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# How do maternal emotional regulation difficulties modulate the mother–infant behavioral synchrony?

Karyn Doba, Laurent Pezard, Jean-Louis Nandrino

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## To cite this version:

Karyn Doba, Laurent Pezard, Jean-Louis Nandrino. How do maternal emotional regulation difficulties modulate the mother–infant behavioral synchrony?. Infancy, 2022, Infancy, 27 (3), pp.582-608. 10.1111/infa.12461 . hal-03661666

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# How do maternal emotional regulation difficulties modulate the mother-infant behavioral synchrony?

## A short running title: Maternal emotional regulation and behavioral synchrony

Karyn Doba, Laurent Pezard, Jean-Louis Nandrino
## Research Highlights

* Mothers touched their 6-month-old infant more often in the reunion condition after a stressful situation than in the initial condition.

* The synchrony between mothers' motor behaviors and infant global behavioral involvement was higher during the reunion episode following a stressful separation than during the initial play episode.

* Maternal anxiety mediates the relationships between mothers' emotion regulation difficulties and gaze, vocal and motor synchrony between mothers and infants in both the initial and reunion conditions.

* Findings emphasize the importance of the dynamic quantification of mother-infant interactions as a complement to static description.
Mother-infant synchrony is one of the most important processes in the development of socio-affective competencies in children. While maternal abilities and psychopathology are related to maladaptive mother-infant synchrony, it is as yet unclear how maternal emotion regulation difficulties contribute to it. Based on a panel of behavioral indicators (i.e. gaze, vocal and motor), the present study examined mother-infant synchrony at 6 months of age in a modified version of Ainsworth's Strange Situation (n=72 dyads).

Mother-infant interaction sequences were characterized by indicators of complexity (LZ complexity of joint behavioral sequences) and of synchronization quality (cross-recurrence plot quantification). Results showed that mothers' touch was greater in the reunion condition than in the initial condition. Mothers' motor behaviors were associated with the global levels of infants' behavioral involvement in the reunion condition, unlike the symmetrical influence observed between mothers and infants in the initial condition.

Results show that maternal anxiety mediates the relationships between mothers' emotion regulation difficulties and gaze, vocal and motor synchrony between mothers and infants in the initial and reunion conditions. This study emphasizes the central role of maternal emotion regulation difficulties in the establishment of maladaptive synchrony and in the adjustments of maternal physical contacts with infants.

Keywords: Mother-child interaction, synchrony, emotion regulation difficulties, maternal anxiety, maternal depression
**Introduction**

In both humans and other mammals, mothers' postpartum behaviors and their coordination with infant states are important for early developmental processes, such as the regulation of distress states in stressful situations (Bowlby 1969; Feldman, Gordon, & Zagoory-Sharon 2011; Kim et al., 2010; Mikulincer, Shaver, & Pereg, 2003). Human infants' extreme immaturity at birth leads them to depend on mothers' behaviors for relatively long periods. This provides specific environmental inputs for the regulation of infants' internal states (Feldman, 2007; Kim et al., 2010). Maternal behavioral cues, such as vocalizations, facial expressions, proximity position, movements, and gaze and affective display, are coordinated with specific neurodevelopmental sensitivities in infants (Abney, Warlaumont, Kimbrough, Wallot, & Kello, 2017; Messinger, Mahoor, Chow, & Cohn, 2009). These maternal and interactive behaviors serve to regulate the organization of neurobiological, sensory, perceptual, emotional, physical, and relational systems in infants (Jaffe et al., 2001; Kochanska, 2002).

From a dynamic systems theory perspective, co-regulation between mothers and infants constitutes a dynamically interactive system organized by the behavioral inputs of both partners (Beebe et al., 2016; Fogel, 2011; Pezard, Doba, Lesne, & Nandrino, 2017; Provenzi et al., 2015; Smith & Thelen, 2003; Sravish, Tronick, Hollenstein, & Beeghly, 2013). This dynamic reciprocal adaptation of the temporal structure of behaviors between mothers and infants involves repetitive cycles of behaviors (Beebe et al., 2016; Coburn, Crnic, & Ross 2015; Sravish et al., 2013). Different types of mothers' behaviors tend to co-occur with some infants' behaviors, and mother-infant interactions tend to cycle
between behaviors in a relatively predictable way (Provenzi et al., 2015; Van der Giessen, Branje, Frijns, & Meeus, 2012; Weinberg, Tronick, Cohn, & Olson, 1999).

The temporal concordance between simultaneous or sequential behaviors across a wide range of physiological or behavioral indicators including eye gaze, facial expressions, prosody, movement and emotional states of partners are usually referred to as synchrony phenomena (Feldman, 2007; Harrist & Waugh, 2002; Leclère et al., 2014). A well-organized and flexible mother-infant interaction is driven by a moderate degree of synchrony between mothers and infants during social interactions (Feldman, 2007; Feldman, Magori-Cohen, Galibi, Singer, & Louzoun, 2011). Several studies have shown that a high level of mother-infant synchrony interferes with infants’ developing abilities to self-regulate and to explore (Leclère et al., 2014; Lotzin, Schiborr, Barkmann, Romer, & Ramsauer, 2015). Indeed, a high level of mother-infant synchrony may reduce the adjustment to both internal and external changes of situation and promote inflexible and invariant affective experiences in infants. Recent empirical research has indicated that co-regulated patterns of interactions show significant developmental shifts at around 6 months of age, with mother-infant interactions becoming increasingly more symmetrical and bidirectional (Cortney & Porter, 2009; Kochanska, 2002).

Despite empirical evidence of the impact of interactive influences on mother-infant synchrony, little is known about the relative importance of each partner in creating these processes or about the identification of behavioral indicators (i.e. gaze, vocal and motor) of mother-infant synchrony that change after a stressful situation induced by maternal separation. Mothers are generally rather efficient in reading their infants’ emotional displays, and sensitive mothers tend to regulate their own affective responses to modulate
their infants' emotional states (Beebe & Steele, 2013; Montague & Walkers-Andrews, 2002). In a developmental perspective, these maternal emotional abilities may depend on the quality of mothers' attachment experiences (Eisenberg, Cumberland, & Spinrad, 1998; Morris, Silk, Steinberg, Myers, & Robinson, 2007) and could be associated with the development of mother-infant synchrony. Studies have shown that maladaptive mother-infant synchrony may depend upon maternal insensitivity, unresponsiveness to the infant and maternal emotional disorders, such as maternal anxiety and depression (Beebe et al., 2011; Lotzin, Schiborr et al., 2015; Lundy, 2002; Sravish et al., 2013).

