signals Wu et al. (2018); Cavallo et al. (2015).

These findings illustrate how the proposed framework can capture differences in the structure of mother–child interactions, as indexed by OSI, and relate this structure to patterns observed across behavioral, neural, and physiological domains. Within this perspective, increased left IFG activation and facial EMG responses may indicate greater affective resonance during social observation, whereas rTPJ activity may be linked to processes involved in anticipating or interpreting others' actions. The OSI framework is therefore best understood as a structural description of interaction organization that provides a way to relate observable social behavior to broader socioemotional processes. Empathy is widely considered a multidimensional construct, involving cognitive and emotional components as well as broader social processes Cuff et al. (2016). The present study suggests that interaction structure, as captured by OSI, aligns with markers of social cognition and affective responsiveness. Further work will be important to clarify how these relationships relate to different aspects of social and affective processing. Studies with larger samples and longitudinal designs will be important for assessing the stability, developmental significance, and generalizability of these patterns across contexts.

In addition to these conceptual considerations, the OSI‐based grouping warrants methodological clarification. Within the proposed framework, OSI is treated as a continuous index of interaction complexity; however, for interpretability, we introduced a grouping based on an observed separation in its distribution. Specifically, the observed distribution suggested a distinction between dyads exhibiting minimal sequential dependencies ($\le 1$) and those showing more complex multi‐step interactions ($\ge 2$). Given this empirical pattern and the limited number of high‐OSI cases, the $\ge 2$ threshold was used as a descriptive cutoff rather than a theoretically defined boundary. Accordingly, the resulting grouping should be understood as a pragmatic representation of two qualitatively distinct interaction regimes, rather than a categorical classification of participants. While this dichotomization simplifies the underlying distribution, it serves to highlight a clear difference in interaction richness observed in the data.

While this study provides initial insights, several limitations should be considered. First, the relatively small sample size may limit generalizability, and future studies with larger and more diverse populations will be important for validating and extending these observations. Second, the gender distribution was uneven, which may have influenced the results. Given evidence of sex‐related differences in empathy and emotion recognition, future research would benefit from a more balanced sample to examine these effects more systematically. Third, although Bayesian Networks offer a flexible framework for modeling complex social interactions, any causal interpretation depends on assumptions such as limited influence from latent variables and minimal selection bias, which require further methodological consideration. In addition, the statistical analyses should be interpreted with caution because multiple comparisons were conducted across behavioral, neural, and physiological modalities. These analyses were intended to identify potential patterns rather than provide confirmatory evidence, and the risk of false positives should therefore be taken into account when interpreting the results. Future work should incorporate formal correction procedures and dimensionality‐reduction approaches, such as principal component analysis (PCA) or multivariate modeling, to better capture shared variance across modalities and reduce the number of independent comparisons. More broadly, this work represents an initial step toward developing a computational framework for structuring naturalistic interaction data. Further refinement with larger and longitudinal datasets will enable stronger inferences regarding developmental trajectories and the replication of the patterns observed here within confirmatory designs. Future work should also extend the present framework by explicitly modeling time‐lagged dependencies between behavioral states and by systematically evaluating the stability and interpretability of OSI.

Despite these limitations, the present study contributes to bridging the gap between objectively measurable interactive behaviors and the complex cognitive and affective processes underlying social cognition. Within this context, the OSI framework provides a descriptive approach for characterizing interaction structure and relating it to broader socioemotional processes, without assuming a direct correspondence with internal states. Beyond developmental research, this approach may also have relevance for educational and therapeutic applications. Quantifying interaction complexity could inform the design of interventions aimed at fostering prosocial engagement, emotional attunement, and social communication in early childhood.

5. Conclusion

This study introduced a computational framework for modeling sequential dependencies in mother–child interactions in naturalistic settings. Using OSI as an index of interaction complexity, the framework enabled comparisons across behavioral, neural, and physiological measures and suggested meaningful links between interaction structure and children's social responsiveness. More broadly, the findings illustrate the potential of network‐based representations to capture important features of naturalistic social behavior and to connect interaction patterns with multimodal measures of development. In this way, the present work provides a methodological foundation for future research on early social cognition. Future studies with larger and longitudinal datasets will help clarify how OSI develops over time and how interaction structure relates to broader developmental trajectories.

Author Contributions

E.N., M.H., and K.S. conceived the idea, Y.M., Y.H., and E.Y. designed the experiments. Y.M., E.Y., and Y.H. collected the data. E.N., H.M., Y.M., and E.Y. performed data analysis. H.M. performed theoretical modeling. E.N and Y.M contributed to data interpretation, E.N. wrote the manuscript. K.S. and Y.M. obtained the research founding and provided critical feedback throughout the project. All authors reviewed the manuscript.

Ethics Statement

The Ethical Committee of the Faculty of Letters at Keio University approved this study (Approval No. 170080001). The experimental protocol was reviewed and approved, and the experiments and data management were conducted in accordance with the relevant guidelines and regulations provided by the ethical committee.

Conflicts of Interest

We have no conflicts of interest to disclose.

Additional Information

All listed authors contributed to the manuscript substantially and have agreed to the final submitted version. The authors declare that they have no competing interests.

Permission to Reproduce Material from Other Sources

We grant permission to reproduce materials included in this article after publication.

Supporting information

Data S1

Data Availability Statement

The processed binary behavioral data derived from video coding, together with the scripts used for OSI estimation, are publicly available at: https://github.com/EMYEYK/Seq.Dep.study. Raw participant data, including physiological measurements and video recordings, cannot be shared publicly due to privacy and ethical constraints. Access to these data may be granted by the corresponding author upon reasonable request, subject to applicable ethical and institutional regulations.