Even though anxiety and depression are often comorbid, several studies also suggest that they are partially distinct, e.g. due to their different symptom time course (Der Wee et al., 2011). Furthermore, empirical evidence suggests that each may have specific effects on child development and mother-infant interaction, and it is important to differentiate their effects on outcomes (Hakanen, et al., 2019; Nolvi, et al., 2016). Anxious mothers are more controlling and intrusive (Feldman, Greenbaum, Mayes, & Erlich, 1997; Stein et al., 2012), exhibit more fearful responses than those without anxiety symptoms (Murray et al., 2008), and display fewer positive emotions (Nicol-Harper, Harvey, & Stein, 2007). Anxiety symptoms in mothers predict higher synchrony in the touch modality, greater frequencies of gaze to infant, and lower affect synchrony in face-to-face play (Beebe et al., 2011; Granat, Gadassi, Gilboa-Schechtman, & Feldman, 2017). Several studies have shown that mothers with depressive symptoms display less gaze, facial affect, vocal and touch behaviors than mothers without depressive symptoms (Field, 2010; Granat et al., 2017; Righetti-Veltema, Conne-Perreard, Bousquet, & Manzano, 2002). Maladaptive mother-infant synchrony in the context of maternal depression is expressed in various forms
including fewer episodes of mutual gaze (Beebe et al., 2008; Feldman & Eidelman, 2007) and a less predictable duration of vocal switch-pauses (Zlochower & Cohn, 1996). Although this research suggests that maternal anxiety and maternal depression are expressed in two specific styles, few studies to date have evaluated their associations with maternal relational behaviors and mother-infant synchrony. Some recent studies also shown that mothers with depressive symptoms are more withdrawn and less intrusive with their infants than those with anxiety symptoms (Feldman et al., 2009; Hakanen, et al., 2019). In both gaze and touch, synchrony was higher in mothers with anxiety than in those with depression (Granat et al., 2017).

Maternal anxiety and depression have been associated with emotion regulation (ER) difficulties corresponding to processes that modulate emotions for appropriately responding to environmental demands. They have also been associated with difficulties in monitoring, evaluating, and modulating or accepting emotional experiences, given the demands of a specific goal or set of goals (Gratz & Roemer, 2004; Gross, 1998). As such, ER difficulties involve several domains, including a lack of awareness of emotion, a poor clarity of emotion (emotional understanding), a non-acceptance of emotion, and a poor ability to access effective emotion regulation strategies. Greater maternal ER difficulties were significantly associated with high levels of facial and gaze synchrony between infants and depressed mothers before and after a stressful situation induced by the still-face paradigm (Lotzin, Romer, et al., 2015; Lotzin, Schiborr, et al., 2015). These paradigms show that the effect of maternal ER difficulties on mother-infant synchrony constitutes a key process for the development of synchrony between infants and depressed mothers in clinical populations. While ER difficulties are core features of maternal anxiety and
maternal depression, their associations with mother-infant synchrony have not yet been systematically investigated in a non-clinical population (Stein et al., 2012). Therefore, it is important to evaluate the impact of maternal ER difficulties, anxiety, and depressive symptoms in the development mother-infant synchrony in a non-clinical population.

The present study examined mother-infant synchrony patterns at 6 months of age based on a modified version of Ainsworth's Strange Situation (Field, Vega-Lahr, Scafidi, & Goldstein, 1986). This version generates typical stress reactions in infants at 6 months of age in a natural condition (Hill-Soderlund et al., 2008; Laurent, Ablow, & Measelle, 2012). Using video microanalysis, the first aim of the study using a panel of behavioral indicators (i.e. gaze, vocal and motor) was to determine the levels of mother-infant synchrony before and after a stressful situation induced by maternal separation (initial condition and reunion condition, respectively). We also sought to determine the degree to which maternal behaviors drive infant behaviors, and vice-versa, in mother-infant synchrony in an initial condition and a reunion condition.

Based on evidence that mothers' ER difficulties might be one pathway by which maternal depression and anxiety are transmitted to higher levels of mother-infant synchrony (Lotzin, Romer, et al., 2015; Lotzin, Schiborr, et al., 2015), the second aim of the study was to examine the relationships between maternal ER difficulties, maternal anxiety, depressive symptoms and gaze, vocal and motor synchrony in mother-infant interactions. We hypothesized that mothers' ER difficulties are associated with higher levels of mother-infant synchrony indirectly through higher levels of maternal anxiety and depression. In addition, as a growing body of research supports the idea that the quality of security of attachment experienced by parents in their own childhood may affect the quality
of the affective experiences and the acquisition of emotional recognition and expression
with their children (Eisenberg et al., 1998; Morris et al., 2007), we expected that poor
parental bonding experienced in mothers' childhood would be related to maternal ER
difficulties.

Because mother-infant interactions are not static, an interactional model for the
measurement of synchrony needs to capture the dynamic of mother-infant interactions over
time. Recent mathematical methods derived from nonlinear dynamics make it possible to
study complex time-varying phenomena (Doba, Nandrini, Lesne, Humez, & Pezard, 2008;
Hollenstein, 2013; Pezard et al., 2017; Tschacher, Rees, & Ramseyer, 2014) and their
application to behavioral sciences to complement time-series analysis such as frequency
and cross correlations (Coburn et al., 2015; Van der Giessen et al., 2012). We used several
indicators, including dynamic indicators that allow the mutual and bidirectional co-
regulation in mother-infant synchrony to be assessed. We quantified the dynamics of
mother-infant interactions using the Lempel-Ziv complexity of joint behavioral sequences
and a cross-recurrence plot across a wide range of synchrony indicators including gaze,
motor, and vocal behaviors.

**Materials and methods**

Participants

The participants were 72 mothers, aged from 22 to 42 years old (M = 30.72, SD = 4.35),
and their 6-month-old infants (M = 6.57, SD = 0.45). All the infants (52.8% male and
47.2% female) included in the study were born at full term after a normal pregnancy and
delivery. Infants' birth weight ranged from 2.18 to 4.12 kg (M = 3.23 kg, SD = 0.45 kg).
At the time of the assessment, their current weight ranged from 6.3 to 8.02 kg (M = 8.02, SD = 0.98). DSM-IV was used as a diagnostic instrument to assess the exclusion criteria only (Andreas, Theisen, Mestel, Koch, & Schulz, 2009). Exclusion criteria for mothers were: mothers with an intellectual impairment, a psychotic disorder, and/or present substance abuse (DSM-IV). Exclusion criteria for infants included the following: intrauterine growth retardation, perinatal asphyxia, genetic or metabolic diseases, deafness, congenital defects, and/or twins. Most of the mothers were married or lived with their partner (94.4% married, and 5.6% no partner). All mothers were fluent French speakers of French and none were immigrants to France. Social class was measured by the mother's own occupational class categorized into: professional and managerial occupations (30.1%), intermediate occupations (employees, self-employees) (27.7%), lower occupations (lower technical occupations, semi-routine and routine occupations) (25.3), and no job (16.9). The education levels of mothers were as follows: 27.8% high school incomplete, 14% high school and 58.2% university degree. The number of pregnancies ranged from 1 to 5 (M = 1.67, SD = 0.95).

## Procedure

The present study was conducted according to guidelines laid down in the Declaration of Helsinki, with written informed consent obtained from a parent or guardian for each child before any assessment or data collection. All procedures involving human subjects in this study were approved by the independent ethics committee (2010-1-S1) at the University of Lille. Mothers were recruited from the maternity ward of the University Hospital. The second day after birth, research assistants visited the ward and invited women who were physically healthy and had delivered a healthy, full-term infant to participate in the study.
When the infant was approximately 6 months old, mothers were contacted by phone and invited to participate in the behavioral observation (i.e. modified version of Ainsworth's Strange Situation). They were visited at home by the child psychologist at the infants' age of 6 months. Each mother received a study information sheet and written informed parental consent was obtained before the start of the behavioral observation. During the home visit, mothers and infants were videotaped for 23 minutes in the modified version of Ainsworth's strange paradigm, and mothers completed self-report measures.

## Measures

### Maternal characteristics

Maternal emotion regulation difficulties were scored using the Difficulties in Emotion Regulation Scale (DERS). This self-report questionnaire includes 36 items rated from 1 (i.e. almost never) to 5 (i.e. almost always) according to the relationship between the item and subject experience (Dan-Glauser & Scherer, 2013; Gratz & Roemer, 2004). The DERS measures nonacceptance of negative emotional responses (Cronbach's α = 0.87) (i.e. When I'm upset, I become irritated with myself), difficulties in engaging in goal-directed behavior (Cronbach's α = 0.90) (i.e. When I'm upset, I have difficulty focusing on other things), difficulties in controlling impulsive behaviors (Cronbach's α = 0.87) (i.e. When I'm upset, I become out of control), lack of emotional awareness (Cronbach's α = 0.80) (i.e. I don't pay attention to or care how I feel), limited access to emotion regulation strategies (Cronbach's α = 0.80) (i.e. When I'm upset, it takes me a long time to feel better), and lack of emotional clarity (Cronbach's α = 0.74) (i.e. I have difficulty making sense out of my feelings). Higher scores indicate greater ER difficulties.
*Maternal postpartum depression* was scored using the Edinburgh Postnatal Depression Scale (EPDS). This self-report questionnaire is designed to detect depression among women in the postpartum period (Cox, Chapman, Murray, & Jones, 1996; Guedeney & Fermanian, 1998). The scale addresses the intensity of depressive symptoms. In the EPDS, the mothers are asked to choose from a set of given options those that best describe their feelings. The scale consists of 10 items scored on a 4-point scale from 0 to 3. The sum score of items ranges from 0 to 30 and higher scores indicate greater maternal postpartum depression. The EPDS showed good internal consistency (Cronbach's α = 0.76). Prior research has suggested a cut-off score of 12 for the identification of depressive symptoms (Cox, Holden, & Saaovskv, 1987).

*Maternal anxiety* was scored using the State Anxiety Inventory (STAI-State). This 20-item scale is designed to measure state anxiety (Spielberger, 1983). The state anxiety scale evaluates current feelings of tension and anxiety. The STAI-State has demonstrated reliability and validity and has been used widely in pregnancy and postpartum studies. Scores range from 20 to 80 and higher scores indicate a higher level of anxiety. The STAI showed good internal consistency (Cronbach's α = 0.73). A cut-off score of 46 is suggested for detecting anxiety symptoms (Granta, McMahonb, & Austina, 2008).

*Parental bonding* was scored using the Parental Bonding Inventory (PBI), which comprises two self-report questionnaires that measure parenting attitudes and behaviors (i.e. care and overprotection) that respondents remember from their first 16 years of life (Mohr, Preising, Fenton, & Ferrero, 1999; Parker, Tupling, & Brown, 1979). The first questionnaire assesses maternal bonding and the second (which is otherwise identical to the first) assesses paternal bonding. Participants rate each parent on a care subscale (comprising 12 items) and on an
overprotection subscale (comprising 13 items). The care subscale evaluates affection, emotional warmth, empathy and closeness (Cronbach's α = 0.89). The overprotection subscale measures intrusion, control, and prevention of independence (Cronbach's α = 0.81). Each of the 50 items is rated on a 4-point scale with "very" or "moderately" like or unlike being among the choices. Higher scores on the care scales represent more positive parental behavior (i.e. higher levels of perceived care), while higher scores on the overprotection scales represent less positive parental behavior (i.e. higher levels of perceived parental intrusiveness and overcontrol).

## Observation of mother-infant interaction

In most observational studies, a Strange Situation procedure is used to classify child attachment behavior at 12 months of age (Ainsworth, Blehar, Waters, & Wall, 1978). In this study, a modified version of Ainsworth's Strange Situation (Field et al., 1986) was used to assess the synchrony between mothers and infants at 6 months of age in a natural condition (Guo, Leu, Barnard, Thompson, & Spieker, 2015; Russel, Belsky, & Von Eye, 1989). The mother places her infant in a chair and directly faces him/her. A camera was placed on a stand 1.2m away and focused on the mother and child, consistent with prior work on synchrony measured in a home setting (Atzil, Hendler, & Feldman, 2011; Feldman & Eidelman, 2004).

The procedure consisted in three episodes:

1. An initial condition of spontaneous interaction between the mother and the infant (10 min);
2. A period during which the infant was separated from his/her mother (3 min) (i.e. mothers left the room) and remained alone with the female stranger (child psychologist);

3. A reunion condition in which the mother and infant reengage in a spontaneous interaction (10 min).

Mothers were instructed to play normally with their children during the initial and reunion conditions. Instructions were: “play with your child as you normally do.” No toys were provided. Mothers used their own toys during both conditions, which they presented to their infants. The restrictions imposed on the stranger’s behavior during the separation episode were to stay in the room and not to play with the child. The female stranger was visible to the infant during the initial and reunion conditions. The female stranger did not interact with anyone during any of the conditions. We quantified the mother-infant interactions during both conditions. The maternal separation condition evokes typical stress reactions in infants (Hill-Soderlund et al., 2008; Laurent et al., 2012).

## Behavioral coding

Coding of the videotapes was conducted in a university laboratory by six graduate students in psychology. For each 3-second interval of video recording, the maternal and infant behaviors within a dyad were coded by the same rater but initial and reunion conditions were coded by independent raters (Feldman, 2007; Pezard et al., 2017; Tronick, Als, & Brazelton, 1980).

Maternal behaviors were encoded according to three categories:
* Verbal behaviors. Mothers' verbal behavior was divided into three categories (Fonagy, 2011; Gros-Louis, West, Goldstein, & King, 2006; Stacks et al., 2014): silence, reflective verbalization, and vocalizations/verbalizations. Mothers' reflective verbalization corresponded to verbal expressions regarding their representations regarding their children, and/or their relationship with them and curiosity about their experience, e.g. by asking open questions about their feelings, beliefs, intentions and desires. Mothers' reflective verbalization corresponded to mothers' ability to infer or mentalize about infants' mental and emotional states. For example, mothers commented on their infants' mental or emotional states, e.g. "I think you are angry? " or Which toy do you prefer? ". Maternal vocalization/verbalization corresponded to an approximation of their infants' vocalization, or attributing some characteristic or value to an object, or making playful vocalizations, such as making sounds and singing.

* Motor behaviors. Mothers' motor behavior was divided into three categories (Granat et al., 2017; Mantis, Stack, Ng, Serbin, & Schwartzman, 2014): no movement, touch, and movement without physical contact. Mother touch corresponded to affectionate touch (i.e. touch that serves no functional purpose and is intended only to express affection, such as stroking, kissing, light touching), moving extremities (i.e. touching infant's arms or legs), touching infant with object (i.e. touching with soft doll). Movement without physical contact referred to voluntary movements (i.e. gestures consisting primarily of hand, arm, and finger movements towards the infant).

* Gaze behaviors. Mothers' gaze behavior referred to direction of gaze and was divided in two categories (Kim, Fonagy, Koss, Dorsett, & Strathearn, 2014; Lotzin, Schiborr,
et al., 2015): gaze toward infant and gaze away (i.e. when the mother gazed away from the infant's face and did not gaze toward him/her).

For the infants, vocal behaviors were divided into three categories (Feldman, 2003): silence, vocalizations and negative vocal behaviors. Vocalizations category corresponded to positive and neutral vocalizations. Negative vocal behaviors category corresponded to crying, screaming and fussing. Vegetative sounds (i.e. burp, hiccup, cough, yawn, heavy breathing) were excluded. Motor behaviors (i.e. movement and no movement) and direction of gaze (i.e. gaze toward mother and gaze away) were also coded. Vocal behaviors, motor behaviors and direction of gaze were taken into account to describe a global state of behavioral involvement (see Table 1) divided into three levels of global behavioral involvement (i.e. low, moderate and high) on a continuum from disengagement to engagement in the interaction (Feldman, Greenbaum, & Yirmiya, 1999; Tronick et al., 1980). The principle for choosing the involvement level was the following: for all combinations, no or one behavioral involvement was rated low, two behavioral involvements were rated moderate and three involvements were rated high. Infants' distress levels were encoded according to the intensity of crying during the three minutes of separation. Crying intensity was divided into four categories: no crying, low (i.e. infant cried a few seconds during the separation episode), moderate (i.e., infant cried for half the time of the separation episode) and high (i.e. infant cried during the three minutes of separation). To test the reliability of the coding procedure, 20% of the video recordings were coded independently by two researchers. The κ-coefficients of inter-rater agreement for the mothers' behaviors (verbal κ = 0.77; motor κ = 0.83; gaze κ = 0.99) and the
infants' behaviors (vocal $κ = 0.69$; motor $κ = 0.78$; gaze $κ = 0.80$) were considered satisfactory (Fliess, 1981).

As a result, infants' and mothers' behaviors were associated with a symbolic sequence encoded according to the respective categories of behavior. For each maternal behavior i.e. verbal behavior, motor behavior and gaze, we thus considered two symbolic sequences $x_t$ and $y_t$ for mother X and infant Y encoded according to alphabets $A = \{α_0, ..., α_{k-1}\}$ and $B = \{β_0, β_1, β_2\}$ respectively, where each symbol represents a category of behavior for the mother i.e. {silence, reflective verbalization, verbalization} for mothers' verbal behavior, {no movement, touch, movement without physical contact} for mothers' motor behavior and {toward infant, away} for mothers' gaze behavior and a level of behavioral involvement for the infant i.e. {low, moderate, high} for infants' global behavioral involvement.

## Dynamic quantification

Four encoded behavioral sequences (one for the infant, i.e. the **level** of global behavioral involvement, and three for the mother, i.e. verbal, motor and gaze) were obtained for each condition and each mother-infant pair. They were used to compute the dynamic indices which characterize the mother-infant interaction. The dynamics of three types of interactions (verbal, motor, and gaze) were quantified using the same procedure for each pair and each condition (initial and reunion).

First, the complexity of the interaction was quantified using Lempel-Ziv complexity (Lempel & Ziv, 1976; Lesne, Blanc, & Pezard, 2009) computed on the joint sequence between infants' global level **of behavioral involvement** and one of the mother's
behavioral sequence (verbal, motor or gaze). The joint sequences correspond to the single
sequence obtained after recoding of the pair of sequences (infant and mother) according to
the cross product of the alphabets of each sequence. Second, interaction was also
characterized using recurrence plots (RP) quantification analysis (Marwan & Webber,
2015) of the joint recurrence matrix which allows one to quantify synchrony (Romano,
Thiel, Kurths, & von Bloh, 2004; Stam & Dijk, 2002) using the percent of determinism
and the Shannon entropy of the frequency distribution of the diagonal line lengths.
Synchronization likelihood (Stam & Dijk, 2002) was also computed as the recurrence rate
of joint recurrence plot. Finally, the direction of coupling between mothers and infants was
obtained using the mean conditional probabilities of recurrence between two sequences
(Zou, Romano, Thiel, & Kurths, 2015) where the sign of the difference of mean conditional
recurrence is an index of the direction of the coupling. Mathematical definitions of these
indices are given in the technical appendix.

**Statistical analysis**

First, we conducted a series of multivariate analyses of variance (MANOVA) and t-tests
to examine the differences between both conditions for maternal behaviors, infant
behaviors and dynamic indices of mother-infant interactions. Cohen's d was used to
illustrate the magnitude of significant effects. The analysis was divided into two levels:
frequency analysis and dynamic analysis. For the frequency analysis, the distribution of
the frequency of the occurrence of symbols for each behavior was analyzed using
MANOVA and paired t tests. In the dynamic analysis, the set of dynamic indices (LZ
complexity, Shannon entropy, percent of determinism, synchronization likelihood and
mean conditional probability of recurrence i.e. direction of coupling) were first studied
using a principal component analysis to reveal the main factors for quantifying the
interaction and possibly reducing the number of dimensions for this description. For the
main factors, t tests were used to assess the difference between the two conditions.

Second, we performed Partial Least Squares Path Modeling (PLS-PM) to evaluate the associations between maternal characteristics and dynamic indices of mother-infant interactions (Vinci, Trinchera, & Amato, 2010). PLS-PM is a method for studying complex multivariate relationships between manifest variables (MVs) and latent variables (LVs). It is a variance-based structural equation modeling technique that does not rely on distributional assumptions and can deal with small sample sizes (Fornell & Bookstein, 1982; Ringle, Wende, & Will, 2010). A full path model is comprised of two submodels: the inner model describes associations between the LVs and the outer model describes associations between each LV and respective MV. The overall quality of the model was assessed by examining R² and the goodness of fit index (GOF) (Hair, Hult, Ringle, & Sarstedt, 2013). The results are shown as path coefficients (β) and their bootstrap (1000 resamples) 95% confidence interval (CI). For analysis, we used R and constructed a PLS-PM model according to the procedure described in Sanchez (2013).

## Results

Table 2 shows the descriptive statistics for ER difficulties (DERS), depression (EPDS), anxiety (STAI), and parental care and overprotection (PBI) in mothers. Scores on the EPDS ranged from 0 to 20 (mean score, 5.97 ± 5.38) with 18.06% of the mothers rated above the cut-off score (≥12) for depressive symptoms. Scores on the STAI traits ranged from 20 to 57 (mean score, 36.61 ± 9.92) with 23.6% of the mothers rated above the cut-off score
(≥46) for anxiety symptoms. Results revealed that 12.5% of the mothers reported above the cut-off score for maternal depression and anxiety.

**Difference between initial condition and reunion condition**

**Frequency analysis.** The frequencies for infants' level of behavioral involvement and maternal behaviors are shown in Table 3. The distributions of infants' levels of behavioral involvement (Pillai *V* = 0.02; *F*[2,70] = 1.02, *p* = 0.36), mothers' verbal behaviors (Pillai *λ* = 0.01; *F*[2,70] = 0.68, *p* = 0.51) and mothers' gaze behaviors (*t* = 0.72, *p* = 0.47) did not differ significantly between initial and reunion conditions. The frequencies of infants' crying intensity were as follows: no crying: 85.2%, low: 5.6, moderate: 1.9% and high: 7.4%. Whereas the distributions of mothers' motor behaviors differed significantly between the two conditions (Pillai *λ* = 0.25; *F*[2,70] = 11.8, *p* < 0.01).

Pairwise t-tests revealed that mothers' touch increased from the initial to the reunion condition (*t*<sub>71</sub> = -4.861, *p* = 0, Cohen's *d* = 0.62), whereas movement without physical contact (*t*<sub>71</sub> = 2.757, *p* = 0.007, Cohen's *d* = 0.28) and the absence of movement (*t*<sub>71</sub> = 3.741, *p* = 0, Cohen's *d* = 0.44) decreased from the initial condition to the reunion condition (Table 3).
**Dynamic analysis.** An example of a dynamic sequence of interaction between mothers and infants is given in Figure 1 for both initial and reunion conditions using grid representation (Hollenstein, 2013). The qualitative changes in dynamic organization were characterized by using both a complexity measure (Lempel-Ziv complexity) and recurrence plots. The recurrence plots and joint recurrence plots for the same sequences are depicted in Figure 2.

The dynamic indices were computed for three categories of mother behavior: motor, verbal and gaze behavior related to the global level of the infant's behavioral involvement. For each mothers' behavior category, a principal component analysis was performed for the set of dynamic characteristics. Figure 3 shows that, for each behavior, there is the same relationship between variables, thus revealing two main factors:

1. a synchronization/desynchronization factor related to LZ and RP indices;

2. a factor related to the direction of the dynamic influence (mother towards infant vs. infant towards mother).

This allowed the mother-infant interaction to be quantified by two factors: the *synchrony* factor (first dimension) and the *driver* factor (second dimension). The synchrony factor quantifies the level of synchronization between mothers and infants from low synchrony for negative values to high synchrony for positive values. The driver factor quantifies the direction of dynamic coupling between mothers and infants: for negative values, the mother drives the infant, whereas the infant drives the mother for positive values and a zero value characterizes a symmetrical interaction. These factors represented more than 90% of the total variance for all three conditions (verbal: synchrony 74.15%, driver
19.08%, total 93.23%; motor: synchrony 73.75%, driver 18.55%, total 92.30%; gaze: synchrony 76.04%, driver 19.16%, total 95.20%).

A summary of statistical results for the synchrony and driver factors for the initial and the reunion conditions is given in Table 4. No significant difference between initial and reunion conditions was observed for gaze (synchrony: $t_{71} = 0.829, p = 0.41$, driver: $t_{71} = -0.237, p = 0.813$) and verbal behavior (synchrony: $t_{71} = 0.898, p = 0.372$, driver: $t_{71} = 0.103, p = 0.918$). For motor behavior, synchrony increased between the initial and reunion condition ($t_{71} = -2.2, p = 0.031$, Cohen's *d* = 0.28) and the driver index decreased ($t_{71} = 2.236, p = 0.028$, Cohen's *d* = 0.27). Since the driver index tended to negative values, it means that, for the reunion condition, the mother drives the infant, whereas a more symmetrical relationship between mothers and infants is apparent in the initial condition. Changes on the Synchronization axis and Driver axis for motor behavior are represented in Figure 4.

## Measurement models with PLS-PM

The relationships between maternal characteristics and dynamic indices of mother-infant interactions were studied by building a PLS-PM model. The theoretical model involved 24 MVs (outer model) loaded on 6 LVs (inner model). The inner model was represented using the following theoretical entities: (1) parental care, (2) parental overprotection, (3) mothers' ER difficulties (4) maternal depression, (5) maternal anxiety and (6) mother-infant synchrony as LVs. LV parental care corresponds to the factors of PBI (i.e. maternal and paternal care), LV parental overprotection refers to the factor of PBI (i.e. maternal and paternal overprotection), mothers' ER difficulties correspond to the factors of DERS, and
maternal depression and anxiety refer to the factors of EPDS and STAI, respectively.

Finally, mother-infant synchrony corresponds to the dynamic indices of mother-infant interactions in the initial and reunion conditions (i.e. motor, verbal and gaze synchrony and interaction-driver). In addition, the control variables (infant gender and mothers' age) were entered into the model because evidence exists that these variables may impact mother-infant synchrony (Leclère et al., 2014). To test whether these variables were associated with mother-infant synchrony, we examined the moderating effects of mothers' age and maternal education on the relationships between maternal anxiety, maternal depression and mother-infant synchrony, and conducted a nonparametric multi-group analysis between female and male infant.

Outer Model

The first steps consisted of selecting MVs to obtain acceptable unidimensionality of LVs ($DG - rho > 0.7$) and significant loadings of MVs on each LV ($loading > 0.7$).
Unidimensionality for parental overprotection was not acceptable ($DG-rho < 0.7$). Small and non-significant loadings between MVs (maternal overprotection and paternal overprotection) and LV parental overprotection were observed. According to the unidimensional and loadings results, LV parental overprotection was removed. In addition, interaction-driver (gaze, verbal and motor) in the initial and reunion conditions was removed (small and non-significant loading) for mother-infant synchrony. As the distribution of infants' crying was low, this variable could not be included in the PLS-PM model.
The resulting model comprised 16 MVs loaded on 5 LVs (Figure 5) corresponding to the factors of PBI (i.e. maternal and paternal care), DERS, EPDS, STAI and dynamic indices of mother-infant interactions (i.e. motor, verbal and gaze synchrony in the initial and reunion conditions). The quality of this outer model was acceptable regarding the unidimensionality of all LVs (all DG-rho > 0.70) and cross-loadings. MVs were always more correlated with their respective LVs. Although correlation between maternal anxiety and maternal depression was 0.66, the quality of the model was acceptable regarding multicollinearity (VIF < 0.5) between these variables. Because each causal subsystem sequence of paths is estimated separately in the PLS-PM approach, the standard practice for PLS-PM estimations is that the sample size should be equal to the larger of the following (Tenenhaus et al., 2005): 10 times the number of indicators of the scale with the largest number of manifest indicators. As such, the sample size should be larger than 60 mothers in the current study, suggesting that the PLS-PM analyses were feasible with the present sample. Construct reliability was also calculated using the average variance extracted for each construct (Tenenhaus et al., 2005). Average Variance Extracted for the LVs of parental care (AVE = 0.66, 95% bootstrap CI [0.49,0.76]), mothers' ER difficulties (AVE = 0.59, 95% bootstrap CI [0.53,0.66]), and mother-infant synchrony (AVE = 0.54, 95% bootstrap CI [0.44,0.62]) were relatively large (Chin 1998).

## Inner Model

The final PLS-PM model is depicted in Figure 5. It comprised 16 MVs (outer model) loaded on 5 LVs (inner model). The final inner model included parental care, mothers' ER difficulties, depression, maternal anxiety and mother-infant synchrony as LVs. The analysis of the PLS-PM model showed that mother-infant synchrony was mostly measured
by motor synchronization, verbal synchronization, and gaze synchronization in the initial
and reunion conditions. Results revealed that the path between parental care and mother-
infant synchrony was not significant ($\beta$ = 0.10, 95% bootstrap CI [-0.15,0.35]). The path
results showed that parental care was significantly negatively associated with mothers' ER
difficulties ($\beta$ = -0.28, 95% bootstrap CI [-0.49, -0.06]). The direct path between
mothers' ER difficulties and mother-infant synchrony ($\beta$ = 0.13, 95% bootstrap CI
[-0.24,0.49]) was not significant.

Results show that mothers' ER difficulties were significantly positively associated
with maternal depression (β = 0.67, 95% bootstrap CI [0.51,0.80]) and maternal anxiety
(β = 0.72, 95% bootstrap CI [0.60,0.81]). There was a significant direct effect between
maternal anxiety and mother-infant synchrony (β = 0.58, 95% bootstrap CI [0.20,0.94])
and no significant direct effect between maternal depression and mother-infant synchrony
(β = -0.27, 95% bootstrap CI [-0.61,0.06]). To examine the mediating effects of
maternal anxiety and depression between mothers' ER difficulties and mother-infant
synchrony, we tested the indirect effects between these LVs (Chin, 2010). The bootstrap
method for testing indirect effects indicated that the indirect effect from mothers' ER
difficulties through maternal anxiety to mother-infant synchrony was significant (β =
0.42, 95% bootstrap CI [0.15,0.72]). These results indicated that mothers' ER difficulties
affected maternal anxiety, which in turn modulated the motor, verbal and gaze synchrony
between mothers and infants in the initial and reunion conditions. The indirect effect from
mothers' ER difficulties through maternal depression to mother-infant synchrony was not
significant (β = -0.19, 95% bootstrap CI [-0.44,0.04]).
The moderating effect of mothers' age on the relationships between maternal anxiety, maternal depression and mother-infant synchrony was tested with the product indicator approach (Chin, Marcolin, & Newsted, 2003) for the interaction effects between these latent variables. Moderating effects of mothers' age were not significant between maternal anxiety and synchrony (β = -0.10,95% bootstrap CI [-0.16,0.36]), or between maternal depression and mother-infant synchrony (β = -0.16,95% bootstrap CI [-0.08,0.36]). Moderating effects of maternal education were not significant between maternal anxiety and synchrony (β = -0.06,95% bootstrap CI [-0.30,0.24]), or between maternal depression and mother-infant synchrony (β = 0.07,95% bootstrap CI [-0.26,0.27]). A nonparametric multi-group analysis was conducted to test for possible differences between female and male infants using the PLS-MGA method (Hair et al., 2013). Direct path comparisons showed that the effect from maternal anxiety to mother-infant synchrony (β = 0.13,95% bootstrap CI [-0.06,0.98]) and the effect from maternal depression to mother-infant synchrony (β = 0.53,95% bootstrap CI [-0.77, -0.04]) were not significantly different between female and male infants.

$R^2$ for the LVs of mothers' ER difficulties (0.10), mother-infant synchrony (0.31), maternal depression (0.46) and maternal anxiety (0.52), indicating moderate-to-large values (Vinci, Trinchera, & Amato, 2010), and model quality (GoF = 0.51) were satisfactory (Tenenhaus et al., 2005).

## Discussion

In the present study, frequential analysis revealed that mothers touched their infants more often in the reunion condition than in the initial condition. Several studies previously
reported that maternal touch attenuates infants’ physiological stress responses, such as
cardiac vagal tone and cortisol reactivity (Feldman, Singer, & Zagoory-Sharon, 2010).
Touch behaviors during periods of early maternal deprivation are known to buffer the
disruptions to the HPA-axis stress regulating system and the negative effects of stress on
infants’ physiological reactivity (Weller & Feldman, 2003). Moreover, touching during the
maternal still-face paradigm reduced infants’ distress, such as crying, self-soothing
behaviors and gaze aversion (Jean, Stack, & Fogel, 2009; Stack & Muir, 1992). Several
studies reported that high maternal touch in early infant development (5 and 9 weeks)
reduced the associations between maternal antenatal anxiety or depression and emotional
problems in children at 2.5 years of age (Sharp, Hill, Hellier & Pickles, 2015; Sharp et al.,
2012). Parental touch is a central mode of parent-infant interactions, particularly in infants
younger than 6 months old (Feber, Feldman, & Makhoul, 2007; Feldman, Gordon, &
Zagoory-Sharon, 2011; Mantis et al., 2014), and it facilitates infants’ cognitive and
neurobehavioral development (Feldman & Eidelman, 2007).

Another main finding of the current study is that motor synchrony between mothers
and infants was greater in the reunion condition than in the initial condition. This result
reflects the simultaneous synchrony between the levels of activation of mothers’ motor
behaviors and those of infants’ global states (Feldman, 2007; Leclère et al., 2014).
Importantly, it confirms and extends previous data (Feldman, Magori-Cohen, et al., 2011;
Leclère et al., 2014; Moore & Calkins, 2004) by demonstrating how mothers adapt their
motor responses to infants’ states of behavioral involvement after a stressful situation
induced by maternal separation around the age of 6 months. Motor interaction has been
shown to be an influential channel through which mothers and their infants convey emotion
and affection, and establish a strong connection (Moszkowski, Stack, & Chiarella, 2009; Stack, 2010; Waters, West, Karnilowicz, Mendes, 2017). Feldman, Gordon, and Zagoory-Sharon (2010) underscored the central role of early experiences of parent-infant synchrony in organizing the structural and functional features of the oxytocinergic system. They showed that parents' and infants' salivary oxytocin levels were correlated when parent-child interaction was characterized by a higher level of touch synchrony in 6-month-old infants. In line with this putative biobehavioral synchrony model (Feldman, 2012; Pratt, Singer, Kanat-Mayon, & Feldman, 2015), the experiences of touch and motor synchrony between mothers and infants during the first months of life could be an example of the critical environmental input required for the affective development of infants. In addition to affectionate touch and physical contact, mother-infant synchrony has been observed very early in the development in the form of vocalizations and gaze orientations (Feldman, 2007; Harrist & Waugh, 2002; Leclère et al., 2014). The present findings show that the simultaneous synchrony between mothers' vocal and visual behaviors and levels of infants' global behavioral involvement did not differ between the initial and reunion conditions. They suggest that mothers' behaviors take place predominantly through tactile and motor modes rather than through visual and vocal ones to regulate the behavioral involvement of infants after a stressful situation during the first 6 months of life. Since several interactive configurations change in frequency between the ages of 3 and 9 months (Feldman, 2007), it is possible that mothers' vocal and visual behaviors may become central modalities for the regulation of infants' behavioral involvement after stressful situations during the second 6 months.
Developmental theorists have long postulated that infants show an ongoing tendency to adapt to the behavioral and emotional patterns of their parents (Ainsworth et al., 1978; Morris et al., 2007; Tronick et al., 1980). Nevertheless, it is not clear from previous studies whether infants' responses lead mothers to behave in a certain way or whether mothers' behaviors lead infants to respond in a particular manner. A key contribution of the present study is the quantification of the influence of mothers' and infants' behaviors in the development of mother-infant synchrony. Based on methods derived from non-linear dynamics, the present findings show that it is particularly mothers' motor behaviors that influence the global levels of infants' behavioral involvement in the reunion condition, and that the opposite is the case in the initial condition. This evidence of the direction of effects between mothers and infants sheds new light on the processes underpinning mother-infant synchrony after a stressful situation. Taken together, these findings reinforce attachment theory by demonstrating the central role played by mothers when they adjust their physical contact with their infants according to the states of behavioral involvement of the latter during the first 6 months of life.

The second aim of the study was to examine how the indicators of the quality of parental care, maternal ER difficulties, maternal anxiety, and depression impact mother-infant synchrony. Our results reveal that the incidence of anxiety symptoms and/or depressive symptoms was not different from that of the general population (Dennis, Falah-Hassani, & Shiri, 2017; Wang, Wu, Anderson, & Florence, 2011). The results show that maternal anxiety mediates the relationships between mothers' ER difficulties and mother-infant synchrony in both the initial and reunion conditions. Thus, if mothers are less able to regulate their emotions, it is likely that they will experience anxiety symptoms and
exhibit heightened levels of gaze synchrony, verbal synchrony and motor synchrony in both conditions. Therefore, it seems that high levels of ER difficulties and anxiety symptoms in mothers are associated with a greater synchrony between the levels of infants' global states and the levels of activation of gaze, motor and verbal behaviors in mothers.

Previous studies reported that maternal anxiety symptoms predicted higher mother-infant synchrony in the motor modality, greater frequencies of gaze to infant, and lower affect synchrony in face-to-face play between mothers and infants during the first year of life (Beebe et al., 2011; Granat et al., 2017). Our findings expand on those studies by showing the crucial role of mothers' ER difficulties in the development of maternal anxiety and high levels of mother-infant synchrony in various situations (i.e. initial and reunion conditions) and modalities (i.e. gaze, vocal and motor behaviors). These high levels of mother-infant synchrony may reduce the adjustment to both internal and external changes of situation and promote inflexible and invariant affective experiences in infants (Jaffe et al., 2001).

High levels of mother-infant synchrony may reflect interpersonal difficulties in mother-infant interactions and appear to be related to intrusive and hypervigilance behaviors in mothers (Beebe et al., 2008; Kaitz & Maytal, 2005).

Importantly, the results also reveal a direct association between a high level of maternal ER difficulties and a high level of maternal depression. Nevertheless, the indirect path indicates that maternal depression does not contribute to greater mother-infant synchrony in the gaze, motor, and vocal modalities. These findings contradict the results of previous studies indicating that depressed mothers show greater synchrony in facial expressions (Lotzin, Schiborr, et al., 2015), less synchrony in the touch modalities (Granat et al., 2017), and either lowered or heightened synchrony in the gaze modalities (Beebe et
al., 2008; Lotzin, Romer, et al., 2015). These discrepancies in results could be explained by the severity of mothers' depressive symptoms (Beebe et al., 2012). Our data, along with the results of previous studies, support the idea that high levels of maternal depression and anxiety affect mother-infant synchrony in the gaze, motor and vocal modalities in different ways (Feldman et al., 2009; Granat et al., 2017; Hakanen, et al., 2019). They suggest that maternal depression and maternal anxiety have two separate effects on the development of the mother-infant synchrony during the first months of life.

Another finding is that parental care was not associated with mother-infant synchrony. Nevertheless, a low level of parental care may lead to an increase in mothers' ER difficulties, which might in turn contribute to the emergence of maternal anxiety and depression. These results suggest that the quality of parental care that mothers experience in childhood and adolescence might modulate their ability to monitor, evaluate, and modulate their emotional experiences according to the demands of a specific context or set of goals, but that it might not affect mother-infant synchrony.

The present findings emphasize the importance of the dynamic quantification of mother-infant synchrony as a complement to static descriptions. The methodology proposed herein is based on the encoding of behavior into symbolic sequences and the computation of dynamic indices, as in the field of complex systems. These indices may then be used to investigate the nature and directionality of mother-infant synchrony. Our data suggest that the precursors of mother-infant synchrony may be observed during the first 6 months of life, and that touch behaviors between mothers and infants should be offered in psychoeducation programs. In addition, clinical or psychoeducational interventions for mothers might target not only maternal anxiety but also ER difficulties.
Video feedback (Bakermans-Kranenburg, Van Ijzendoorn, & Juffer, 2003) could also be
used to focus on maternal ER difficulties.

The current study has some limitations. First, the results are based on self-report
measures for the evaluation of ER difficulties. Replication with other methods of data
collection (e.g. observer ratings or physiological and neurobiological indicators of ER)
would be useful in future research. From a demographic point of view, the higher
percentages of managerial occupations (managerial occupations :30.1% vs 16% in French
women) and university degrees (58.2% university degree vs 49% in French women)
(INSEE; 2020) in our sample limit the generalizability of our results. Second, the cross-
sectional design of this study precludes any causal interpretations. Longitudinal studies
employing measures of synchrony at multiple time-points might help to clarify how
maternal ER difficulties shape the pathways to maternal anxiety and mother-infant
synchrony at different ages. Another shortcoming is the simplification of infants' behavior
to a global behavioral involvement and the lack of specific measurements of the stress
response, i.e. physiological responses. Further research should be designed specifically to
cover the variety of infant behaviors and emotional reactions more thoroughly. A future
expansion of this research would be to explore affective synchrony (e.g. vocal affect, facial
affect) between mothers and their 6-month-old infants. Indeed, the ability of a mother-
infant dyad to go from non-matching to matching affective states may be one of the
mechanisms through which dyadic synchrony affects the development of self-regulation in
infants. Longitudinal studies using measures of infants' crying at multiple time-points
might help clarify how individual differences in separation distress are associated with
maternal and infant reunion behaviors. Finally, fathers should also be studied to examine
whether high levels of paternal ER difficulties reinforce the relationships between maternal anxiety and mother-infant synchrony.
The recurrence matrix $R(x)$ of $x_t$ (resp. $R(y)$ of $y_t$) is the matrix with elements:

$$R_{i,j}(x) = \delta_{i,j}$$

where $\delta_{i,j}$ is based on Kronecker delta with $\delta_{i,j} = 1$ if $x_i = x_j$ (resp. $y_i = y_j$) and $\delta_{i,j} = 0$ otherwise. This matrix makes it possible to define a recurrence plot (RP) where the recurrence matrix is represented with black dots for elements equal to 1.

The joint recurrence matrix $J(x, y)$ of $x_t$ and $y_t$ is the matrix with elements:

$$J_{i,j}(x, y) = R_{i,j}(x)R_{i,j}(y) = \delta_{i,j}^{x} \delta_{i,j}^{y}$$

The joint recurrence plot (JRP) is the representation of this matrix with black dots for elements equal to 1.

First, the histogram of the lengths of the diagonal structure of the JRP,

$$H_D(l) = \sum_{i,j=1}^{N} (1 - J_{i-1,j-1})(1 - J_{i+1,j+1}) \prod_{k=0}^{l-1} J_{i+k,j+k}$$

was computed to define the *percent of determinism D*:

$$D = \frac{\sum_{l=2}^{N} l H_D(l)}{\sum_{i,j=1}^{N} J_{i,j}}$$

and the *Shannon entropy of the frequency distribution of the diagonal line lengths S*:

$$S = - \sum_{l=2}^{N} p(l) \ln(p(l)) \quad \text{with} \quad p(l) = \frac{H_D(l)}{\sum_{l=2}^{N} H_D(l)}$$

The *recurrence rate RR* of joint recurrence plot is defined as:
$$RR = \frac{1}{N^2 - N} \sum_{i,j=1; i \neq j}^{N} J_{i,j}$$

The mean conditional probabilities of recurrence M between two sequences x and y is defined as:

$$M(Y \lor X) = \frac{1}{N} \sum_{i=1}^{N} p(y_i \lor x_i) = \frac{1}{N} \sum_{i=1}^{N} \frac{\sum_{j=1}^{N} J_{i,j}(x,y)}{\sum_{j=1}^{N} R_{i,j}(x)}$$

and

$$M(X \lor Y) = \frac{1}{N} \sum_{i=1}^{N} p(x_i \lor y_i) = \frac{1}{N} \sum_{i=1}^{N} \frac{\sum_{j=1}^{N} J_{i,j}(x,y)}{\sum_{j=1}^{N} R_{i,j}(y)}$$

The criterion that detects the asymmetry of the coupling is the following:

* If X drives Y, $M(Y \lor X) < M(X \lor Y)$

* If Y drives X, $M(X \lor Y) < M(Y \lor X)$

* Symmetrical coupling, $M(Y \lor X) = M(X \lor Y)$
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<table><caption>Table 1. Recoding of infant behavior to account for global behavioral involvement</caption><thead><tr><th>Motor behaviors</th><th>Vocal behaviors</th><th>Gaze behaviors</th><th>Global behavioral involvement</th></tr></thead><tbody><tr><td>No movement</td><td>Silence</td><td>Gaze away</td><td>Low</td></tr><tr><td>No movement</td><td>Silence</td><td>Gaze toward mother</td><td>Low</td></tr><tr><td>No movement</td><td>Vocalization</td><td>Gaze away</td><td>Low</td></tr><tr><td>No movement</td><td>Vocalization</td><td>Gaze toward mother</td><td>Moderate</td></tr><tr><td>No movement</td><td>Negative</td><td>Gaze away</td><td>Low</td></tr><tr><td>No movement</td><td>Negative</td><td>Gaze toward mother</td><td>Moderate</td></tr><tr><td>Movement</td><td>Silence</td><td>Gaze away</td><td>Low</td></tr><tr><td>Movement</td><td>Silence</td><td>Gaze toward mother</td><td>Moderate</td></tr><tr><td>Movement</td><td>Vocalization</td><td>Gaze away</td><td>Moderate</td></tr><tr><td>Movement</td><td>Vocalization</td><td>Gaze toward mother</td><td>High</td></tr><tr><td>Movement</td><td>Negative</td><td>Gaze away</td><td>Moderate</td></tr><tr><td>Movement</td><td>Negative</td><td>Gaze toward mother</td><td>High</td></tr></tbody></table>
<table><caption>Table 2. Descriptive statistics of maternal characteristics</caption><thead><tr><th>Maternal Characteristics</th><th></th><th>Mean</th><th>SD</th><th>Min.</th><th>Max.</th></tr></thead><tbody><tr><td rowspan="6">DERS</td><td>Nonacceptance</td><td>8.43</td><td>3.57</td><td>3</td><td>18</td></tr><tr><td>Goals</td><td>9.08</td><td>3.32</td><td>3</td><td>16</td></tr><tr><td>Impulsivity</td><td>6.14</td><td>3</td><td>3</td><td>15</td></tr><tr><td>Awareness</td><td>7.72</td><td>3.53</td><td>3</td><td>18</td></tr><tr><td>Strategies</td><td>7.26</td><td>3.18</td><td>3</td><td>18</td></tr><tr><td>Clarity</td><td>7.08</td><td>2.99</td><td>3</td><td>15</td></tr><tr><td>EPDS</td><td>Depression</td><td>5.97</td><td>5.39</td><td>0</td><td>21</td></tr><tr><td>STAI</td><td>Anxiety</td><td>36.6</td><td>9.92</td><td>20</td><td>57</td></tr><tr><td rowspan="4">PBI</td><td>Maternal Care</td><td>27.65</td><td>7.37</td><td>7</td><td>36</td></tr><tr><td>Paternal Care</td><td>23.81</td><td>8.87</td><td>3</td><td>36</td></tr><tr><td>Maternal Overprotection</td><td>12.4</td><td>6.74</td><td>2</td><td>32</td></tr><tr><td>Paternal Overprotection</td><td>10.96</td><td>6.45</td><td>0</td><td>31</td></tr></tbody></table>

Note. DERS: Difficulties of Emotion Regulation Scale; EPDS: Edinburgh Postnatal Depression Scale; STAI: State-Trait Anxiety Inventory; PBI: Parental Bonding Inventory.
<table><caption>Table 3. Infant's level of behavioral involvement and maternal behaviors in initial and reunion conditions scored by modified version of Ainsworth's Strange Situation</caption><thead><tr><th rowspan="2"></th><th colspan="4">Initial condition</th><th colspan="4">Reunion Condition</th></tr><tr><th>Mean</th><th>SD</th><th>Min.</th><th>Max.</th><th>Mean</th><th>SD</th><th>Min.</th><th>Max.</th></tr></thead><tbody><tr><td>Infant</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Low level</td><td>0.59</td><td>0.19</td><td>0.12</td><td>0.94</td><td>0.56</td><td>0.19</td><td>0.03</td><td>0.94</td></tr><tr><td>Moderate level</td><td>0.31</td><td>0.12</td><td>0.06</td><td>0.57</td><td>0.33</td><td>0.12</td><td>0.05</td><td>0.61</td></tr><tr><td>High level</td><td>0.09</td><td>0.09</td><td>0</td><td>0.42</td><td>0.10</td><td>0.11</td><td>0</td><td>0.54</td></tr><tr><td>Mothers' verbal behaviors</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Silence</td><td>0.30</td><td>0.20</td><td>0.02</td><td>0.99</td><td>0.31</td><td>0.20</td><td>0.02</td><td>0.99</td></tr><tr><td>Reflective verbalization</td><td>0.14</td><td>0.17</td><td>0</td><td>0.77</td><td>0.13</td><td>0.16</td><td>0</td><td>0.82</td></tr><tr><td>Vocalization/verbalization</td><td>0.54</td><td>0.24</td><td>0</td><td>0.95</td><td>0.54</td><td>0.23</td><td>0</td><td>0.93</td></tr><tr><td>Mothers' motor behaviors</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>No movement</td><td>0.37</td><td>0.24</td><td>0.01</td><td>0.95</td><td>0.30</td><td>0.24</td><td>0</td><td>0.93</td></tr><tr><td>Touch</td><td>0.44</td><td>0.25</td><td>0.01</td><td>0.95</td><td>0.55</td><td>0.27</td><td>0.02</td><td>0.99</td></tr><tr><td>Movement without physical contact</td><td>0.17</td><td>0.14</td><td>0</td><td>0.68</td><td>0.14</td><td>0.13</td><td>0</td><td>0.49</td></tr><tr><td>Mothers' gaze behaviors</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Gaze away</td><td>0.12</td><td>0.09</td><td>0</td><td>0.47</td><td>0.13</td><td>0.11</td><td>0</td><td>0.55</td></tr><tr><td>Gaze toward infant</td><td>0.87</td><td>0.09</td><td>0.53</td><td>1</td><td>0.86</td><td>0.11</td><td>0.44</td><td>1</td></tr></tbody></table>
<table><caption>Table 4. Values of two main factors obtained using Principal Component Analysis of dynamical indices</caption><thead><tr><th rowspan="2"></th><th colspan="4">Initial Condition</th><th colspan="4">Reunion Condition</th></tr><tr><th>Mean</th><th>SD</th><th>Min.</th><th>Max.</th><th>Mean</th><th>SD</th><th>Min.</th><th>Max.</th></tr></thead><tbody><tr><td><strong>Verbal</strong></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td><em>Synchrony</em></td><td>0.10</td><td>2.15</td><td>-2.94</td><td>6.28</td><td>-0.10</td><td>2.09</td><td>-3.26</td><td>5.97</td></tr><tr><td><em>Driver</em></td><td>0.005</td><td>1.1</td><td>-2.9</td><td>2.19</td><td>-0.005</td><td>1.06</td><td>-2.6</td><td>2.19</td></tr><tr><td><strong>Motor</strong></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td><em>Synchrony</em></td><td>-0.26</td><td>2.02</td><td>-3.42</td><td>5.41</td><td>0.26</td><td>2.18</td><td>-3.35</td><td>6.02</td></tr><tr><td><em>Driver</em></td><td>0.15</td><td>1.06</td><td>-2.32</td><td>2.65</td><td>-0.15</td><td>1.04</td><td>-2.21</td><td>2.69</td></tr><tr><td><strong>Gaze</strong></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td><em>Synchrony</em></td><td>0.09</td><td>2.24</td><td>-3.26</td><td>6.84</td><td>-0.09</td><td>2.05</td><td>-3.78</td><td>5.99</td></tr><tr><td><em>Driver</em></td><td>0.01</td><td>1.09</td><td>-1.94</td><td>3.44</td><td>-0.01</td><td>1.06</td><td>-2.0</td><td>3.08</td></tr></tbody></table>